Professor of Applied Mathematics,
Ecole Polytechnique, Centre de Mathématiques Appliquées, France.
Associate Professor of Computer Science at the Courant Institute of Mathematical Science, New York University, New York, U.S.A.
Professor Mallat works in applied mathematics for signal and information processing, as well as in computer vision. He made some fundamental contributions to the development of the wavelet theory and its applications to the characterization of transients in sounds and images. The analysis of complex signals often requires computing adaptive decompositions over feature vectors that are selected to match the local signal structures. Professor Mallat studies the underlying non-linear approximation theory issues and has developed algorithms for music synthesis and image segmentation in particular. He is currently investigating a characterization of locally stationary processes and robust procedures to estimate the variations of the local spectrum in speech and seismic recordings.
A Wavelet Tour of Signal Processing, Academic Press, 2nd edition, 1999.
Une Exploration des Signaux en Ondelettes, Editions de l'Ecole Polytechnique, Ellipses diffusion, 2000.
A theory for multiresolution signal decomposition : the wavelet representation, IEEE Transaction on Pattern Analysis and Machine Intelligence, vol. 11, p. 674-693, July 1989.
Multiresolution approximation and wavelet orthonormal bases of L2, Transaction of the American Mathematical Society, vol. 315, p. 69-87, Sept. 1989.
Multifrequency channel decompositions of images and wavelet models, IEEE Transaction in Acoustic Speech and Signal Processing, vol. 37, p. 2091-2110, Dec. 1989.
Zero-Crossings of a Wavelet Transform, IEEE Transactions on Information Theory, vol. 37, p. 1019-1033, July 1991.
with W.L. Hwang, Singularity detection and processing with wavelets, IEEE Transactions on Information Theory, vol. 32, no. 2, March 1992.
with S. Zhong, Characterization of signals from multiscale edges, IEEE Transaction on Pattern Analysis and Machine Intelligence, vol. 14, No. 7, p. 710-732, July 1992.
with E. Bacry, G. Papanicolaou, A wavelet based space-time adaptive numerical method for partial differential equations, Mathematical Modeling and Numerical Analysis,vol. 26, No. 7, p. 793, 1992.
with S. Zhang, Matching Pursuits With Time-Frequency Dictionaries, IEEE Transactions on Signal Processing, December 1993.
with Wen Liang Hwang, Characterization of Self-Similar Multifractals with Wavelet Maxima, Applied and Computational Harmonic Analysis, vol. 1, p. 316-328, 1994.
with G. Davis, and Z. Zhang, Adaptive Time-Frequency Decompositions, SPIE Journal of Optical Engineering, vol. 33, No. 7, p. 2183-2191, July 1994.
with G. Davis, and M. Avelaneda, Adaptive Greedy Approximations, Jour. of Constructive Approximation, vol. 13, No. 1, pp. 57-98, 1997.
Wavelets for a Vision, Proceeding of the IEEE, vol. 4, no. 4, p. 604-614, April 1996.
with F.Bergeaud, Matching Pursuit: Adaptative representations of images, Computational and Applied Mathematics, Vol. 15, no. 2, Birkhauser, Boston, October 1996.
with F. Falzon, Analysis of low bit image transform coding, IEEE Transactions on Signal Processing, April 1998.
with G. Papanicolaou and Z. Zhang, Adaptive Covariance Estimation of Locally Stationary Processes, Annals of Statistics, vol. 26, no. 1, February 1998.
with S. Jaggi, W. Karl, and A. Willsky, High resolution pursuit for feature extraction, Applied and Computational Harmonic Analysis, vol. 5, p. 428-449, 1998.
with S. Jaggi, W. Karl, and A. Willsky, Silhouette Recognition using High Resolution Pursuit Pattern Recognition, vol. 23, no. 5, p 753-771, May 1999.
Applied Mathematics Meets Signal Processing, International Congress of Mathematicians, Berlin 1998, Documenta Mathematica, Journal Der Deutschen Mathematiker-Vereinigung, vol. 1.
with H. Krim, D. Tucker, and D. Donoho, On Denoising and Best Signal Representation, IEEE Trans. on Information Theory, vol. 14, no. 8, November 1999.
with E. Chang, and C. Yap, Wavelet-based foveation, Applied and Computational Harmonic Analysis, vol 9., p. 312-335, 2000.
with J. Kalifa, and B. Rouge, Deconvolution by Thresholding in Mirror Wavelet Bases, IEEE Trans. on Image Processing,vol. 12, no. 4, pp. 446-457, 2003.
with J. Kalifa, Thresholding Estimators for Linear Inverse Problems and Deconvolutions, Annals of Statistics, vol. 31, no. 1, pp 58-109, February 2003.
with M. Clerc, The Texture Gradient Equation for Recovering Shape from Texture, IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 24 no. 4, pp. 536-549, April 2002.
with M. Clerc, Estimating Deformations of Stationary Processes,vol. 31, no. 6, December 2003.
with D. Donoho, R. von Sachs and Y. Samuelides, Signal and covariance estimation with macrotiles, IEEE Trans. on Signal Processing, vol. 53, no. 3, pp. 614-627, 2003.
Foveal detection and approximations for singularities, Applied and Computational Harmonic Analysis, vol 14, pp. 133-180, 2003.
with E. LePennec, Sparse Geometric Image Representation with Bandelets, IEEE Trans. on Image Processing, vol 14, no. 4, p. 423-438, April 2005.
with E. LePennec, Bandelet Image Approximation and Compression, SIAM Journ. of Multiscale Modeling and Simulation, vol. 4, no. 3, p. 992-1039, 2005.
with G. Peyre, Surface Compression With Geometric Bandelets, ACM Transactions on Graphics (SIGGRAPH'05), vol 14, no. 3, 2005.
with G. Peyre, Discrete Bandelets with Geometric Orthogonal Filters , Proceedings of ICIP, September 2005.