Temics: Jean-jacques Fuchs

My current research interests are in array processing, sparse representations, joint detection and estimation schemes and robust detection.

I am working on sparse representations for more than ten years though this domain has only been identified as such recently. At the beginning I considered it as a new and say computer-intensive way to solve identification or estimation problems, i.e., I always assumed that there exists indeed an exact sparse underlying representation and that the aim was to recover it.

All this started when I realized that the Pisarenko method which is actually based on a theorem by Caratheodory on the trigonometric moment problem (compute the minimal eigenvector of a covariance matrix, root the polynomial associated with this vector, the information lies in the roots that are on the unit circle, ..) can indeed be seen as what is now known as 'basis pursuit': \min_x subject to Ax=b, x >=0.

Teaching

Some recent publications

	J. J. Fuchs and S. Maria A new approach to variable selection using the TLS approach IEEE Trans. on Signal Processing, vol. 55, no. 1, pp. 10—19, January, 2007.
	J. J. Fuchs A robust matched detector IEEE Trans. on Signal Processing, vol. 55, no. 11, pp. 5133—5142, November, 2007.
	J. J. Fuchs Convergence of a sparse representations algorithm applicable to real or complex data IEEE Journal on Selected Topics in Signal Processing, Special issue on Convex Optimization Methods in Signal Processing, vol. 1, no. 4, pp. 598—605, December, 2007.
	A. Drémeau , C. Herzet , C. Guillemot and J.-J. Fuchs Sparse Optimization with Directional DCT Bases for Image Compression Proc. IEEE Int'l Conf. on Acoustics, Speech and Signal Processing (ICASSP), pp. 1290-1293, Dallas, March, 2010.
	A. Drémeau , C. Herzet , C. Guillemot and J.-J. Fuchs Anisotropic Multi-scale Sparse Learned Bases for Image Compression Proc. IS&T/SPIE Electronic Imaging, vol. 7543, San Jose, January, 2010.
	A. Drémeau , M. Turkan, C. Herzet , C. Guillemot and J.-J. Fuchs Spatial intra-prediction based on mixtures of sparse representations Proc. IEEE Int. Workshop on Multimedia Signal Process. (MMSP), Saint-Malo, France, October, 2010.
	J. J. Fuchs Fast implementation of a $\ell_1-\ell_1$ regularized sparse representation algorithm. Proc.of ICASSP, IEEE Int. Conference on Acoustics, Speech and Signal Processing, pp. 3329-3332, Taipei, April, 2009.
	J. J. Fuchs Identification of real sinusoids in noise, the Global Matched Filter approach. 14th Ifac-Ifors symposium on Identification and system Parameter Estimation, pp. 1127—1132, Saint-Malo, France, July, 2009.
	A. Martin , J-J Fuchs , C. Guillemot and D. Thoreau Atomic decomposition dedicated to AVC and spatial SVC prediction ICIP08 15th IEEE International Conference on Image Processing, 2008.
	G. Rath , C. Guillemot , J-J. Fuchs Sparse approximations for joint source-channel coding and its application to image transmission IEEE Intl. Workshop on Multimedia Signal Processing, IEEE-MMSP, October, 2008.
	J. J. Fuchs On the use of the Global Matched Filter for DOA estimation in the presence of correlated waveforms. 41st Asilomar Conference on Signals, Systems and Computers, pp. 269—273, Pacific Grove, California, November, 2008.
	J. J. Fuchs On the use of sparse representations in the identification of line spectra 17th World Congress IFAC, pp. 10225—10229, Seoul,, July, 2008.
	J. J. Fuchs A sparse representation criterion: recovery conditions and implementation issues 17th World Congress IFAC, pp. 12425—12429, Seoul,, July, 2008.
	A. Martin and J-J Fuchs and C. Guillemot and D. Thoreau Sparse Representation for Image Prediction EUSIPCO, 15th European Signal Processing Conference, Poznan, Poland, September, 2007.
	J. J. Fuchs Matched detector and estimator with signature uncertainty 40st Asilomar Conference on Signals, Systems and Computers, pp. 2177-2181, Pacific Grove, California, November, 2007.
	J. J. Fuchs and C. Guillemot Fast implementation of $\ell_\infty-\ell_1$ penalized sparse represenations algorithm : applications in image denoising and coding 40st Asilomar Conference on Signals, Systems and Computers, pp. 508-512, Pacific Grove, California, November, 2007.
	J.J. Fuchs Towards a new matrix decomposition Proceedings of the 17th Int. Symp. on Mathematical Theory of Networks and Systems, Kyoto, Japan, July, 2006.
	J.J. Fuchs A robust signal detection scheme Proc.of 14th European Signal Processing conference, EUSIPCO, September, 2006.
	J.J. Fuchs Recovery conditions of sparse representations in the presence of noise Proceedings of the IEEE Conference on Acoustic, Speech and Signal Processing, Toulouse, France, May, 2006.
	S. Maria and J.J. Fuchs and L. Ferro-Famil and E. Pottier Application of the Global Matched Filter to Space-Time Adaptive Processing Proceedings of EUSAR'06, Dresden, Germany, May, 2006.
	S. Maria and J.J. Fuchs Detection performance for GMF applied to STAP data Proc.of 14th European Signal Processing conference, EUSIPCO, September, 2006.
	S. Maria and J.J. Fuchs Application of the Global Matched Filter to STAP data: an efficient algorithmic approach Proceedings of the IEEE Conference on Acoustic, Speech and Signal Processing, Toulouse, France, May, 2006.
	J.J. Fuchs Sparse representations and realization theory Proceedings of the 17th Int. Symp. on Mathematical Theory of Networks and Systems, Kyoto, Japan, July, 2006.

Commented list of my publications concerning sparse representations: journal papers

	J.J. Fuchs Extension of the Pisarenko method to sparse linear arrays IEEE-T-SP, vol.~45, p.~2413--2421, oct. 1997.
	Pisarenko can be seen as : $\min_x \\|x\\|_1$ sur $Ax=b$ , $x\ge0 $ with $b$ the covariances and the columns in $A$ the elementary contribution of sources as well as the noise contributions, extension = arbitrary shape or sampling interval and bound on the $\ell\{\infty}$ reconstruction error.
	J.J. Fuchs Multipath time-delay detection and estimation IEEE-T-SP, vol.~47, p.~237--243, jan. 1999.
	delay estimation between replicas of a known signal, $b$ is the sum of a few replicas, in $A$ all the potential delays one minimizes the $\ell_1$ norm of the weights under exact or approximate ($\ell_{2}$) reconstruction.
	J.J. Fuchs and B Delyon Minimum $L_1$-norm reconstruction function for oversampled signals: Application to time-delay estimation. IEEE-T-IT, vol.~46, p.~1666--1673, juillet 2000.
	the min-$L_1$ interpolation function in case of a oversampled signal, it exibits parsimony !
	J.J. Fuchs On the application of the global matched filter to DOA estimation with uniform circular arrays. IEEE-T-SP, vol.~49, p.~702--709, avr. 2001.
	the $\ell_2-\ell_1$ criterion applied to the souce localizations circular array, tuning of the hyper-parameter.
	J.J. Fuchs On sparse representations in arbitrary redundant basis. IEEE-T-IT, vol.~50, 6, p.~1341--1344, juin 2004.
	recovery condition for the $\ell_1$ and $\ell_2-\ell_1$ criterion.
	J.J. Fuchs Recovery of exact sparse representations in the presence of bounded noise. IEEE-T-IT, vol.~51, 10, p.~3601--3608, oct.2005.
	exact recovery condition in the presence of noise

Commented list of my publications concerning sparse representations: conference papers

	J.J. Fuchs Extension of the Pisarenko method to sparse linear arrays IEEE - ICASSP, Detroit, vol. 3, pp. 2100-2103, may 1995.
	Pisarenko can be seen as : $\min_x \\|x\\|_1$ sur $Ax=b$ , $x\ge0 $ with $b$ the covariances and the columns in $A$ the elementary contribution of sources as well as the noise contributions, extension = arbitrary shape or sampling interval.
	J.J. Fuchs Linear programming in spectral estimation. Application to array processing IEEE - ICASSP, Atlanta, vol.6, pp. 3161-3164, may 1996.
	source localization with arbitrary array, $b$ is the output of beamformers, the columns of $A$ model sources contributions, white or non white noise, one minimizes the $\ell_1$ norm of the weights and approximate ($\ell_{\infty}$) reconstruction.
	J.J. Fuchs Multipath time-delay estimation IEEE - ICASSP, Munich, vol. 1, pp. 527-530, 1997.
	delay estimation between replicas of a known signal, $b$ is the sum of a few replicas, in $A$ all the potential delays, one minimizes the $\ell_1$ norm of the weights under exact or approximate ($\ell_{\infty}$) reconstruction.
	J.J. Fuchs Source localization in the presence of unknown colored noise. 11th Ifac-Ifors symposium on Identification and system Parameter Estimation, Fukuoka, vol. 2, pp. 517-522, juillet 1997.
	similar to ICASSP 96 with $\ell_{\infty}$ bounded reconstruction errors.
	J.J. Fuchs and B. Delyon The sampling theorem and time delay estimation. 11th Ifac-Ifors symposium on Identification and system Parameter Estimation, Fukuoka, vol. 2, pp. 505-510, juillet 1997.
	when estimating delays as in Icassp 97, the weights are samples from a min-$L_1$ interpolation function instead of the sinus cardinal which is the min-$L_2$ interpolation function.s
	J.J. Fuchs Une approche à l'estimation et l'identification simultanées.. 16ème GRETSI, Grenoble,vol. 2, pp. 1273-1276, sept. 1997.
	all the problems that can be handled with the $\ell_2-\ell_1$ criterion, optimality conditions, and a beginning of the analysis of the recovery conditions.
	N. Moal et J.J. Fuchs Estimation de l'ordre et identification des paramètres d'un processus ARMA. 16ème GRETSI, Grenoble,vol.1, pp. 511-514, sept. 1997
	sparse representations used to identify an ARMA model, in $b$ the estimated covariance sequence, in $A$ the elementary contribution of real poles or.. , $\min \ell_1$ under $\ell_{\infty}$ reconstruction errors.
	J.J. Fuchs Detection and estimation of superimposed signals. IEEE - ICASSP, vol. III, pp. 1649-1652, Seattle, 1998.
	same as gretsi 97, the $\ell_2-\ell_1$ criterion, optimality conditions, applied to a generic model.
	N. Moal and J.J. Fuchs Sinusoids in white noise~: a quadratic programming approach. IEEE - ICASSP, vol. IV, pp. 2221-2224, Seattle, 1998.
	$\ell_2-\ell_1$ criterion, optimality conditions, apllied to recovering cosines with zero initial phases!.
	J.J. Fuchs An inverse problem approach to robust regression. IEEE - ICASSP, ol. IV, pp. 1809-1812, Phoenix, 1999.
	the $\ell_2-\ell_1$ criterion as a way to minimize Huber's function.
	J.J. Fuchs A new approach to robust linear regression. 14th IFAC world congress vol. H, pp. 427-432, juillet 99, Beijing.
	the $\ell_2-\ell_1$ criterion as a way to minimize Huber's function.
	J.J. Fuchs and F. Le Chevalier Détection d'une cible mobile en présence de fouillis à l'aide d'un radar très large bande. 17ème GRETSI, tome 2, pp.532-534, Vannes, sept. 1999.
	the $\ell_2-\ell_1$ criterion applied to radar signals
	N. Moal et J.J. Fuchs Détection et estimation de sinusoïdes dans du bruit coloré de matrice de covariance inconnue. 17ème GRETSI, tome 2, pp.571-574, Vannes, sept. 1999.
	the $\ell_2-\ell_1$ criterion applied to the estimated covariances (in $b$) of real sinusoids in arma noise.
	J.J. Fuchs The global matched filter: Application to DOA estimation with a uniform circular array. SAM 2000 Cambridge Ma.
	the $\ell_2-\ell_1$ criterion applied to the souce localizations circular array, tuning of the hyper-parameter.
	J.J. Fuchs More on sparse representations in arbitrary bases. 13th Ifac-Ifors symposium on Identification and system Parameter Estimation, Fukuoka, vol. 2, pp. 1357-1362, Rotterdam, aug. 2003.
	recovery condition for the $\ell_1$ and $\ell_2-\ell_1$ criterion.
	J.J. Fuchs Solution parcimonieuse pour des systèmes linéaires sous déterminés. 18ème GRETSI, tome 1, pp.189-192, Paris, sept. 2003.
	recovery condition for the $\ell_1$ and $\ell_2-\ell_1$ criterion
	J.J. Fuchs Recovery of exact sparse representations in the presence of noise. IEEE - ICASSP, vol. II, pp. 533-536, Montreal, may 2004.
	exact recovery condition in the presence of noise
	J.J. Fuchs Sparsity and Uniqueness for some Specific Under-determined Linear Systems. IEEE - ICASSP, vol V, pp.729-732, Philadelphia, march 2005
	recovery condition for sinusoids or vandermonde columns
	J.J. Fuchs Some further results on the recovery algorithms. SPARS, Rennes, 2005.
	towards fast recovery algorithms for the $\ell_1-\ell_1$ and $\ell_1-\ell_{\infty}$ criterion
	J.J. Fuchs Recovery conditions of sparse representations in the presence of noise. IEEE - ICASSP, Toulouse 2006.
	recovery condition $\ell_1-\ell_1$ and $\ell_1-\ell_{\infty}$ criterion
	S. Maria and J.J. Fuchs Application of the global matched filter to STAP data: an efficient algorithmic approach. IEEE - ICASSP, Toulouse 2006.
	the $\ell_2-\ell_1$ criterion applied to STAP data and the lars algorithm.
	S. Maria et al. Application of the global matched filter to Space-Time Adaptive Processing. EUSAR, Dresden 2006.
	the $\ell_2-\ell_1$ criterion applied to STAP data and the lars algorithm.
	J.J. Fuchs Sparse representations and realization theory. MTNS, Kyoto 2006.
	overview, connection with realization theory.

Webmaster:
Last time modified: 2008-08-20

Jean-jacques Fuchs

Contact Information

Profile

Research Activities

Teaching

Some recent publications

Commented list of my publications concerning sparse representations: journal papers

Commented list of my publications concerning sparse representations: conference papers