Stéphane Mallat

Stéphane G. Mallat (born in Paris, France) made some fundamental contributions to the development of wavelet theory in the late 1980s and early 1990s. He has also done work in applied mathematics, signal processing, music synthesis and image segmentation.

Specifically, he collaborated with Yves Meyer to develop the Multiresolution Analysis (MRA) construction for compactly supported wavelets, which made the implementation of wavelets practical for engineering applications by demonstrating the equivalence of wavelet bases and conjugate mirror filters used in discrete, multirate filter banks in signal processing. He also developed (with Sifen Zhong) the Wavelet transform modulus maxima method for image characterization, a method that uses the local maxima of the wavelet coefficients at various scales to reconstruct images.

He introduced the scattering transform that constructs invariance for object recognition purposes. Mallat is the author of A Wavelet Tour of Signal Processing (ISBN 012466606X), a common text in some applied mathematics and engineering courses.

He has taught at New York University, Massachusetts Institute of Technology, Tel Aviv University,^[1] École polytechnique and at the Ecole normale supérieure.^[2]

Publications

• A wavelet tour of signal processing: the sparse way, Academic Press, 1998, 3rd edn. 2009
• "A theory for multiresolution signal decomposition: the wavelet representation" (PDF). IEEE Transactions on Pattern Recognition and Machine Intelligence. 11 (7): 674–693. 1989. doi:10.1109/34.192463.
• "Multiresolution approximations and wavelet orthonormal bases of $L^2 (R)$". Transactions AMS. 315: 69–87. 1989. doi:10.1090/s0002-9947-1989-1008470-5. MR 1008470.
• "Wavelets for a vision". Proc. IEEE (in French). 84 (4): 604–614. 1996. doi:10.1109/5.488702.
• Stéphane Mallat, Une exploration des signaux en ondelettes, Editions de l'Ecole Polytechnique, Palaiseau (France), 2000.

References

1. Yu, Guoshen; Mallat, Stéphane (2008). "Audio Denoising by Time-Frequency Block Thresholding" (PDF). IEEE TRANSACTIONS ON SIGNAL PROCESSING. 56 (5): 1830–1839. doi:10.1109/TSP.2007.912893.
2. Stéphane Mallat at the Ecole normale supérieure (Paris).

External links

• Home page at École polytechnique
• Stéphane Mallat at the Mathematics Genealogy Project