Stéphane Mallat

Matching pursuits with time-frequency dictionaries

The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of fun...

Adaptive greedy approximations

Singularity detection and processing with wavelets

The mathematical characterization of singularities with Lipschitz exponents is reviewed. Theorems that estimate local Lipschitz exponents of functions from the evolution across ...

Adaptive time-frequency decompositions

Computing the optimal expansion of a signal in a redundant dictionary of waveforms is an NP-hard problem. We introduce a greedy algorithm, called a matching pursuit, which compu...

A theory for multiresolution signal decomposition: the wavelet representation

Multiresolution representations are effective for analyzing the information content of images. The properties of the operator which approximates a signal at a given resolution w...

Multiresolution approximations and wavelet orthonormal bases of 𝐿²(𝑅)

A multiresolution approximation is a sequence of embedded vector spaces <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altt...