Stéphane G. Mallat 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 Zhang) 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.
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 and Ecole Polytechnique.