### Publications

### Books

[1] "Quaternion Fourier transforms for signal and image processing",

T.A. Ell, N. Le Bihan and S.J. Sangwine, ISTE-Wiley, FOCUS Series, May 2014, (ISBN 978-1-84821-478-1)

### Submitted papers

[1] "Spectral analysis of stationary random bivariate signals",

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

Submitted to IEEE Transactions on Signal Processing, Mar. 2017. (ArXiV version)

[2] "Time-frequency analysis of bivariate signals",

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

Submitted to Applied and Computational Harmonic Analysis, Sept. 2016. (ArXiV version)

[3] "SALZA: Soft algorithmic complexity estimates for clustering and causality inference",

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

Submitted to IEEE Transactions on Information Theory, Jul. 2016. (ArXiV version)

### Journal Papers

[29] " The geometry of proper quaternion random variables",

N. Le Bihan

to appear in Signal Processing, . (ArXiV version)

[28] "Density Estimation on the rotation group using Diffusive wavelets",

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

to appear in ISIF Journal of Advances in Information Fusion, 2016. (ArXiV version)

[27] "Isotropic multiple scattering processes on hyperspheres",

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

IEEE Transactions on Information Theory , Vol. 62, Issue 10, pp. 5740-5752, 2016. (ArXiV version)

[26] "Analysis of seismic waves crossing the Santa Clara Valley using the three-component MUSIQUE array algorithm",

M. Hobiger, C. Cornou, P.-Y. Bard, N. Le Bihan and W. Imperaton

Geophysical Journal International, doi: 10.1093/gji/ggw289, 2016.

[25] " Expansion-Maximization-Compression algorithm with spherical harmonics for single particle imaging with X-ray lasers",

J. Flamant, N. Le Bihan, A.V. Martin and J.H. Manton

Physical Review E, 93 (5), 053302, 2016. (ArXiV version)

[24] "Filtering from Observations on Stiefel Manifolds",

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

Signal Processing, Vol. 122, pp. 52-64, 2016. (ArXiV version)

[23] "Instantaneous frequency and amplitude of orthocomplex modulated signals based on quaternion Fourier transform",

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

Signal Processing, Vol. 94, pp. 308-318, 2014. (Online version)

[22] "Stochastic description of geometric phase for polarized waves in random media",

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

J. Phys. A: Math. Theor. 46, 035203, 2013. (ArXiv version)

[21] "Ground structure imaging by inversions of Rayleigh wave ellipticity:
sensitivity analysis and application to European stron-motion sites",

M. Hobiger, C. Cornou, M. Wathelet, G. Di Giulio, B. Knapmeyer-Endrun, F. Renalier, P.-Y. Bard, A. Savvaidis, S. Hailemikael, N. Le Bihan, M. Ohrnberger and N. Theodoulidis

Geophysical Journal International, doi: 10.1093/gji/ggs005, 2012.

[20] "Geodesic normal distribution on the circle",

J.F. Coeurjolly and N. Le Bihan,

Metrika, 75(7), pp. 977-995, 2012. (ArXiV version).

[19] "Multicomponent Signal Processing for Rayleigh Wave Ellipticity Estimation: Application to Seismic Hazard Assessment",

M. Hobiger, N. Le Bihan, C. Cornou and P.Y. Bard,

IEEE Signal Processing magazine, Volume 29, Issue 3, pp. 29-39, 2012.

[18] "Observation of a non-adiabatic geometric phase for elastic waves",

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

Annals of Physics, Volume 327, Issue 3, Pages 952-958, March 2012. (ArXiV version).

[17] "Fundamental representations and algebraic properties of biquaternions or complexified quaternions",

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

Advances in Applied Clifford Algebras, Volume 21, Issue 3, pp. 697-636, 2011. (ArXiV version)

[16] "Decompounding on compact Lie groups",

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

IEEE Transactions on Information Theory, Vol. 56, Issue 6, pp. 2766-2777, 2010. (ArXiV version)

(doi:10.1109/TIT.2010.2046216)

[15] "Quaternion polynomial matrix diagonalization for the separation of polarized convolutive mixture",

G.M. Menanno and N. Le Bihan,

Signal Processing, Vol. 90, Issue 7, pp. 1229-1337, 2010.

(doi:10.1016/j.sigpro.2010.02.003)

[14] "Quaternion Polar Representation with a Complex Modulus and Complex Argument Inspired by the Cayley-Dickson Form",

S.J. Sangwine and N. Le Bihan,

Advances in Applied Clifford Algebras, Vol. 36, No 1, pp. 111-120, 2010. (ArXiV version)

(doi:10.1007/s00006-008-0128-1)

[13] "Single Station Determination of Rayleigh Wave Ellipticity by Using the Random Decrement Technique (RayDec)",

M. Hobiger, P.-Y. Bard, C. Cornou and N. Le Bihan,

Geophysical Research Letters, 36, L14303, 2009.

(doi:10.1029/2009GL038863)

[12] "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, 80, 016601, 2009. (ArXiV version)

(doi:10.1103/PhysRevE.80.016601)

[11]"Polarized Signal Classification by Complex and Quaternionic MLPs",

S. Buchholz and N. Le Bihan,

International Journal of Neural Systems, Volume 18, No. 2, pp. 75-85, 2008.

[10]"Higher Order Statistics of Stokes Parameters in a Random Birefringent Medium",

S. Said and N. Le Bihan,

Waves in Random and Complex Media, Volume 18, No. 2, pp. 275-292, 2008. (ArXiV version)

(doi:10.1080/17455030701762636)

[9] "Fast complexified quaternion Fourier transform",

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

IEEE Transactions on Signal Processing, Volume 56, No. 4, pp 1522-1531, 2008. (ArXiV version)

(doi:10.1109/TSP.2007.910477)

[8] "MUSIC algorithm for vector-sensors array using biquaternions",

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

IEEE Transactions on Signal Processing, Volume 55, No. 9, pp. 4523-4533, 2007.

(doi:10.1109/TSP.2007.896067)

[7] "Jacobi Method For Quaternion Matrix Singular Value Decomposition",

N. Le Bihan and S.J. Sangwine,

Applied Mathematics and Computation, Volume 187, Issue 2, pp. 1265-1271, 2007.

(doi: 10.1016/j.amc.2006.09.055)

[6] "Quaternion Singular Value Decomposition based on Bidiagonalization to a Real or Complex Matrix using Quaternion Householder Transformations",

S.J. Sangwine and N. Le Bihan,

Applied Mathematics and Computation, Volume 182, Issue 1, pp. 727-738, 2006. (ArXiV version)

(doi:10.1016/j.amc.2006.04.032)

[5] "Multicomponent wave separation using HOSVD - unimodal ICA subspace method",

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

Geophysics, Volume 71, Issue 5, pp. V133-V143, 2006.

(doi: 10.1190/1.2335387)

[4] "Quaternion-MUSIC for vector-sensor array processing",

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

IEEE Transactions on Signal Processing, Volume 54, No. 4, 1218 - 1229, 2006.

(doi: 10.1109/TSP.2006.870630)

[3] "Vector-MUSIC for Polarized Seismic Source Localisation",

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

EURASIP Journal on Applied Signal Processing, Volume 2005, Issue 1, pp. 74-84, 2005.

[2] "Singular Value Decomposition of Matrices of Quaternions: A New Tool for Vector-Sensor Signal Processing",

N. Le Bihan and J. Mars,

Signal Processing, Vol. 84, Issue 7, pp. 1177-1199, 2004.

(doi: 10.1016/j.sigpro.2004.04.001)

[1]"Three-Mode Dataset Analysis Using Higher Order Subspace Method: Application to Sonar and Seismo-acoustic Signal Processing",

N. Le Bihan and G. Ginolhac,

Signal Processing, Vol. 84, Issue 5, pp. 919-942, 2004.

(doi:10.1016/j.sigpro.2004.02.003)

### Chapters in Books

[3] "Quaternionic spectral analysis of non-stationnary improper complex signals",

N. Le Bihan and S.J. Sangwine,

In Quaternion and Clifford Fourier transforms and wavelets, edited
by E. Hitzer and S.J. Sangwine, Trends in mathematics (TIM), Birkhauser, Basel, 2013.

[2] "Hypercomplex models and processing for vector images",

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

In Multivariate Image Processing, edited by J. Chanussot, C. Collet and K. Chehdi, John Wiley Sons, 2010.

[1] "Multidimensional seismic data decomposition by higher order SVD and unimodal-ICA",

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

In Signal and Image Processing for remote sensing, edited by C.H. Chen, CRC Press (Taylor and Francis books), 2006.

### Conference papers

[55] "Polarization spectrogram of bivariate signals",

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

IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), New-Orleans, USA, March 2017.

[54] "Low-Resolution reconstruction of intensity functions on the sphere for single-particle diffraction imaging",

J. Flamant, N. Le Bihan, A.V. Martin and J.H. Manton,

IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shangai, China, March 2016.

[53] "C. Elegans locomotion analysis using algorithmic information theory",

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

International Conference of the IEEE Engineering in Medecine and Biology Society (EMB), Milano, Italy, August 2015.

[52] "Parameter estimation for multiple scattering process on the sphere",

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

IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brisbane, Australia, April 2015.

[51] "Monte-Carlo estimation from observation on Stiefel manifold",

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

IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Florence, Italy, May 2014.

[50] "Von Mises-Fisher approximation of multiple scattering process on the hypersphere",

F. Chatelain, and N. Le Bihan,

IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vancouver, Canada, May 2013.

[49] "Wiener filtering of rotation processes using ordered exponentials",

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

IEEE International workshop on statistical signal processing (SSP), Ann Arbor, USA, August 2012.

[48] "Quaternion Wigner-Ville distribution",

N. Le Bihan and T.A. Ell,

Applied geometric algebras in computer science and engineering (AGACSE), La Rochelle, France, July 2012.

[47} "Quaternionic spectral analysis of non-stationary improper complex signals",

N. Le Bihan and S.J. Sangwine,

International Conference on Clifford algebras and Applications (ICCAA), Weimar, Germany, July 2011.

[46] "Phase géométrique des signaux polarisés en milieux aléatoires ",

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

Colloque GRETSI, Bordeaux, France, September 2011.

[45] "MUSIQUE: A Quaternion-Based Array Processing Technique for Surface Wave Polarization Analysis",

M. Hobiger, N. Le Bihan, C. Cornou and P.-Y. Bard,

IEEE International Workshop on Statistical Signal Processing (SSP), Nice, France, June 2011.

[44] "Blind extraction of improper quaternion sources",

S. Javidi, C. Cheong Took, C. Jahanchahi, N. Le Bihan and D. Mandic,

IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic, May 2011.

[43] "Inférence statistique sur la fonction de phase des milieux aléatoires par diffusion multiple des ondes",

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

Colloque GRETSI, Dijon, France, September 2009.

[42] " Rayleigh wave ellipticity estimation from ambient seismic noise using single and multiple vector-sensor techniques",

M. Hobiger, N. Le Bihan, C. Cornou and P.-Y. Bard,

XVII European Signal Processing Conference (EUSIPCO), Glasgow, Scotland, August 2009.

[41] "A stability approach to the analysis of rotation time series",

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

15th IFAC Symposium on systems identification, Saint-Malo, France, July 2009.

[40] "Nonparametric estimation for compound Poisson processes on compact Lie groups",

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

IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Taipei, Taiwan, April 2009.

[39] "About the extension of the 1D analytic signal to improper complex valued signals",

N. Le Bihan and S.J. Sangwine,

8th IMA Conference on Mathematics in Signal Processing, Cirencester, UK, December 2008.

[38] "A functional approach to signal processing under nonlinear constraints",

S. Said and N. Le Bihan,

8th IMA Conference on Mathematics in Signal Processing, Cirencester, UK, December 2008.

[37] "Decompounding on compact Lie groups",

S. Said, C. Lageman, N. Le Bihan, L. Margerin and J.H. Manton,

8th IMA Conference on Mathematics in Signal Processing, Cirencester, UK, December 2008.

[36] "The H-analytic signal",

N. Le Bihan and S.J. Sangwine,

XVI European Signal Processing Conference (EUSIPCO), Lausanne, Switzerland, August 2008.

[35] "Hypercomplex analytic signals: extension of the analytic signal concept to complex signals",

S.J. Sangwine and N. Le Bihan,

XV European Signal Processing Conference (EUSIPCO), Poznan, Poland, September 2007.

[34] "Exact principal geodesic analysis for data on SO(3)",

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

XV European Signal Processing Conference (EUSIPCO), Poznan, Poland, September 2007.

[33] "Neyman-Pearson detection on SU(2): an application to polarized signals",

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

Workshop on Physics in Signal and Image Processing (PSIP), Mulhouse, France, January 2007.

[32] "Detection and estimation of Gaussian proper quaternion valued random processes",

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

7th IMA Conference on Mathematics in Signal Processing, Cirencester, UK, December 2006.

[31] "Quaternionic independent component analysis using hypercomplex nonlinearities",

N. Le Bihan and S. Buchholz,

7th IMA Conference on Mathematics in Signal Processing, Cirencester, UK, December 2006.

[30] "Computing the SVD of a quaternion matrix",

S.J. Sangwine and N. Le Bihan,

7th IMA Conference on Mathematics in Signal Processing, Cirencester, UK, December 2006.

[29] "Optimal separation of polarized signals by quaternionic neural networks",

S. Buchholz and N. Le Bihan,

XIV European Signal Processing Conference (EUSIPCO), Florence, Italy, September 2006.

[28] "High resolution vector-sensor array processing based on biquaternions",

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

IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Toulouse, France, May 2006.

[27] "Diagonalisation de matrices polynomiales quaternioniques : application à la séparation de mélanges convolutifs d'ondes polarisées",

N. Le Bihan,

Colloque GRETSI, Louvain-La-Neuve, Belgium, September 2005.

[26] "Etude des performances du modèle quaternionique en traitement d'antenne vectorielle",

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

Colloque GRETSI, Louvain-La-Neuve, Belgium, September 2005.

[25] "High resolution vector-sensor array processing using quaternions",

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

IEEE Workshop on Statistical Signal Processing (SSP), Bordeaux, France, July 2005.

[24] "Improving speckle filtering with SVD to extract ocean parameters from altimeter radar echoes",

A. Ollivier, N. Le Bihan, J.-L. Lacoume and O.Z. Zanife,

Workshop on Physics in Signal and Image Processing (PSIP), Toulouse, France, January 2005.

[23] "On properness of quaternion valued random variables",

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

6th IMA Conference on Mathematics in Signal Processing Conference, Cirencester, UK, December 2004.

[22] "Polarized source characterization using vector-MUSIC",

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

XII European Signal Processing Conference (EUSIPCO), Vienna, Austria, September 2004.

[21] "Joint estimation of direction of arrival and polarization parameters for multicomponent sensor array",

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

66th Conference of the EAGE, Paris, France, June 2004.

[20] "Utilisation de la transformée de Fourier quaternionique en tatouage d'images couleur",

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

Colloque GRETSI, Paris, France, September 2003.

[19] "Analyse de signaux vectoriels basée sur le modèle quaternionique",

N. Le Bihan and S.J. Sangwine,

Colloque GRETSI, Paris, France, September 2003.

[18] "Extension de la SVD aux données multidimensionnelles, Application à la séparation de sources",

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

Colloque GRETSI, Paris, France, September 2003.

[17] "Quaternion principal component analysis of color images",

N. Le Bihan and S.J. Sangwine,

IEEE International Conference on Image Processing (ICIP), Barcelona, Spain, September 2003.

[16] "Color image decomposition using quaternion singular value decomposition",

N. Le Bihan and S.J. Sangwine,

IEE International Conference on Visual Information Engineering (VIE), Guildford, UK, July 2003.

[15] "Color watermarking using quaternion Fourier transform",

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

IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Hong-Kong, June 2003.

[14] "Multidimensional signal processing using quaternions",

S. Miron, M. Guillon, N. Le Bihan and J. Mars,

Workshop on Physics in Signal and Image Processing (PSIP), Grenoble, France, January 2003.

[13] "Multidimensional SVD processing: an overview",

J.I. Mars, J.-L. Mari, F. Glangeaud, N. Le Bihan and V. Vrabie,

1st Norht African Meeting of the EAGE, Tunis, Tunisie, October 2003.

[12] "3D-SVD and partial ICA for 3D array sensor",

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

72nd Conference of the Society of Exploration Geophysicists (SEG), Salt Lake City, USA, October 2002.

[11] "Subspace method for vector-sensor wave separation based on quaternion algebra",

N. Le Bihan and J. Mars,

XI European Signal Processing Conference (EUSIPCO), Toulouse, France, September 2002.

[10] "Noise rejection by multicomponent SVD-Wiener filters",

N. Le Bihan, F. Glangeaud, J. Mars, J.-L. Mari and J. Meunier,

64th Conference of the EAGE, Florence, Italy, May 2002.

[9] "New 2D complex and hypercomplex seismic attributes",

N. Le Bihan and J.I. Mars,

71st Conference of the Society of Exploration Geophysicists (SEG), San Antonio, USA, September 2001.

[8] "Seismic cube decomposition before reservoir characterization",

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

71st Conference of the Society of Exploration Geophysicists (SEG), San Antonio, USA, September 2001.

[7] "Séparation d'ondes sur un réseau de capteurs multidimensionnel",

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

Colloque GRETSI, Toulouse, France, September 2001.

[6] "Subspace methods on 3D array",

N. Le Bihan and G. Ginolhac,

Workshop on Physics in Signal and Image Processing (PSIP), Marseille, France, January 2001.

[5] "Techinque d'algèbre multilinéaire pour le traitement sismique multicomposantes",

N. Le Bihan and J.I. Mars,

5èmes journées d'acoustique sous-marine (ASM), Brest, France, December 2000.

[4] "Blind wave separation using vector-sensors",

N. Le Bihan and J.I. Mars,

IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Istanbul, Turquey, June 2000.

[3] "Wavefield separation on multicomponent sensors",

N. Le Bihan, J.I. Mars and H. Pedersen,

62nd Conference of the EAGE, Glasgow, Scotland, Expanded-Abstract L-03, June 2000.

[2] "Complex seismic signal and blind wave separation",

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

61st Conference of the EAGE, Helsinki, Finland, Expanded-Abstract 6-22, June 1999.

[1] "Traitement des ondes sismo-acoustiques UBF multicomposantes",

N. Le Bihan, J.-L. Lacoume, F. Glangeaud and S. Gaffet,

4èmes journées d'acoustique sous-marine, Brest, France, December 1998.

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