• Publications
  • Influence
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
  • S. Mallat
  • Computer Science
    IEEE Trans. Pattern Anal. Mach. Intell.
  • 1 July 1989
TLDR
It is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2/Sup j/ can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions.
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 functions. These
Characterization of Signals from Multiscale Edges
  • S. Mallat, S. Zhong
  • Computer Science
    IEEE Trans. Pattern Anal. Mach. Intell.
  • 11 August 2011
TLDR
The authors describe an algorithm that reconstructs a close approximation of 1-D and 2-D signals from their multiscale edges and shows that the evolution of wavelet local maxima across scales characterize the local shape of irregular structures.
Singularity detection and processing with wavelets
TLDR
It is proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their Lipschitz exponents.
A Wavelet Tour of Signal Processing - The Sparse Way, 3rd Edition
TLDR
The central concept of sparsity is explained and applied to signal compression, noise reduction, and inverse problems, while coverage is given to sparse representations in redundant dictionaries, super-resolution and compressive sensing applications.
A Wavelet Tour of Signal Processing, 2nd Edition
TLDR
This a wavelet tour of signal processing 2nd edition is well known book in the world, of course many people will try to own it and this is it the book that you can receive directly after purchasing.
Multiresolution approximations and wavelet orthonormal bases of L^2(R)
TLDR
It is proved that a multiresolution approximation is characterized by a 2π periodic function which is further described and provides a new approach for understanding and computing wavelet orthonormal bases.
Group Invariant Scattering
TLDR
This paper constructs translation-invariant operators on L 2 .R d /, which are Lipschitz-continuous to the action of diffeomorphisms, and extendsScattering operators are extended on L2 .G/, where G is a compact Lie group, and are invariant under theaction of G.
Invariant Scattering Convolution Networks
  • Joan Bruna, S. Mallat
  • Computer Science
    IEEE Transactions on Pattern Analysis and Machine…
  • 5 March 2012
TLDR
The mathematical analysis of wavelet scattering networks explains important properties of deep convolution networks for classification.
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