Publications | Nicolas Le Bihan

2025

SSP

Damped ellipse decomposition for bivariate signals

P. Flores, J. Flamant, P.-O. Amblard, and 1 more author

In 2025 IEEE Statistical Signal Processing Workshop (SSP), 2025

@inproceedings{flores2025ssp,
  author = {Flores, P. and Flamant, J. and Amblard, P.-O. and {Le Bihan}, N.},
  booktitle = {2025 IEEE Statistical Signal Processing Workshop (SSP)},
  title = {Damped ellipse decomposition for bivariate signals},
  year = {2025},
}

IEEE SPL

Beyond R-barycenters: an effective averaging method on Stiefel and Grassmann manifolds

F. Bouchard, N. Laurent, S. Said, and 1 more author

to appear in IEEE Signal processing Letters, 2025

DOI arXiv Bib

@article{bouchard2025IEEESPL,
  title = {{Beyond R-barycenters: an effective averaging method on Stiefel and Grassmann manifolds}},
  author = {Bouchard, F. and Laurent, N. and Said, S. and {Le Bihan}, N.},
  journal = {to appear in IEEE Signal processing Letters},
  year = {2025},
  doi = {10.1109/LSP.2025.3562735},
}

2024

EUSIPCO

The geometric phase of bivariate signals

N. Le Bihan, J. Flamant, and P.-O. Amblard

In 32nd European Signal Processing Conference, EUSIPCO 2024, 2024

DOI Bib

@inproceedings{lebihan2024eusipco,
  title = {{The geometric phase of bivariate signals}},
  author = {{Le Bihan}, N. and Flamant, J. and Amblard, P.-O.},
  booktitle = {{32nd European Signal Processing Conference, EUSIPCO 2024}},
  address = {Lyon, France},
  year = {2024},
  hal = {hal-04691994/file/0002562.pdf},
  hal_id = {hal-04691994},
  doi = {10.23919/EUSIPCO63174.2024.10715274},
}

2023

GRETSI

Une implantation de la théorie de l’information

F. Cayre, N. Le Bihan, and I. Sivignon

In 29ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2023

Bib

@inproceedings{cayre2023gretsi,
  author = {Cayre, F. and {Le Bihan}, N. and Sivignon, I.},
  title = {Une implantation de la théorie de l'information},
  booktitle = {{29ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}},
  address = {Grenoble, France},
  year = {2023},
  hal = {hal-04256174/file/2023_cayre1331.pdf},
  hal_id = {hal-04256174},
}

GRETSI

Estimation de barycentres sur variétés de Stiefel : une approche par projection

N. Laurent, F. Bouchard, S. Said, and 1 more author

In 29ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2023

Bib

@inproceedings{laurent2023gretsi,
  title = {{Estimation de barycentres sur vari{\'e}t{\'e}s de Stiefel : une approche par projection}},
  author = {Laurent, N. and Bouchard, F. and Said, S. and {Le Bihan}, N.},
  booktitle = {{29ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}},
  address = {Grenoble, France},
  year = {2023},
  hal = {hal-04228051/file/2023_lebihan1379.pdf},
  hal_id = {hal-04228051},
}

GRETSI

Modèles physiques à deux états pour les signaux bivariés : modulation de polarisation et phase géométrique

N. Le Bihan, J. Flamant, and P.-O. Amblard

In 29ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2023

Bib

@inproceedings{lebihan2023gretsi,
  title = {{Mod{\`e}les physiques {\`a} deux {\'e}tats pour les signaux bivari{\'e}s : modulation de polarisation et phase g{\'e}om{\'e}trique}},
  author = {{Le Bihan}, N. and Flamant, J. and Amblard, P.-O.},
  booktitle = {{29ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}},
  address = {Grenoble, France},
  year = {2023},
  hal = {hal-04194522/file/2023_lebihan1217.pdf},
  hal_id = {hal-04194522},
}

GRETSI

Modèles physiques à deux états pour les signaux bivariés : un système d’oscillateurs harmoniques couplés

J. Flamant, P.-O. Amblard, and N. Le Bihan

In 29ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2023

Bib

@inproceedings{flamant2023gretsi,
  title = {{Mod{\`e}les physiques {\`a} deux {\'e}tats pour les signaux bivari{\'e}s : un syst{\`e}me d'oscillateurs harmoniques coupl{\'e}s}},
  author = {Flamant, J. and Amblard, P.-O. and {Le Bihan}, N.},
  booktitle = {{29ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}},
  address = {Grenoble, France},
  year = {2023},
  hal = {hal-04194520/file/2023_flamant1215.pdf},
  hal_id = {hal-04194520},
}

GRETSI

Algorithme proximal efficace pour l’approximation Hankel rang faible

F. Chatelain, J. Flamant, and N. Le Bihan

In 29ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2023

Bib

@inproceedings{chatelain2023gretsi,
  title = {{Algorithme proximal efficace pour l'approximation Hankel rang faible}},
  author = {Chatelain, F. and Flamant, J. and {Le Bihan}, N.},
  booktitle = {{29ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}},
  address = {Grenoble, France},
  year = {2023},
  hal = {hal-04217832v1/file/chatelain1155.pdf},
  hal_id = {hal-04217832v1},
}

GRETSI

Contrainte de polarisation pour la reconstruction d’ondes gravitationnelles

C. Cano, N. Le Bihan, and E. Chassande-Mottin

In 29ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2023

Bib

@inproceedings{cano2023gretsi,
  title = {{Contrainte de polarisation pour la reconstruction d'ondes gravitationnelles}},
  author = {Cano, C. and {Le Bihan}, N. and Chassande-Mottin, E.},
  url = {https://hal.science/hal-04217821},
  booktitle = {{29ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}},
  address = {Grenoble, France},
  year = {2023},
  hal = {hal-04217821/file/cano1117.pdf},
  hal_id = {hal-04217821},
}

IEEE SPM

Quaternions in Signal and Image Processing: A comprehensive and objective overview

S. Miron, J. Flamant, N. Le Bihan, and 2 more authors

IEEE Signal Processing Magazine, 2023

DOI Bib

@article{miron2023spm,
  title = {{Quaternions in Signal and Image Processing: A comprehensive and objective overview}},
  author = {Miron, S. and Flamant, J. and {Le Bihan}, N. and Chainais, P. and Brie, D.},
  url = {https://hal.science/hal-04199725},
  journal = {{IEEE Signal Processing Magazine}},
  publisher = {{Institute of Electrical and Electronics Engineers}},
  volume = {40},
  number = {6},
  pages = {26-40},
  year = {2023},
  doi = {10.1109/MSP.2023.3278071},
  hal = {hal-04199725/file/SPM_Quaternions_HAL.pdf},
  hal_id = {hal-04199725},
}

ICASSP
Polarized signal singular spectrum analysis with complex SSA

S. Journé, N. Le Bihan, F. Chatelain, and 1 more author

In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2023

Abs DOI Bib

This paper considers the analysis of bivariate signals using com- plex Singular Spectrum Analysis (SSA). It introduces a pseudo-correlation based criterion in the grouping step of complex SSA. The advantage of using pseudo-correlation rather than correlation measures when analyzing polarized signals with complex SSA is demonstrated theoretically. This criterion is shown to be effective to extract bivariate signals modeled as particular complex Linear Recurrence Relations (LRR) of order 2. These elementary complex bricks offer a high interpretability in terms of polarization. Illustration of the proposed grouping technique is made through polarized component extraction on a real-world data example.
@inproceedings{journe2023icassp, title = {{Polarized signal singular spectrum analysis with complex SSA}}, author = {Journé, S. and {Le Bihan}, N. and Chatelain, F. and Flamant, J.}, booktitle = {{IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}}, address = {Rhodes, Greece}, publisher = {{IEEE}}, year = {2023}, doi = {10.1109/ICASSP49357.2023.10095954}, hal_id = {hal-04104834}, hal = {hal-04104834/file/4405.pdf}, }

2022

EUSIPCO

Fast and accurate gravitational-wave modelling with principal component regression

C. Cano, E. Chassande-Mottin, and N. Le Bihan

In 30th European Signal Processing Conference (EUSIPCO), 2022

DOI Bib

@inproceedings{cano2022eusipco,
  title = {{Fast and accurate gravitational-wave modelling with principal component regression}},
  author = {Cano, C. and Chassande-Mottin, E. and {Le Bihan}, N.},
  booktitle = {{30th European Signal Processing Conference (EUSIPCO)}},
  address = {Belgrade, Serbia},
  year = {2022},
  hal = {hal-03868278/file/paper.pdf},
  hal_id = {hal-03868278},
  doi = {10.23919/EUSIPCO55093.2022.9909752},
}

GRETSI

Compromis performance-complexité pour les statistiques en grande dimension

R. Couillet, F. Chatelain, and N. Le Bihan

In 28ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2022

Bib PDF

@inproceedings{couillet2022gretsi,
  title = {{Compromis performance-complexit{\'e} pour les statistiques en grande dimension}},
  author = {Couillet, R. and Chatelain, F. and {Le Bihan}, N.},
  booktitle = {{28ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}},
  address = {Nancy, France},
  year = {2022},
  pages = {621--624},
  hal = {hal-03868290/file/2022_lebihan1026.pdf},
  hal_id = {hal-03868290},
}

GRETSI

Polarisation des modes en acoustique sous-marine

J. Flamant, J. Bonnel, and N. Le Bihan

In 28ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2022

Bib PDF

@inproceedings{flamant2022gretsi,
  title = {{Polarisation des modes en acoustique sous-marine}},
  author = {Flamant, J. and Bonnel, J. and {Le Bihan}, N.},
  booktitle = {{28ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}},
  address = {Nancy, France},
  year = {2022},
  pages = {1325--1328},
  hal = {hal-03726813/file/flamant771-4.pdf},
  hal_id = {hal-03726813},
}

GRETSI
Modèles polarisés pour la simulation rapide de formes d’ondes gravitationnelles

C. Cano, E. Chassande-Mottin, and N. Le Bihan

In 28ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2022

Abs Bib PDF

L’analyse des données provenant des observatoires terrestres d’ondes gravitationnelles repose sur l’ajustement aux observations de modèles d’ondes obtenus à partir de modèles astrophysiques. La génération de modèles peut demander des ressources importantes de calcul pour des tâches telles que l’estimation des paramètres astrophysiques qui nécessite la capacité de générer rapidement un grand nombre de modèles de formes d’onde. Nous abordons ce problème en utilisant la régression de composantes principales et des caractéristiques soigneusement choisies. Nous étudions tout d’abord le cas simple des fusions binaires compactes avec des orbites "sans précession" qui conduisent à des ondes polarisées circulairement, et le cas plus compliqué "avec précession orbitale" qui conduit à une plus grande variété de polarisation et nécessitent donc une représentation géométrique spécifique.
@inproceedings{cano2022gretsi, author = {Cano, C. and Chassande-Mottin, E. and {Le Bihan}, N.}, title = {Modèles polarisés pour la simulation rapide de formes d'ondes gravitationnelles}, booktitle = {{28ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}}, year = {2022}, pages = {13--16}, hal = {hal-03868307}, address = {Nancy, France}, }
GRETSI
Estimation de position en intérieur : une approche basée sur l’anti-développement et le filtre de Kalman étendu

R. Cherfi, C. Prieur, and N. Le Bihan

In 28ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2022

Abs Bib PDF

Cet article présente une méthode d’estimation de position en intérieur basée sur la combinaison d’un pré-filtrage et d’un filtre de Kalman étendu. Les résultats obtenus avec différents types de pré-filtrages sont présentés et comparés. Les conclusions principales suggèrent un impact perceptible du pré-filtrage sur le gain en performance de la méthode par rapport à l’état de l’art.
@inproceedings{cherfi2022gretsi, author = {Cherfi, R. and Prieur, C. and {Le Bihan}, N.}, title = {Estimation de position en intérieur : une approche basée sur l'anti-développement et le filtre de Kalman étendu}, booktitle = {{28ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}}, year = {2022}, pages = {677--680}, hal = {hal-03868304}, address = {Nancy, France}, }

2021

JASA

Polarization of ocean acoustic normal modes

J. Bonnel, J. Flamant, D.R. Dall’Osto, and 2 more authors

Journal of the Acoustical Society of America, 2021

DOI Bib

@article{bonnel2021jasa,
  title = {Polarization of ocean acoustic normal modes},
  author = {Bonnel, J. and Flamant, J. and Dall'Osto, D.R. and {Le Bihan}, N. and Dahl, P.H.},
  journal = {Journal of the Acoustical Society of America},
  volume = {150},
  issue = {3},
  pages = {1897-1911},
  year = {2021},
  doi = {10.1121/10.0006108},
}

ICML

Two-way kernel matrix puncturing: towards resource-efficient PCA and spectral clustering

R. Couillet, F. Chatelain, and N. Le Bihan

In 38th International Conference on Machine Learning (ICML), 2021

arXiv Bib

@inproceedings{couillet2021icml,
  title = {Two-way kernel matrix puncturing: towards resource-efficient PCA and spectral clustering},
  author = {Couillet, R. and Chatelain, F. and {Le Bihan}, N.},
  booktitle = {38th International Conference on Machine Learning (ICML)},
  address = {Vienna, Austria},
  year = {2021},
}

GSI

From Bayesian Inference to MCMC and Convex Optimisation in Hadamard Manifolds

S. Said, N. Le Bihan, and J.H. Manton

In Geometric Science of Information (GSI), 2021

DOI Bib

@inproceedings{said2021gsi,
  title = {{From Bayesian Inference to MCMC and~Convex Optimisation in Hadamard Manifolds}},
  author = {Said, S. and Le Bihan, N. and Manton, J.H.},
  hal = {hal-03376378},
  booktitle = {{Geometric Science of Information (GSI)}},
  editor = {F.(ed), Nielsen and (ed), Barbaresco F.},
  publisher = {{Springer International Publishing}},
  series = {Lecture Notes in Computer Science},
  volume = {12829},
  pages = {3-11},
  year = {2021},
  doi = {10.1007/978-3-030-80209-7\_1},
}

MTNS

Hidden Markov chains and fields with observations in Riemannian manifolds

S. Said, N. Le Bihan, and J.H. Manton

In 24th International Symposium on Mathematical theory of networks and systems (MTNS), 2021

DOI arXiv Bib

@inproceedings{said2021mtns,
  title = {Hidden Markov chains and fields with observations in Riemannian manifolds},
  author = {Said, S. and {Le Bihan}, N. and Manton, J.H.},
  booktitle = {24th International Symposium on Mathematical theory of networks and systems (MTNS)},
  address = {Cambridge, UK},
  year = {2021},
  hal = {hal-03376388/document},
  doi = {10.1016/j.ifacol.2021.06.135},
}

MTNS

On Riemannian and non-Riemannian Optimisation, and Optimisation Geometry

J. Lefevre, F. Bouchard, S. Said, and 2 more authors

In 24th International Symposium on Mathematical theory of networks and systems (MTNS), 2021

Bib

@inproceedings{lefevre2021mtns,
  title = {On Riemannian and non-Riemannian Optimisation, and Optimisation Geometry},
  author = {Lefevre, J. and Bouchard, F. and Said, S. and {Le Bihan}, N. and Manton, J.H.},
  booktitle = {24th International Symposium on Mathematical theory of networks and systems (MTNS)},
  address = {Cambridge, UK},
  year = {2021},
  hal = {hal-03376397/document},
}

EUSIPCO

An optimisation geometry framework for the Rayleigh quotient

J. Lefevre, N. Le Bihan, and J.H. Manton

In 30th European Signal Processing Conference (EUSIPCO), 2021

Bib

@inproceedings{lefevre2021eusipco,
  title = {An optimisation geometry framework for the Rayleigh quotient},
  author = {Lefevre, J. and {Le Bihan}, N. and Manton, J.H.},
  booktitle = {{30th European Signal Processing Conference (EUSIPCO)}},
  address = {Amsterdam, Netherlands},
  year = {2021},
  hal = {hal-03376426/document},
}

2020

JSWSC

On the nightglow polarisation for space weather exploration

L. Bosse, J. Lilensten, N. Gillet, and 13 more authors

Journal of Space Weather and Space Climate, 2020

DOI Bib

@article{bosse2020jswsc,
  title = {{On the nightglow polarisation for space weather exploration}},
  author = {Bosse, L. and Lilensten, J. and Gillet, N. and Rochat, S. and Delboulb{\'e}, A. and Curaba, S. and Roux, A. and Magnard, Y. and Johnsen, M.G. and L{{\o}}vhaug, U.-P. and Amblard, P.-O. and {Le Bihan}, N. and Nabon, M. and Marif, H. and Auriol, F. and No{\u}s, C.},
  journal = {{Journal of Space Weather and Space Climate}},
  publisher = {{EDP sciences}},
  volume = {10},
  pages = {35},
  year = {2020},
  doi = {10.1051/swsc/2020036},
  hal = {hal-02909104/file/swsc200009.pdf},
}

MLSP

Performance-Complexity Trade-Off in Large Dimensional Statistics

T. Zarrouk, R. Couillet, F. Chatelain, and 1 more author

In 30th IEEE International Workshop on Machine Learning for Signal Processing (MLSP), 2020

DOI Bib

@inproceedings{zarrouk2020mlsp,
  title = {{Performance-Complexity Trade-Off in Large Dimensional Statistics}},
  author = {Zarrouk, T. and Couillet, R. and Chatelain, F. and {Le Bihan}, N.},
  booktitle = {{30th IEEE International Workshop on Machine Learning for Signal Processing (MLSP)}},
  address = {Espoo (virtual), Finland},
  year = {2020},
  doi = {10.1109/MLSP49062.2020.9231568},
  hal = {hal-02961057/file/MLSP_2020_wo_copyright.pdf},
}

2019

ACHA

Time-frequency analysis of bivariate signals

J. Flamant, N. Le Bihan, and P. Chainais

Applied and Computational Harmonic Analysis, 2019

DOI arXiv Bib Code

@article{Flamant2019acha,
  title = {Time-frequency analysis of bivariate signals},
  author = {Flamant, J. and {Le Bihan}, N. and Chainais, P.},
  journal = {Applied and Computational Harmonic Analysis},
  volume = {46},
  issue = {2},
  pages = {351-383},
  year = {2019},
  doi = {10.1016/j.acha.2017.05.007},
  hal = {hal-01362586/document},
}

ISIT

Complexity and Similarity for Sequences using LZ77-based conditional information measure

F. Cayre, and N. Le Bihan

In IEEE International Symposium on Information Theory (ISIT), 2019

DOI Bib

@inproceedings{cayre2019isit,
  author = {Cayre, F. and {Le Bihan}, N.},
  booktitle = {IEEE International Symposium on Information Theory (ISIT)},
  title = {Complexity and Similarity for Sequences using LZ77-based conditional information measure},
  year = {2019},
  address = {Paris, France},
  volume = {},
  number = {},
  pages = {2454-2458},
  doi = {10.1109/ISIT.2019.8849610},
  hal = {hal-02346520},
}

ICASSP

Exact Distribution and High-dimensional Asymptotics for Improperness Test of Complex Signals

F. Chatelain, and N. Le Bihan

In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2019

DOI Bib

@inproceedings{chatelainicassp2019,
  title = {{Exact Distribution and High-dimensional Asymptotics for Improperness Test of Complex Signals}},
  author = {Chatelain, F. and {Le Bihan}, N.},
  booktitle = {{IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}},
  address = {Brighton, United Kingdom},
  publisher = {{IEEE}},
  pages = {8509-8513},
  year = {2019},
  doi = {10.1109/ICASSP.2019.8683518},
  hal = {hal-02148428/file/Properness_et_RMT_icassp.pdf},
}

ICASSP

Estimation of Widely Factorizable Hypercomplex Signals with Uncertain Observations

R. Fernandez-Alcala, J. Jimenez-Lepez, J. Navarro-Moreno, and 2 more authors

In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2019

DOI Bib

@inproceedings{fernandezalcala2019icassp,
  title = {{Estimation of Widely Factorizable Hypercomplex Signals with Uncertain Observations}},
  author = {Fernandez-Alcala, R. and Jimenez-Lepez, J. and Navarro-Moreno, J. and Ruiz-Molina, J. and {Le Bihan}, N.},
  booktitle = {{IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}},
  address = {Brighton, United Kingdom},
  pages = {8504-8508},
  year = {2019},
  doi = {10.1109/ICASSP.2019.8683146},
  hal = {hal-02346547},
}

GRETSI

Recursive algorithm for estimation of mixture models on Riemannian symmetric space

S. Said, N. Le Bihan, and J. Zhou

In 27ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2019

Bib PDF

@inproceedings{zhou2019gretsi,
  title = {{Recursive algorithm for estimation of mixture models on Riemannian symmetric space}},
  author = {Said, S. and {Le Bihan}, N. and Zhou, J.},
  booktitle = {{27ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}},
  address = {Lille, France},
  year = {2019},
  pages = {573--576},
  hal = {hal-02927638/file/GRETSI_2019.pdf},
}

GRETSI

Reconstruction et caractérisation des polarisations d’une onde gravitationnelle

F. Feng, J. Flamant, P. Chainais, and 2 more authors

In 27ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2019

Bib PDF

@inproceedings{feng2019gretsi,
  title = {{Reconstruction et caract{\'e}risation des polarisations d'une onde gravitationnelle}},
  author = {Feng, F. and Flamant, J. and Chainais, P. and Chassande-Mottin, E. and {Le Bihan}, N.},
  booktitle = {{27ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}},
  address = {Lille, France},
  year = {2019},
  pages = {549--552},
  hal = {hal-02410728/file/19gretsi-reco-polar.pdf},
}

GRETSI

Classification de séquences basée sur une distance universelle algorithmique

F. Cayre, O. Michel, and N. Le Bihan

In 27ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2019

Bib PDF

@inproceedings{cayre2019gretsi,
  author = {Cayre, F. and Michel, O. and {Le Bihan}, N.},
  title = {Classification de séquences basée sur une distance universelle algorithmique},
  booktitle = {{27ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}},
  address = {Lille, France},
  year = {2019},
  pages = {505--508},
}

GRETSI
Régime asymptotique des statistiques de test de circularité

F. Chatelain, and N. Le Bihan

In 27ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2019

Abs Bib PDF

Dans le cas Gaussien, tester la circularité d’un vecteur aléatoire complexe revient à identifier une structure de corrélation spécifique entre la partie réelle et la partie imaginaire. Dans cet article, nous nous intéressons à définir un test invariant par transformation linéaire, ce qui revient à construire un tel test à l’aide des valeurs propres de la matrice de corrélation empirique des observations. Nous donnons la distribution des valeurs propres ainsi que de la valeur propre maximale dans le régime asymptotique où la taille des vecteurs et la taille de l’échantillon tendent vers l’infini pendant que leur rapport reste commensurable. Enfin, nous comparons dans ce régime asymptotique le test de Roy, qui repose sur la statistique de la plus grande valeur propre, avec le GLRT sur des simulations.
@inproceedings{chatelain2019gretsi, author = {Chatelain, F. and {Le Bihan}, N.}, title = {Régime asymptotique des statistiques de test de circularité}, booktitle = {{27ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}}, year = {2019}, pages = {1177--1180}, address = {Lille, France}, }

2018

IEEE TSP

A Complete Framework for Linear Filtering of Bivariate Signals

J. Flamant, P. Chainais, and N. Le Bihan

IEEE Transactions on Signal Processing, 2018

DOI arXiv Bib Code

@article{flamant2018ieeetsp,
  author = {Flamant, J. and Chainais, P. and {Le Bihan}, N.},
  title = {A Complete Framework for Linear Filtering of Bivariate Signals},
  year = {2018},
  journal = {IEEE Transactions on Signal Processing},
  volume = {66},
  number = {17},
  pages = {4541-4552},
  doi = {10.1109/TSP.2018.2855659},
  hal = {hal-02017824},
}

SSP

Linear Filtering of Bivariate Signals Using Quaternions

J. Flamant, P. Chainais, and N. Le Bihan

In 2018 IEEE Statistical Signal Processing Workshop (SSP), 2018

DOI Bib

@inproceedings{flamant2018ssp,
  author = {Flamant, J. and Chainais, P. and {Le Bihan}, N.},
  booktitle = {2018 IEEE Statistical Signal Processing Workshop (SSP)},
  title = {Linear Filtering of Bivariate Signals Using Quaternions},
  year = {2018},
  volume = {},
  number = {},
  pages = {154-158},
  doi = {10.1109/SSP.2018.8450687},
  hal = {hal-02017832},
}

EUSIPCO

Non-parametric characterization of gravitational-wave polarizations

J. Flamant, P. Chainais, E. Chassande-Mottin, and 2 more authors

In 26th European Signal Processing Conference (EUSIPCO), 2018

DOI Bib

@inproceedings{flamant2018eusipco,
  author = {Flamant, J. and Chainais, P. and Chassande-Mottin, E. and Feng, F. and {Le Bihan}, N.},
  title = {Non-parametric characterization of gravitational-wave polarizations},
  booktitle = {26th European Signal Processing Conference (EUSIPCO)},
  year = {2018},
  hal = {hal-02017827},
  doi = {10.23919/EUSIPCO.2018.8552942},
}

2017

IEEE TSP
Spectral analysis of stationary random bivariate signals

J. Flamant, N. Le Bihan, and P. Chainais

IEEE Transactions on Signal Processing, 2017

Abs DOI arXiv Bib Code

A novel approach toward the spectral analysis of stationary random bivariate signals is proposed. Unlike existing approaches, the proposed framework exhibits a natural link between well-defined statistical objects and physical parameters for bivariate signals. Using the quaternion Fourier transform, we introduce a quaternion-valued spectral representation of random bivariate signals seen as complex-valued sequences. This makes possible the definition of a scalar quaternion-valued spectral density and the corresponding autocovariance for bivariate signals. This spectral density can be meaningfully interpreted in terms of frequency-dependent polarization attributes. A natural decomposition of the spectral density of any random bivariate signal in terms of unpolarized and polarized components is introduced. Nonparametric spectral density estimation is investigated, and we introduce the polarization periodogram of a random bivariate signal. Numerical experiments support our theoretical analysis, illustrating the relevance of the approach on synthetic data
@article{flamant2017ieeetsp, title = {{Spectral analysis of stationary random bivariate signals}}, author = {Flamant, J. and {Le Bihan}, N. and Chainais, P.}, doi = {10.1109/TSP.2017.2736494}, issn = {1053587X}, journal = {IEEE Transactions on Signal Processing}, number = {23}, pages = {6135--6145}, volume = {65}, year = {2017}, hal = {hal-01655097/document}, }

The geometry of proper quaternion random variables

N. Le Bihan

Signal Processing, 2017

DOI arXiv Bib

@article{lebihan2017sp,
  title = {{The geometry of proper quaternion random variables}},
  author = {{Le Bihan}, N.},
  journal = {Signal Processing},
  number = {23},
  pages = {106--116},
  volume = {138},
  year = {2017},
  hal = {hal-01550207},
  doi = {10.1016/j.sigpro.2017.03.017},
}

GRETSI
Analyse spectrale des signaux aléatoires bivariés

J. Flamant, N. Le Bihan, and P. Chainais

In 26ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2017

Abs Bib PDF

Nous proposons un nouveau formalisme pour l’analyse spectrale des signaux bivariés décrits sous forme complexe. A la différence des approches existantes, nous démontrons un lien naturel entre grandeurs statistiques et paramètres physiques du signal. L’approche est fondée sur la définition de la densité spectrale quaternionique d’un processus bivarié. Une décomposition originale de tout signal bivarié stationnaire en composantes polarisée et non-polarisée est présentée. Un exemple illustre la pertinence du formalisme
@inproceedings{flamant2017gretsi1, title = {{Analyse spectrale des signaux aléatoires bivari{\'e}s}}, author = {Flamant, J. and {Le Bihan}, N. and Chainais, P.}, booktitle = {{26ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}}, address = {Juan-les-Pins, France}, year = {2017}, pages = {53--56}, hal = {hal-01691274/document}, }

GRETSI

Spectrogramme de polarisation pour l’analyse des signaux bivariés

J. Flamant, N. Le Bihan, and P. Chainais

In 26ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2017

Bib PDF

@inproceedings{flamant2017gretsi2,
  title = {{Spectrogramme de polarisation pour l'analyse des signaux bivari{\'e}s}},
  author = {Flamant, J. and {Le Bihan}, N. and Chainais, P.},
  booktitle = {{26ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}},
  address = {Juan-les-Pins, France},
  year = {2017},
  pages = {49--52},
  hal = {hal-01691276/document},
}

ICASSP

Polarization spectrogram of bivariate signals

J. Flamant, N. Le Bihan, and P. Chainais

In IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2017

DOI Bib

@inproceedings{flamant2017icassp,
  title = {Polarization spectrogram of bivariate signals},
  author = {Flamant, J. and {Le Bihan}, N. and Chainais, P.},
  booktitle = {{IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)}},
  address = {New Orleans, USA},
  year = {2017},
  doi = {10.1109/ICASSP.2017.7952905},
  hal = {hal-01655120/document},
}

GRETSI
Classification à l’aide d’un estimateur de complexité algorithmique

M. Revolle, F. Cayre, and N. Le Bihan

In 26ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2017

Abs Bib PDF

Dans le cas où les données ne se prêtent pas aisément à la modélisation probabiliste, on peut préférer le pendant algorithmique de la théorie de l’information, fondée sur la complexité de Kolmogorov. Dans cette contribution, nous montrons comment estimer une semi-distance algorithmique entre objets binaires quelconques, qui soit à la fois plus précise et moins limitée que l’état de l’art.
@inproceedings{revolle2017gretsi, author = {Revolle, M. and Cayre, F. and {Le Bihan}, N.}, title = {Classification à l’aide d’un estimateur de complexité algorithmique}, booktitle = {{26ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}}, year = {2017}, pages = {61--6}, }

GSI

Riemannian Gaussian distributions on the space of positive-definite quaternion matrices

S. Said, N. Le Bihan, and J.H. Manton

In Geometric Science of Information (GSI), 2017

arXiv Bib

@inproceedings{said2017gsi,
  title = {{Riemannian Gaussian distributions on the space of positive-definite quaternion matrices}},
  author = {Said, S. and {Le Bihan}, N. and Manton, J.H.},
  hal = {hal-01655168},
  booktitle = {{Geometric Science of Information (GSI)}},
  address = {Paris, France},
  year = {2017},
}

GSI

Density estimation for compound Cox processes on hyperspheres

F. Chatelain, N. Le Bihan, and J.H. Manton

In Geometric Science of Information (GSI), 2017

Bib

@inproceedings{chatelain2017gsi,
  title = {{Density estimation for compound Cox processes on hyperspheres}},
  author = {Chatelain, F. and {Le Bihan}, N. and Manton, J.H.},
  hal = {hal-01655180},
  booktitle = {{Geometric Science of Information (GSI)}},
  address = {Paris, France},
  year = {2017},
}

ICIP
On some global topological aspects of manifold learning

J.H. Manton, and N. Le Bihan

In IEEE International Conference on Image Processing (ICIP), 2017

Abs DOI Bib

With the dual purpose of helping place in perspective the diverse approaches to manifold learning, and facilitating future research, this paper steps back and describes the manifold learning problem from a holistic perspective. It is argued that getting the homology right can be crucial to successful classification schemes based on the intrinsic geometry of the learnt manifold, and furthermore, a purely Bayesian approach will not be able to succeed at this in general. Simple examples are given to illustrate the inherent limitations of manifold learning.
@inproceedings{manton2017icip, author = {Manton, J.H. and {Le Bihan}, N.}, booktitle = {{IEEE International Conference on Image Processing (ICIP)}}, title = {On some global topological aspects of manifold learning}, year = {2017}, volume = {}, number = {}, address = {Beijing, China}, pages = {225--229}, doi = {10.1109/ICIP.2017.8296276}, }
EUSIPCO
Clustering and causality inference using algorithmic complexity

M. Revolle, F. Cayre, and N. Le Bihan

In 25th European Signal Processing Conference (EUSIPCO), 2017

Abs DOI Bib

We present a set of algorithmic complexity estimates. We derive a normalized semi-distance that is shown to outperform the state-of-the-art. We also propose estimators for causality inference on directed acyclic graphs. Illustrative applications include clustering of human writing systems and causality assessment on novel drafts.
@inproceedings{revolle2017eusipco, title = {{Clustering and causality inference using algorithmic complexity}}, author = {Revolle, M. and Cayre, F. and {Le Bihan}, N.}, hal = {hal-01655109}, booktitle = {{25th European Signal Processing Conference (EUSIPCO)}}, address = {Kos Island, Greece}, year = {2017}, pages = {843--847}, doi = {10.23919/EUSIPCO.2017.8081326}, }

2016

IEEE IT

Isotropic multiple scattering processes on hyperspheres

N. Le Bihan, F. Chatelain, and J.H. Manton

IEEE Transactions on Information Theory, 2016

DOI arXiv Bib

@article{lebihan2016ieeeit,
  title = {{Isotropic multiple scattering processes on hyperspheres}},
  author = {{Le Bihan}, N. and Chatelain, F. and Manton, J.H.},
  journal = {IEEE Transactions on Information Theory},
  number = {10},
  pages = {5740--5752},
  volume = {62},
  year = {2016},
  doi = {10.1109/TIT.2015.2508932},
  hal = {hal-01322340/file/1408.2887v2.pdf},
}

Phys Rev E

Expansion-maximization-compression algorithm with spherical harmonics for single particle imaging with x-ray lasers

J. Flamant, N. Le Bihan, A.V. Martin, and 1 more author

Physical Review E, 2016

DOI arXiv

ISIF

Density estimation on the rotation group using diffusive wavelets

N. Le Bihan, J. Flamant, and J.H. Manton

Journal of Advances in Information Fusion, 2016

arXiv Bib

@article{lebihan2016diffusive,
  author = {{Le Bihan}, N. and Flamant, J. and Manton, J.H.},
  journal = {{Journal of Advances in Information Fusion}},
  title = {Density estimation on the rotation group using diffusive wavelets},
  publisher = {{ISIF}},
  volume = {11},
  issue = {2},
  pages = {173--185},
  year = {2016},
  hal = {hal-01550211},
}

GJI
Analysis of seismic waves crossing the Santa Clara Valley using the three-component MUSIQUE array algorithm

M. Hobiger, C. Cornou, P.-Y. Bard, and 2 more authors

Geophysical Journal International, 2016

Abs DOI Bib

We introduce the MUSIQUE algorithm and apply it to seismic wavefield recordings in California. The algorithm is designed to analyse seismic signals recorded by arrays of three-component seismic sensors. It is based on the MUSIC and the quaternion-MUSIC algorithms. In a first step, the MUSIC algorithm is applied in order to estimate the backazimuth and velocity of incident seismic waves and to discriminate between Love and possible Rayleigh waves. In a second step, the polarization parameters of possible Rayleigh waves are analysed using quaternion-MUSIC, distinguishing retrograde and prograde Rayleigh waves and determining their ellipticity. In this study, we apply the MUSIQUE algorithm to seismic wavefield recordings of the San Jose Dense Seismic Array. This array has been installed in 1999 in the Evergreen Basin, a sedimentary basin in the Eastern Santa Clara Valley. The analysis includes 22 regional earthquakes with epicentres between 40 and 600 km distant from the array and covering different backazimuths with respect to the array. The azimuthal distribution and the energy partition of the different surface wave types are analysed. Love waves dominate the wavefield for the vast majority of the events. For close events in the north, the wavefield is dominated by the first harmonic mode of Love waves, for farther events, the fundamental mode dominates. The energy distribution is different for earthquakes occurring northwest and southeast of the array. In both cases, the waves crossing the array are mostly arriving from the respective hemicycle. However, scattered Love waves arriving from the south can be seen for all earthquakes. Combining the information of all events, it is possible to retrieve the Love wave dispersion curves of the fundamental and the first harmonic mode. The particle motion of the fundamental mode of Rayleigh waves is retrograde and for the first harmonic mode, it is prograde. For both modes, we can also retrieve dispersion and ellipticity curves. Wave motion simulations for two earthquakes are in good agreement with the real data results and confirm the identification of the wave scattering formations to the south of the array, which generate the scattered Love waves visible for all earthquakes.
@article{hobiger2016gji, author = {Hobiger, M. and Cornou, C. and Bard, P.-Y. and {Le Bihan}, N. and Imperatori, W.}, title = {{Analysis of seismic waves crossing the Santa Clara Valley using the three-component MUSIQUE array algorithm}}, journal = {Geophysical Journal International}, publisher = {{Oxford University Press (OUP)}}, volume = {207}, number = {1}, pages = {439--456}, year = {2016}, issn = {0956-540X}, doi = {10.1093/gji/ggw289}, hal = {hal-01550304/file/ggw289.pdf}, }

ICASSP

Low-Resolution reconstruction of intensity functions on the sphere for single-particle diffraction imaging

J. Flamant, N. Le Bihan, A.V. Martin, and 1 more author

In IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2016

DOI Bib

@inproceedings{flamant2016icassp,
  title = {Low-Resolution reconstruction of intensity functions on the sphere for single-particle diffraction imaging},
  author = {Flamant, J. and {Le Bihan}, N. and Martin, A.V. and Manton, J.H.},
  booktitle = {{IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)}},
  address = {Shangai, China},
  year = {2016},
  doi = {10.1109/ICASSP.2016.7471758},
  hal = {hal-01655131},
}

2015

EMBC
C. Elegans locomotion analysis using algorithmic information theory

R. Skandari, N. Le Bihan, and J.H. Manton

In 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 2015

Abs DOI Bib

This article investigates the use of algorithmic information theory to analyse C. elegans datasets. The ability of complexity measures to detect similarity in animals’ behaviours is demonstrated and their strengths are compared to methods such as histograms. Introduced quantities are illustrated on a couple of real two-dimensional C. elegans datasets to investigate the thermotaxis and chemotaxis behaviours.
@inproceedings{skandari2015ecmb, title = {{C. Elegans locomotion analysis using algorithmic information theory}}, author = {Skandari, R. and {Le Bihan}, N. and Manton, J.H.}, hal = {hal-01655148}, booktitle = {{37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)}}, address = {Milan, Italy}, year = {2015}, doi = {10.1109/EMBC.2015.7319878}, }

ICASSP

Parameter estimation for multiple scattering process on the sphere

F. Chatelain, N. Le Bihan, and J.H. Manton

In 40th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2015

DOI Bib

@inproceedings{chatelain2015icassp,
  title = {{Parameter estimation for multiple scattering process on the sphere}},
  author = {Chatelain, F. and {Le Bihan}, N. and Manton, J.H.},
  hal = {hal-01655153},
  booktitle = {{40th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}},
  address = {Brisbane, Australia},
  year = {2015},
  pages = {3976-3980},
  doi = {10.1109/ICASSP.2015.7178717},
}

2014

Wiley Book

Quaternion Fourier Transforms for Signal and Image Processing

T. Ell, N. Le Bihan, and S. Sangwine

2014

DOI Bib

@book{ell2014book,
  title = {{Quaternion Fourier Transforms for Signal and Image Processing}},
  author = {Ell, T. and {Le Bihan}, N. and Sangwine, S.},
  hal = {hal-00987367},
  publisher = {{Wiley-ISTE}},
  year = {2014},
  doi = {10.1002/9781118930908},
}

SP

Instantaneous frequency and amplitude of orthocomplex modulated signals based on quaternion Fourier transform

N. Le Bihan, Stephen J. Sangwine, and Todd A. Ell

Signal Processing, 2014

Abs DOI arXiv

The ideas of instantaneous amplitude and phase are well understood for signals with real-valued samples, based on the analytic signal which is a complex signal with one-sided Fourier transform. We explore the extension of these ideas to signals with complex-valued samples, using a quaternion-valued equivalent of the analytic signal obtained from a one-sided quaternion Fourier transform which we refer to as the hypercomplex representation of the complex signal. We discuss its derivation and properties and show how to obtain a complex envelope and a real phase from it. A classical result in the case of real signals is that an amplitude modulated signal may be decomposed into its envelope and carrier using the analytic signal provided that the modulating signal has frequency content not overlapping with that of the carrier. We show that this idea extends to the complex case, provided that the complex signal modulates an orthonormal complex exponential. Examples are presented to demonstrate these concepts.

ICASSP

Monte-Carlo estimation from observation on Stiefel manifold

J. Boulanger, N. Le Bihan, S. Said, and 1 more author

In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2014

DOI Bib

@inproceedings{boulanger2014icassp,
  title = {{Monte-Carlo estimation from observation on Stiefel manifold}},
  author = {Boulanger, J. and {Le Bihan}, N. and Said, S. and Manton, J.H.},
  hal = {hal-01655158},
  booktitle = {{IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}},
  address = {Florence, Italy},
  year = {2014},
  pages = {4195-4199},
  doi = {10.1109/ICASSP.2014.6854392},
}

2013

J. Phys. A

Stochastic description of geometric phase for polarized waves in random media

J. Boulanger, N. Le Bihan, and V. Rossetto

Journal of Physics A: Mathematical and Theoretical, 2013

DOI arXiv Bib

@article{boulanger2013jpa,
  title = {{Stochastic description of geometric phase for polarized waves in random media}},
  author = {Boulanger, J. and {Le Bihan}, N. and Rossetto, V.},
  journal = {{Journal of Physics A: Mathematical and Theoretical}},
  publisher = {{IOP Publishing}},
  volume = {46},
  pages = {035203},
  year = {2013},
  doi = {10.1088/1751-8113/46/3/035203},
  hal = {hal-01075284/file/RANL-8VUCN2.pdf},
}

GJI

Ground structure imaging by inversions of Rayleigh wave ellipticity: sensitivity analysis and application to European strong-motion sites

M. Hobiger, C. Cornou, M. Wathelet, and 9 more authors

Geophysical Journal International, 2013

DOI Bib PDF

@article{hobiger2012gji,
  title = {{Ground structure imaging by inversions of Rayleigh wave ellipticity: sensitivity analysis and application to European strong-motion sites}},
  author = {Hobiger, M. and Cornou, C. and Wathelet, M. and Giulio, G. Di and Knapmeyer-Endrun, B. and Renalier, F. and Bard, P.-Y. and Savvaidis, A. and Hailemikael, S. and {Le Bihan}, N. and Ohrnberger, M. and Theodoulidis, N.},
  journal = {{Geophysical Journal International}},
  publisher = {{Oxford University Press (OUP)}},
  volume = {192},
  number = {1},
  pages = {207--229},
  year = {2013},
  doi = {10.1093/gji/ggs005},
  hal = {insu-01741793},
}

ICASSP

Von Mises-Fisher approximation of multiple scattering process on the hypersphere

F. Chatelain, and N. Le Bihan

In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2013

DOI Bib

@inproceedings{chatelain2013icassp,
  author = {Chatelain, F. and {Le Bihan}, N.},
  booktitle = {{IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}},
  title = {{Von Mises-Fisher approximation of multiple scattering process on the hypersphere}},
  year = {2013},
  volume = {},
  number = {},
  address = {Vancouver, Canada},
  pages = {6461--6465},
  doi = {10.1109/ICASSP.2013.6638910},
  hal = {hal-00865968},
}

2012

Metrika

Geodesic normal distribution on the circle

J.-F. Coeurjolly, and N. Le Bihan

Metrika, 2012

DOI arXiv Bib

@article{coeurjolly2021metrika,
  author = {Coeurjolly, J.-F. and {Le Bihan}, N.},
  title = {Geodesic normal distribution on the circle},
  year = {2012},
  volume = {75},
  number = {7},
  pages = {977--995},
  journal = {{Metrika}},
  hal = {hal-00548828},
  doi = {10.1007/s00184-011-0363-7},
}

IEEE SPM

Multicomponent Signal Processing for Rayleigh Wave Ellipticity Estimation: Application to Seismic Hazard Assessment

M. Hobiger, N. Le Bihan, C. Cornou, and 1 more author

IEEE Signal Processing Magazine, 2012

DOI Bib

@article{hobiger2012ieeespm,
  author = {Hobiger, M. and {Le Bihan}, N. and Cornou, C. and Bard, P.-Y.},
  journal = {{IEEE Signal Processing Magazine}},
  title = {Multicomponent Signal Processing for Rayleigh Wave Ellipticity Estimation: Application to Seismic Hazard Assessment},
  year = {2012},
  volume = {29},
  number = {3},
  pages = {29--39},
  doi = {10.1109/MSP.2012.2184969},
  hal = {hal-00787723},
}

Ann. Phys.
Observation of a non-adiabatic geometric phase for elastic waves

J. Boulanger, N. Le Bihan, S. Catheline, and 1 more author

Annals of Physics, 2012

Abs DOI arXiv Bib

We report the experimental observation of a geometric phase for elastic waves in a waveguide with helical shape. The setup reproduces the experiment by Tomita and Chiao [A. Tomita, R.Y. Chiao, Phys. Rev. Lett. 57 (1986) 937–940, 2471] that showed first evidence of a Berry phase, a geometric phase for adiabatic time evolution, in optics. Experimental evidence of a non-adiabatic geometric phase has been reported in quantum mechanics. We have performed an experiment to observe the polarization transport of classical elastic waves. In a waveguide, these waves are polarized and dispersive. Whereas the wavelength is of the same order of magnitude as the helix’s radius, no frequency dependent correction is necessary to account for the theoretical prediction. This shows that in this regime, the geometric phase results directly from geometry and not from a correction to an adiabatic phase.
@article{boulanger2012annphy, title = {Observation of a non-adiabatic geometric phase for elastic waves}, journal = {Annals of Physics}, volume = {327}, number = {3}, pages = {952--958}, year = {2012}, issn = {0003-4916}, doi = {10.1016/j.aop.2011.11.014}, author = {Boulanger, J. and {Le Bihan}, N. and Catheline, S. and Rossetto, V.}, hal = {hal-00665640}, }

SSP

Wiener filtering of rotation processes using ordered exponentials

J. Boulanger, N. Le Bihan, and J.H. Manton

In IEEE Workshop on Statistical Signal Processing (SSP), 2012

Bib

@inproceedings{boulanger2012ssp,
  title = {{Wiener filtering of rotation processes using ordered exponentials}},
  author = {Boulanger, J. and {Le Bihan}, N. and Manton, J.H.},
  hal = {hal-00788246},
  booktitle = {{IEEE Workshop on Statistical Signal Processing (SSP)}},
  address = {Ann Arbor, Michigan, United States},
  pages = {61--64},
  year = {2012},
}

AGACSE

Quaternion Wigner-Ville distribution

N. Le Bihan, and T. Ell

In 5th conference on Applied Geometric Algebras in Computer Science and Engineering (AGACSE), 2012

Bib

@inproceedings{lebihan2012agacse,
  title = {{Quaternion Wigner-Ville distribution}},
  author = {{Le Bihan}, N. and Ell, T.},
  hal = {hal-00788244},
  booktitle = {{5th conference on Applied Geometric Algebras in Computer Science and Engineering (AGACSE)}},
  address = {La Rochelle, France},
  publisher = {{Birkh{\"a}user Basel}},
  pages = {39},
  year = {2012},
}

2011

AACA

Fundamental representations and algebraic properties of biquaternions or complexified quaternions

S. Sangwine, T. Ell, and N. Le Bihan

Advances in Applied Clifford Algebras, 2011

DOI arXiv Bib

@article{sangwine2011AACA,
  title = {{Fundamental representations and algebraic properties of biquaternions or complexified quaternions}},
  author = {Sangwine, S. and Ell, T. and {Le Bihan}, N.},
  hal = {hal-00788240},
  journal = {{Advances in Applied Clifford Algebras}},
  publisher = {{Springer Verlag}},
  volume = {21},
  number = {3},
  pages = {607--636},
  year = {2011},
  doi = {10.1007/s00006-010-0263-3},
}

ICAA

Quaternionic spectral analysis of non-stationary improper complex signals

N. Le Bihan, and S. Sangwine

In 9th International Conference on Clifford algebras and Applications (ICAA), 2011

Bib

@inproceedings{lebihan2011icaa,
  title = {{Quaternionic spectral analysis of non-stationary improper complex signals}},
  author = {{Le Bihan}, N. and Sangwine, S.},
  hal = {hal-00682588},
  booktitle = {{9th International Conference on Clifford algebras and Applications (ICAA)}},
  address = {Weirmar, Germany},
  pages = {135},
  year = {2011},
}

GRETSI
Phase géométrique des signaux polarisés en milieux aléatoires

J. Boulanger, N. Le Bihan, and V. Rossetto

In 23ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2011

Abs Bib PDF

Lors de la propagation dans un milieu diffusant, les ondes polarisées sont affectées par les diffuseurs à la fois dans leur direction de propagation et leur polarisation. Dans cet article, nous proposons un modèle de processus aléatoire sur le groupe des rotations avec transport parallèle qui décrit le comportement des ondes polarisées dans ce type de milieu. En particulier, notre modèle permet de prédire la distribution de la phase géométrique des ondes polarisées. Cette phase est uniquement fonction de la trajectoire de l’onde dans le milieu et caractérise donc la géométrie de celle-ci. Nous montrons également comment notre modèle prédit la dépolarisation des ondes et permet d’estimer certains paramètres du milieu diffusant.
@inproceedings{boulanger2011gretsi, author = {Boulanger, J. and {Le Bihan}, N. and Rossetto, V.}, title = {Phase géométrique des signaux polarisés en milieux aléatoires}, booktitle = {{23ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}}, year = {2011}, pages = {565--568}, hal = {hal-00682584}, }

SSP

MUSIQUE: A Quaternion-Based Array Processing Technique for Surface Wave Polarization Analysis

M. Hobiger, N. Le Bihan, C. Cornou, and 1 more author

In IEEE Workshop on Statistical Signal Processing (SSP), 2011

DOI Bib

@inproceedings{hobiger2011ssp,
  title = {{MUSIQUE: A Quaternion-Based Array Processing Technique for Surface Wave Polarization Analysis}},
  author = {Hobiger, M. and {Le Bihan}, N. and Cornou, C. and Bard, P.-Y.},
  hal = {hal-00682579},
  booktitle = {{IEEE Workshop on Statistical Signal Processing (SSP)}},
  address = {Nice, France},
  pages = {5--8},
  year = {2011},
  doi = {10.1109/SSP.2011.5967770},
}

ICASSP

Blind extraction of improper quaternion sources

S. Javidi, C. Cheong Took, C. Jahanchahi, and 2 more authors

In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2011

DOI Bib

@inproceedings{javidi2011icassp,
  author = {Javidi, S. and Cheong Took, C. and Jahanchahi, C. and {Le Bihan}, N. and Mandic, D. P.},
  booktitle = {{IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}},
  title = {Blind extraction of improper quaternion sources},
  year = {2011},
  address = {{Prague, Czech Republic}},
  volume = {},
  number = {},
  pages = {3708--3711},
  doi = {10.1109/ICASSP.2011.5947156},
  hal = {hal-00682578},
}

2010

IEEE IT

Decompounding on Compact Lie Groups

S. Said, C. Lageman, N. Le Bihan, and 1 more author

IEEE Transactions on Information Theory, 2010

DOI arXiv Bib

@article{said2010ieeeit,
  author = {Said, S. and Lageman, C. and {Le Bihan}, N. and Manton, J.H.},
  journal = {{IEEE Transactions on Information Theory}},
  title = {{Decompounding on Compact Lie Groups}},
  year = {2010},
  volume = {56},
  number = {6},
  pages = {2766--2777},
  doi = {10.1109/TIT.2010.2046216},
}

Quaternion polynomial matrix diagonalization for the separation of polarized convolutive mixture

G.M. Menanno, and N. Le Bihan

Signal Processing, 2010

DOI Bib

@article{menanno2010sp,
  title = {{Quaternion polynomial matrix diagonalization for the separation of polarized convolutive mixture}},
  author = {Menanno, G.M. and {Le Bihan}, N.},
  hal = {hal-00515653},
  journal = {{Signal Processing}},
  publisher = {{Elsevier}},
  volume = {90},
  number = {7},
  pages = {1229--1337},
  year = {2010},
  doi = {10.1016/j.sigpro.2010.02.003},
}

AACA

Quaternion Polar Representation with a Complex Modulus and Complex Argument Inspired by the Cayley-Dickson Form

S. Sangwine, and N. Le Bihan

Advances in Applied Clifford Algebras, 2010

DOI arXiv Bib

@article{sangwine2010aaca,
  title = {Quaternion Polar Representation with a Complex Modulus and Complex Argument Inspired by the Cayley-Dickson Form},
  author = {Sangwine, S. and {Le Bihan}, N.},
  journal = {{Advances in Applied Clifford Algebras}},
  volume = {20},
  number = {1},
  pages = {111,120},
  year = {2010},
  doi = {10.1007/s00006-008-0128-1},
}

2009

PRE

Nonparametric estimation of the heterogeneity of a random medium using Compound Poisson Process modeling of wave multiple scattering

N. Le Bihan, and L. Margerin

Physical Review E, 2009

DOI arXiv

GRL

Single station determination of Rayleigh wave ellipticity by using the random decrement technique (RayDec)

M. Hobiger, P.-Y. Bard, C. Cornou, and 1 more author

Geophysical Research Letters, 2009

DOI Bib

@article{hobiger2009grl,
  title = {{Single station determination of Rayleigh wave ellipticity by using the random decrement technique (RayDec)}},
  author = {Hobiger, M. and Bard, P.-Y. and Cornou, C. and {Le Bihan}, N.},
  journal = {{Geophysical Research Letters}},
  publisher = {{American Geophysical Union}},
  volume = {36},
  pages = {L14303},
  year = {2009},
  doi = {10.1029/2009GL038863},
  hal = {hal-00413407/file/2009GL038863.pdf},
}

GRETSI
Inférence statistique sur la fonction de phase des milieux aléatoires par diffusion multiple des ondes

N. Le Bihan, L. Margerin, and S. Said

In 22ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2009

Abs Bib PDF

Nous proposons un modele de type Processus de Poisson sur un groupe de Lie compact pour la description et l’etude de la diffusion multiple dans les milieuax aleatoires. Cette approche permet d’inferer sur le milieu et en particulier d’estimer la fonction de phase du milieu qui donne acces au spectre d’heterogeneite, grendeur caracteristique du milieu. La technique d’inference proposee consiste en une decomposition du processus de Poisson modelisant le phenomene de diffusion multiple. Nous validons la technique proposee en testant les estimateurs sur des donnees de simulation Monte Carlo.
@inproceedings{lebihan2009gretsi, author = {{Le Bihan}, N. and Margerin, L. and Said, S.}, title = {Inférence statistique sur la fonction de phase des milieux aléatoires par diffusion multiple des ondes}, booktitle = {{22ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}}, year = {2009}, address = {Dijon, France}, }

2008

IJNS

Polarized signal classification by complex and quaternionic multi-layer perceptrons

S. Buchholz, and N. Le Bihan

International Journal of Neural Systems, 2008

DOI Bib

@article{buchholz2008ijns,
  title = {{Polarized signal classification by complex and quaternionic multi-layer perceptrons}},
  author = {Buchholz, S. and {Le Bihan}, N.},
  journal = {{International Journal of Neural Systems}},
  publisher = {{World Scientific Publishing}},
  volume = {18},
  number = {2},
  pages = {75--85},
  year = {2008},
  doi = {10.1142/S0129065708001403},
  hal = {hal-00276964},
}

WRCM

Higher-order statistics of Stokes parameters in a random birefringent medium

S. Said, and N. Le Bihan

Waves in Random and Complex Media, 2008

DOI arXiv Bib

@article{said2008wrcm,
  title = {{Higher-order statistics of Stokes parameters in a random birefringent medium}},
  author = {Said, S. and {Le Bihan}, N.},
  hal = {hal-00276731},
  journal = {{Waves in Random and Complex Media}},
  publisher = {{Taylor \& Francis}},
  volume = {18},
  number = {2},
  pages = {275--292},
  year = {2008},
  doi = {10.1080/17455030701762636},
}

IEEE TSP

Fast Complexified Quaternion Fourier Transform

S. Said, N. Le Bihan, and S. Sangwine

IEEE Transactions on Signal Processing, 2008

DOI arXiv Bib

@article{said2008ieeetsp,
  title = {{Fast Complexified Quaternion Fourier Transform}},
  author = {Said, S. and {Le Bihan}, N. and Sangwine, S.},
  journal = {{IEEE Transactions on Signal Processing}},
  volume = {56},
  number = {4},
  pages = {1522--1531},
  year = {2008},
  doi = {10.1109/TSP.2007.910477},
  hal = {hal-00268009},
}

EUSIPCO

The H-analytic signal

N. Le Bihan, and S. Sangwine

In 16th European Signal Processing Conference (EUSIPCO), 2008

Bib

@inproceedings{lebihan2008eusipco,
  title = {{The H-analytic signal}},
  author = {{Le Bihan}, N. and Sangwine, S.},
  hal = {hal-00337657},
  booktitle = {{16th European Signal Processing Conference (EUSIPCO)}},
  address = {Lausanne, Switzerland},
  pages = {P8-1},
  year = {2008},
}

2007

IEEE TSP

MUSIC Algorithm for Vector-Sensors Array Using Biquaternions

N. Le Bihan, S. Miron, and J.I. Mars

IEEE Transactions on Signal Processing, 2007

DOI Bib

@article{lebihan2007ieeetsp,
  title = {{MUSIC Algorithm for Vector-Sensors Array Using Biquaternions}},
  author = {{Le Bihan}, N. and Miron, S. and Mars, J.I.},
  hal = {hal-00170946},
  journal = {{IEEE Transactions on Signal Processing}},
  publisher = {{Institute of Electrical and Electronics Engineers}},
  volume = {55},
  number = {9},
  pages = {4523--4533},
  year = {2007},
  doi = {10.1109/TSP.2007.896067},
}

AMC
Jacobi method for quaternion matrix singular value decomposition

N. Le Bihan, and S.J. Sangwine

Applied Mathematics and Computation, 2007

Abs DOI Bib

The study of quaternion matrices has gained interest in many areas in recent years, and the problem of diagonalizing such matrices has also attracted attention. In this article, we present an algorithm for computing the SVD of a matrix with quaternion coefficients directly in quaternion arithmetic using a generalization of classical complex Jacobi methods. The extension of the Jacobi transformation to the quaternion case is introduced for the diagonalization of a Hermitian quaternion valued matrix. Based on this, an implicit Jacobi algorithm is proposed for computing the SVD of a quaternion matrix. The performance of the proposed algorithm is presented and compared with an already known algorithm using a complex equivalent of the quaternion matrix, and shown to be superior in execution time and accuracy.
@article{lebihan2007amc, title = {Jacobi method for quaternion matrix singular value decomposition}, journal = {{Applied Mathematics and Computation}}, volume = {187}, number = {2}, pages = {1265--1271}, year = {2007}, issn = {0096-3003}, doi = {10.1016/j.amc.2006.09.055}, author = {{Le Bihan}, N. and Sangwine, S.J.}, hal = {hal-00201795}, }

EUSIPCO

Hypercomplex analytic signals : extension of the analytic signal concept to complex signals

N. Le Bihan, and S. Sangwine

In 15th European Signal Processing Conference (EUSIPCO), 2007

Bib

@inproceedings{lebihan2007eusipco,
  title = {{Hypercomplex analytic signals : extension of the analytic signal concept to complex signals}},
  author = {{Le Bihan}, N. and Sangwine, S.},
  hal = {hal-00170947},
  booktitle = {{15th European Signal Processing Conference (EUSIPCO)}},
  address = {Poznan, Poland},
  pages = {A5P-H-8376},
  year = {2007},
}

EUSIPCO

Exact Principal Geodesic Analysis for Data on SO(3)

S. Said, N. Courty, N. Le Bihan, and 1 more author

In 15th European Signal Processing Conference (EUSIPCO), 2007

Bib

@inproceedings{said2007eusipco,
  title = {{Exact Principal Geodesic Analysis for Data on SO(3)}},
  author = {Said, S. and Courty, N. and {Le Bihan}, N. and Sangwine, S.J.},
  hal = {hal-00494170},
  booktitle = {{15th European Signal Processing Conference (EUSIPCO)}},
  address = {Poznan, Poland},
  pages = {1700--1705},
  year = {2007},
}

PSIP

Neyman-Pearson detection on SU(2): an application to polarized signals

S. Said, N. Le Bihan, and J.H. Manton

In Fifth International Symposium on Physics in Signal and Image Processing (PSIP), 2007

Bib

@inproceedings{said2007psip,
  title = {{Neyman-Pearson detection on SU(2): an application to polarized signals}},
  author = {Said, S. and {Le Bihan}, N. and Manton, J.H.},
  hal = {hal-00138166},
  booktitle = {{Fifth International Symposium on Physics in Signal and Image Processing (PSIP)}},
  address = {Mulhouse, France},
  year = {2007},
}

2006

AMC

Quaternion Singular Value Decomposition based on Bidiagonalization to a Real or Complex Matrix using Quaternion Householder Transformations

S. Sangwine, and N. Le Bihan

Applied Mathematics and Computation, 2006

DOI arXiv Bib

@article{sangwine2006amc,
  title = {{Quaternion Singular Value Decomposition based on Bidiagonalization to a Real or Complex Matrix using Quaternion Householder Transformations}},
  author = {Sangwine, S. and {Le Bihan}, N.},
  hal = {hal-00125823},
  journal = {{Applied Mathematics and Computation}},
  publisher = {{Elsevier}},
  volume = {182},
  number = {1},
  pages = {727--738},
  year = {2006},
  doi = {10.1016/j.amc.2006.04.032},
}

Geophysics

Multicomponent wave separation using HOSVD-Unimodal ICA subspace Method

V. Vrabie, N. Le Bihan, and J.I. Mars

Geophysics, 2006

DOI Bib

@article{vrabie2006geophysics,
  title = {{Multicomponent wave separation using HOSVD-Unimodal ICA subspace Method}},
  author = {Vrabie, V. and {Le Bihan}, N. and Mars, J.I.},
  hal = {hal-00257951},
  journal = {{Geophysics}},
  publisher = {{Society of Exploration Geophysicists}},
  volume = {71},
  number = {5},
  pages = {133--143},
  year = {2006},
  doi = {10.1190/1.2335387},
}

IEEE TSP

Quaternion-MUSIC for vector-sensor array processing

S. Miron, N. Le Bihan, and J.I. Mars

IEEE Transactions on Signal Processing, 2006

DOI Bib

@article{miron2006ieeetsp,
  author = {Miron, S. and {Le Bihan}, N. and Mars, J.I.},
  journal = {IEEE Transactions on Signal Processing},
  title = {{Quaternion-MUSIC for vector-sensor array processing}},
  year = {2006},
  volume = {54},
  number = {4},
  pages = {1218-1229},
  hal = {hal-00067992},
  doi = {10.1109/TSP.2006.870630},
}

IMA Math Sig

Detection and Estimation of Gaussian Proper Quaternion Valued Random Processes

N. Le Bihan, and P.-O. Amblard

In IMA Conference on Mathematics in Signal Processing, 2006

Bib

@inproceedings{lebihan2006ima1,
  title = {{Detection and Estimation of Gaussian Proper Quaternion Valued Random Processes}},
  author = {{Le Bihan}, N. and Amblard, P.-O.},
  hal = {hal-00096539},
  booktitle = {{IMA Conference on Mathematics in Signal Processing}},
  address = {Cirenceister, {UK}},
  year = {2006},
}

IMA Math Sig

Quaternionic independent component analysis using hypercomplex nonlinearities

N. Le Bihan, and S. Buchholz

In IMA Conference on Mathematics in Signal Processing, 2006

Bib PDF

@inproceedings{lebihan2006ima2,
  title = {{Quaternionic independent component analysis using hypercomplex nonlinearities}},
  author = {{Le Bihan}, N. and Buchholz, S.},
  booktitle = {{IMA Conference on Mathematics in Signal Processing}},
  address = {Cirenceister, {UK}},
  year = {2006},
}

IMA Math Sig

Computing the SVD of a quaternion matrix

N. Le Bihan, and S. Sangwine

In IMA Conference on Mathematics in Signal Processing, 2006

Bib

@inproceedings{lebihan2006ima3,
  title = {{Computing the SVD of a quaternion matrix}},
  author = {{Le Bihan}, N. and Sangwine, S.},
  booktitle = {{IMA Conference on Mathematics in Signal Processing}},
  address = {Cirenceister, {UK}},
  year = {2006},
}

EUSIPCO

Optimal separation of polarized signals by quaternionic neural networks

S. Buchholz, and N. Le Bihan

In 14th European Signal Processing Conference (EUSIPCO), 2006

Bib

@inproceedings{buchholz2006eusipco,
  author = {Buchholz, S. and {Le Bihan}, N.},
  booktitle = {14th European Signal Processing Conference (EUSIPCO)},
  title = {Optimal separation of polarized signals by quaternionic neural networks},
  year = {2006},
  volume = {},
  number = {},
  pages = {1-5},
  hal = {hal-00068010},
}

ICASSP

High Resolution Vector-Sensor Array Processing Based on Biquaternions

S. Miron, N. Le Bihan, and J.I. Mars

In IEEE International Conference on Acoustics Speech and Signal Processing Proceedings (ICASSP), 2006

DOI Bib

@inproceedings{miron2006icassp,
  author = {Miron, S. and {Le Bihan}, N. and Mars, J.I.},
  booktitle = {{IEEE International Conference on Acoustics Speech and Signal Processing Proceedings (ICASSP)}},
  title = {High Resolution Vector-Sensor Array Processing Based on Biquaternions},
  year = {2006},
  volume = {4},
  number = {},
  pages = {IV-IV},
  doi = {10.1109/ICASSP.2006.1661159},
}

2005

JASP

Vector-Sensor MUSIC for Polarized Seismic Sources Localization

S. Miron, N. Le Bihan, and J.I. Mars

Eurasip Journal on Applied Signal Processing, 2005

Bib

@article{miron2005eurasipjasp,
  title = {{Vector-Sensor MUSIC for Polarized Seismic Sources Localization}},
  author = {Miron, S. and {Le Bihan}, N. and Mars, J.I.},
  hal = {hal-00257974},
  journal = {{Eurasip Journal on Applied Signal Processing}},
  publisher = {{Hindawi Publishing Corporation}},
  volume = {1},
  pages = {74--84},
  year = {2005},
  doit = {10.1155/ASP.2005.74},
}

GRETSI
Étude des performances du modèle quaternionique en traitement d’antenne vectorielle

S. Miron, N. Le Bihan, and J.I. Mars

In 20ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2005

Abs Bib PDF

Nous analysons dans cette communication les performances du modèle quaternionique pour une onde polarisée captée par une antenne de capteurs vectoriels à deux composantes. La borne du Cramer-Rao est dérivée pour le modèle proposé et une comparaison avec le modèle long-vecteur est réalisée. Nous montrons que l’utilisation des quaternions permet de réduire le temps de calcul et améliore la résolution des algorithmes de type MUSIC.
@inproceedings{miron2005gretsi, author = {Miron, S. and {Le Bihan}, N. and Mars, J.I.}, title = {Étude des performances du modèle quaternionique en traitement d'antenne vectorielle}, booktitle = {{20ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}}, year = {2005}, pages = {77--80}, address = {Louvain, Belgique}, }
GRETSI
Diagonalisation de matrices polynômiales quaternioniques : application à la séparation de mélanges convolutifs d’ondes polarisées

N. Le Bihan

In 20ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2005

Abs Bib PDF

L’utilisation des quaternions et des biquaternions permet une formulation simple et compacte des mélanges convolutifs de signaux polarisés. Une technique de séparation à l’ordre 2 des signaux est alors possible à l’aide d’une étape de diagonalisation d’une matrice polynômiale quaternionique. Nous présentons un algorithme de type Jacobi permettant cette diagonalisation et montrons les avantages de l’approche proprosée vis-à-vis des techniques matricielles classiques de type long-vecteur. Particulièrement, l’approche quaternionique autorise une estimation des paramètres de polarisation plus robuste au bruit que les techniques long-vecteur.
@inproceedings{lebihan2005gretsi, author = {{Le Bihan}, N.}, title = {Diagonalisation de matrices polynômiales quaternioniques : application à la séparation de mélanges convolutifs d'ondes polarisées}, booktitle = {{20ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}}, year = {2005}, pages = {246--249}, address = {Louvain, Belgique}, }

SSP

High resolution vector-sensor array processing using quaternions

S. Miron, N. Le Bihan, and J.I. Mars

In 13th IEEE Workshop on Statistical Signal Processing (SSP), 2005

DOI Bib

@inproceedings{miron2005ssp,
  author = {Miron, S. and {Le Bihan}, N. and Mars, J.I.},
  booktitle = {{13th IEEE Workshop on Statistical Signal Processing (SSP)}},
  title = {High resolution vector-sensor array processing using quaternions},
  year = {2005},
  volume = {},
  number = {},
  address = {Bordeaux, France},
  hal = {hal-00068001},
  pages = {918--923},
  doi = {10.1109/SSP.2005.1628725},
}

PSIP

Improving speckle filtering with SVD to extract ocean parameters from altimeter radar echoes

A. Ollivier, N. Le Bihan, J.-L. Lacoume, and 1 more author

In Fourth International Symposium on Physics in Signal and Image Processing (PSIP), 2005

Bib

@inproceedings{ollivier2005psip,
  title = {{Improving speckle filtering with SVD to extract ocean parameters from altimeter radar echoes}},
  author = {Ollivier, A. and {Le Bihan}, N. and Lacoume, J.-L. and Zanife, O.Z.},
  booktitle = {{Fourth International Symposium on Physics in Signal and Image Processing (PSIP)}},
  address = {Toulouse, France},
  year = {2005},
}

2004

SP
Singular value decomposition of quaternion matrices: a new tool for vector-sensor signal processing

N. Le Bihan, and J.I. Mars

Signal Processing, 2004

Abs DOI Bib

We present a new approach for vector-sensor signal modelling and processing, based on the use of quaternion algebra. We introduce the concept of quaternionic signal and give some primary tools to characterize it. We then study the problem of vector-sensor array signals, and introduce a subspace method for wave separation on such arrays. For this purpose, we expose the extension of the Singular Value Decomposition (SVD) algorithm to the field of quaternions. We discuss in more details Singular Value Decomposition for matrices of Quaternions (SVDQ) and linear algebra over quaternions field. The SVDQ allows to calculate the best rank-α approximation of a quaternion matrix and can be used in subspace method for wave separation over vector-sensor array. As the SVDQ takes into account the relationship between components, we show that SVDQ is more efficient than classical SVD in polarized wave separation problem.
@article{lebihan2004sp1, title = {Singular value decomposition of quaternion matrices: a new tool for vector-sensor signal processing}, journal = {Signal Processing}, volume = {84}, number = {7}, pages = {1177-1199}, year = {2004}, issn = {0165-1684}, doi = {10.1016/j.sigpro.2004.04.001}, hal = {hal-00257964}, author = {{Le Bihan}, N. and Mars, J.I.}, }
SP
Three-mode data set analysis using higher order subspace method: application to sonar and seismo-acoustic signal processing

N. Le Bihan, and G. Ginolhac

Signal Processing, 2004

Abs DOI Bib

In this paper, a three-mode subspace technique based on higher order singular value decomposition (HOSVD) is presented. This technique is then used in the context of wave separation. It can be regarded as the extension to three-mode arrays of the well-known subspace technique proposed by Eckart and Young (Psychometrica 1 (1936) 211) for matrices. Three-mode data sets are increasingly encountered in signal processing and are classically processed using matrix algebra techniques. The proposed approach aims to process naturally three-mode data with multilinear algebra tools. So in the proposed algorithms, the structure of the data set is preserved and no reorganization is performed on it. The choice of HOSVD for subspace method is explained, studying the rank definition for three-mode arrays and orthogonality between subspaces. A projector formulation for three-mode signal and noise subspaces is also given and the improvement of separation with the three-mode approach over a componentwise approach is shown. We study two applications for the proposed Higher Order Subspace approach: the reverberation problem in sonar, and the polarized seismo-acoustic wave separation problem. For the first application, we propose a three-mode version of the Principal Component Inverse algorithm (IEEE Trans. Aerospace Electron. Systems 30(1) (1994) 55). We apply the proposed technique on simulated data as well as on real sonar data where the three modes are angle, delay and distance. For the second application, we consider the polarization of the seismic wave as the third mode (in addition to time and distance modes) and show the resulting improvement of wave separation using the proposed Higher Order approach.
@article{lebihan2004sp2, title = {Three-mode data set analysis using higher order subspace method: application to sonar and seismo-acoustic signal processing}, journal = {Signal Processing}, volume = {84}, number = {5}, pages = {919--942}, year = {2004}, issn = {0165-1684}, doi = {10.1016/j.sigpro.2004.02.003}, author = {{Le Bihan}, N. and Ginolhac, G.}, }

IMA Math Sig

On properness of quaternion valued random variables

P.-O. Amblard, and N. Le Bihan

In 6th IMA Conference on Mathemathics in Signal Processing, 2004

Bib

@inproceedings{Lebihan_04e,
  author = {Amblard, P.-O. and {Le Bihan}, N.},
  title = {On properness of quaternion valued random variables},
  booktitle = {6th IMA Conference on Mathemathics in Signal Processing},
  year = {2004},
  address = {Cirenceister, United Kingdom},
}

EUSIPCO

Polarized source characterization using vector-music

S. Miron, N. Le Bihan, and J.I. Mars

In 12th European Signal Processing Conference (EUSIPCO), 2004

Bib PDF

@inproceedings{miron2004eusipco,
  author = {Miron, S. and {Le Bihan}, N. and Mars, J.I.},
  booktitle = {12th European Signal Processing Conference (EUSIPCO)},
  title = {Polarized source characterization using vector-music},
  year = {2004},
  address = {Vienna, Austria},
  volume = {},
  number = {},
  pages = {421--424},
}

EAGE

Joint estimation of direction of arrival and polarization parameters for multicomponent sensor array

S. Miron, N. Le Bihan, and J.I. Mars

In 66th Conference of the EAGE, 2004

Bib

@inproceedings{miron2004eage,
  author = {Miron, S. and {Le Bihan}, N. and Mars, J.I.},
  booktitle = {66th Conference of the EAGE},
  title = {Joint estimation of direction of arrival and polarization parameters for multicomponent sensor array},
  year = {2004},
  volume = {},
  number = {},
  pages = {},
  address = {Paris, France},
}

2003

GRETSI
Utilisation de la Transformée de Fourier Quaternionique en tatouage d’images couleur

P. Bas, N. Le Bihan, and J.-M. Chassery

In 19ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2003

Abs Bib PDF

Ce travail présente une méthode de tatouage utilisant d’une part un espace de représentation adapté aux images couleur par la transformée de Fourier quaternionique, d’autre part une approche psychovisuelle fondée sur les espaces couleur uniformes. Les quaternions sont des nombres possédant une partie réelle et trois parties imaginaires et peuvent naturellement être utilisés pour représenter des pixels couleur. Nous utilisons une décomposition fréquentielle, la transformée de Fourier quaternionique (TFQ), pour isoler un espace propre à l’insertion d’un tatouage. La TFQ dépendant d’un quaternion pur μ, nous utilisons ce degré de liberté afin d’obtenir un espace de décomposition optimal au sens perceptif. Le choix de μ dans l’espace RGB est obtenu par calcul différentiel sur les espaces perceptifs uniformes Lab et Luv. L’information est ensuite insérée dans l’image couleur par une méthode de quantification. Enfin les résultats offerts par cette méthode montrent qu’elle permet d’obtenir un compromis invisibilité/robustesse important pour des traitements affectant la luminance de l’image.
@inproceedings{bas2003gretsi, author = {Bas, P. and {Le Bihan}, N. and Chassery, J.-M.}, title = {Utilisation de la Transformée de Fourier Quaternionique en tatouage d'images couleur}, booktitle = {{19ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}}, year = {2003}, pages = {1061--1064}, address = {Paris, France}, }
GRETSI
Extensions de la SVD aux données multidimensionnelles : Application à la séparation de sources

J.I. Mars, N. Le Bihan, and V. Vrabie

In 19ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2003

Abs Bib PDF

Dans de nombreux domaines d’application on utilise des données multidimensionnelles (cube de données, enregistrements multicomposantes), mais peu d’outils de séparation de sources prennent en compte la multidimensionnalité de ces données. A partir du filtrage SVD (méthode reconnue en séparation de sources), nous présentons quelques extensions de cette technique prenant en compte cet aspect multidimensionnel. Une extension présentée combine la SVD et l’ICA et permet d’améliorer la séparation de sources en proposant une contrainte d’orthogonalité moins forte sur les vecteurs de propagation. Une deuxième extension concerne la définition d’une méthode de filtrage purement multidimensionnelle; la 3D SVD et la SVD Quatemionique. Des illustrations synthétiques et réelles sont présentées.
@inproceedings{mars2003gretsi, author = {Mars, J.I. and {Le Bihan}, N. and Vrabie, V.}, title = {Extensions de la SVD aux données multidimensionnelles : Application à la séparation de sources}, booktitle = {{19ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}}, year = {2003}, pages = {320-323}, address = {Paris, France}, }

ICIP

Quaternion principal component analysis of color images

N. Le Bihan, and S.J. Sangwine

In IEEE International Conference on Image Processing (ICIP), 2003

DOI Bib

@inproceedings{lebihan2003icip,
  author = {{Le Bihan}, N. and Sangwine, S.J.},
  booktitle = {{IEEE International Conference on Image Processing (ICIP)}},
  title = {Quaternion principal component analysis of color images},
  year = {2003},
  volume = {1},
  number = {},
  address = {Barcelona, Spain},
  pages = {I-809},
  doi = {10.1109/ICIP.2003.1247085},
}

VIE

Color image decomposition using quaternion singular value decomposition

N. Le Bihan, and S.J. Sangwine

In International Conference on Visual Information Engineering (VIE), 2003

DOI Bib

@inproceedings{lebihan2003vie,
  author = {{Le Bihan}, N. and Sangwine, S.J.},
  booktitle = {{International Conference on Visual Information Engineering (VIE)}},
  title = {Color image decomposition using quaternion singular value decomposition},
  year = {2003},
  volume = {},
  number = {},
  pages = {113-116},
  doi = {10.1049/cp:20030500},
}

ICASSP

Color Image Watermarking Using Quaternion Fourier Transform

P. Bas, N. Le Bihan, and J.-M. Chassery

In IEEE International Conference on Acoustics Speech and Signal Processing Proceedings (ICASSP), 2003

DOI Bib

@inproceedings{bas2003icassp,
  title = {{Color Image Watermarking Using Quaternion Fourier Transform}},
  author = {Bas, P. and {Le Bihan}, N. and Chassery, J.-M.},
  hal = {hal-00166555},
  booktitle = {{IEEE International Conference on Acoustics Speech and Signal Processing Proceedings (ICASSP)}},
  address = {Hong Kong, China},
  year = {2003},
  doi = {10.1109/ICASSP.2003.1199526},
}

PSIP

Multidimensional signal processing using quaternion

S. Miron, M. Guillon, N. Le Bihan, and 1 more author

In Third International Symposium on Physics in Signal and Image Processing (PSIP), 2003

Bib

@inproceedings{miron2003psip,
  title = {{Multidimensional signal processing using quaternion}},
  author = {Miron, S. and Guillon, M. and {Le Bihan}, N. and Mars, J.},
  booktitle = {{Third International Symposium on Physics in Signal and Image Processing (PSIP)}},
  address = {Grenoble, France},
  year = {2003},
}

EAGE

Multidimensional SVD processing: an overview

J.I. Mars, J.-L. Mari, F. Glangeaud, and 2 more authors

In First north african meeting of the EAGE, 2003

Bib

@inproceedings{mars2005eage,
  title = {{Multidimensional SVD processing: an overview}},
  author = {Mars, J.I. and Mari, J.-L. and Glangeaud, F. and {Le Bihan}, N. and Vrabie, V.},
  booktitle = {{First north african meeting of the EAGE}},
  address = {Tunis, Tunisia},
  year = {2003},
}

2002

EUSIPCO

Quaternion subspace method for vector-sensor wave separation

N. Le Bihan, and J. Mars

In 11th European Signal Processing Conference (EUSIPCO), 2002

DOI Bib

@inproceedings{lebihan2022eusipco,
  author = {{Le Bihan}, N. and Mars, J.},
  booktitle = {{11th European Signal Processing Conference (EUSIPCO)}},
  title = {Quaternion subspace method for vector-sensor wave separation},
  year = {2002},
  volume = {},
  number = {},
  pages = {1--4},
  doi = {},
}

EAGE

Noise rejection by multicomponent SVD-Wiener filters

In 64th Conference of the EAGE, 2002

DOI Bib

@inproceedings{lebihan2002eage,
  author = {},
  title = {Noise rejection by multicomponent SVD-Wiener filters},
  booktitle = {64th Conference of the EAGE},
  address = {Florence, Italy},
  year = {2002},
  doi = {10.3997/2214-4609-pdb.5.P017},
}

2001

SEG

New 2D attributes based on complex and hypercomplex analytic signal

N. Le Bihan, and J.I. Mars

In SEG Technical Program Expanded Abstracts, 2001

DOI Bib

@inproceedings{lebihan2001seg1,
  author = {{Le Bihan}, N. and Mars, J.I.},
  title = {New 2D attributes based on complex and hypercomplex analytic signal},
  booktitle = {SEG Technical Program Expanded Abstracts},
  pages = {1961--1964},
  year = {2001},
  doi = {10.1190/1.1816522},
}

SEG

Seismic cube decomposition before reservoir characterization

N. Le Bihan, S. Lariani, and J.I. Mars

In SEG Technical Program Expanded Abstracts, 2001

DOI Bib

@inproceedings{lebihan2001seg2,
  author = {{Le Bihan}, N. and Lariani, S. and Mars, J.I.},
  title = {Seismic cube decomposition before reservoir characterization},
  booktitle = {SEG Technical Program Expanded Abstracts},
  pages = {1961--1964},
  year = {2001},
  doi = {10.1190/1.1816409},
}

GRETSI
Séparation d’ondes sur un réseau de capteurs multidimensionnel

N. Le Bihan, J.-L. Lacoume, and J.I. Mars

In 18ème Colloque Francophone de Traitement du Signal et des Images (GRETSI), 2001

Abs Bib PDF

Nous proposons une nouvelle méthode de séparation d’ondes pour les réseaux de capteurs multidimensionnels basée sur l’Analyse en composantes Principales (ACP) pour données tridimensionnelles. Nous présentons la 3DSVD, extension de la SVD au cas des volumes de données 3D. Nous montrons également l’intérêt d’utiliser cette méthode plutôt que celle utilisant les long-vecteurs. Nous comparons finalement, sur données réelles, les résultats obtenus par notre approche d’ACP trimodal à ceux obtenus par ACP classique.
@inproceedings{lebihan2001gretsi, author = {{Le Bihan}, N. and Lacoume, J.-L. and Mars, J.I.}, title = {Séparation d'ondes sur un réseau de capteurs multidimensionnel}, booktitle = {{18ème Colloque Francophone de Traitement du Signal et des Images (GRETSI)}}, year = {2001}, pages = {497--500}, address = {Toulouse, France}, }

PSIP

Subspace methods on 3D array

N. Le Bihan, and G. Ginolhac

In Second International Symposium on Physics in Signal and Image Processing (PSIP), 2001

Bib

@inproceedings{lebihan2001psip,
  title = {{Subspace methods on 3D array}},
  author = {{Le Bihan}, N. and Ginolhac, G.},
  booktitle = {{Second International Symposium on Physics in Signal and Image Processing (PSIP)}},
  address = {Marseille, France},
  year = {2001},
}

2000

ASM

Techinque d’algèbre multilinéaire pour le traitement sismique multicomposantes

N. Le Bihan, and J.I. Mars

In 5èmes journées d’acoustique sous-marine (ASM),, 2000

Bib

@inproceedings{lebihan2000Aasm,
  title = {{Techinque d'algèbre multilinéaire pour le traitement sismique multicomposantes}},
  author = {{Le Bihan}, N. and Mars, J.I.},
  booktitle = {{5èmes journées d'acoustique sous-marine (ASM),}},
  address = {Brest, France},
  year = {2000},
}

1999

ASM

Traitement des ondes sismo-acoustiques UBF multicomposantes

N. Le Bihan, J.-L. Lacoume, F. Glangeaud, and 1 more author

In 4èmes journées d’acoustique sous-marine (ASM),, 1999

Bib

@inproceedings{lebihan1999Aasm,
  title = {{Traitement des ondes sismo-acoustiques UBF multicomposantes}},
  author = {{Le Bihan}, N. and Lacoume, J.-L. and Glangeaud, F. and Gaffet, S.},
  booktitle = {{4èmes journées d'acoustique sous-marine (ASM),}},
  address = {Brest, France},
  year = {1999},
}