• Publications
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A wavelet tour of signal processing
Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour.Expand
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A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
  • S. Mallat
  • Computer Science, Mathematics
  • IEEE Trans. Pattern Anal. Mach. Intell.
  • 1 July 1989
TLDR
We show 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/). Expand
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  • 1107
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Matching pursuits with time-frequency dictionaries
  • S. Mallat, Z. Zhang
  • Mathematics, Computer Science
  • IEEE Trans. Signal Process.
  • 1 August 1993
TLDR
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. Expand
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  • 627
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Characterization of Signals from Multiscale Edges
  • S. Mallat, S. Zhong
  • Mathematics, Computer Science
  • IEEE Trans. Pattern Anal. Mach. Intell.
  • 11 August 2011
TLDR
A multiscale Canny edge detection is equivalent to finding the local maxima of a wavelet transform. Expand
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  • 270
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Singularity detection and processing with wavelets
TLDR
The mathematical characterization of singularities with Lipschitz exponents of functions from the evolution across scales of their wavelet transform is reviewed. Expand
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A Wavelet Tour of Signal Processing - The Sparse Way, 3rd Edition
TLDR
A Wavelet Tour of Signal Processing: The Sparse Way, third edition, is an invaluable resource for researchers and R&D engineers wishing to apply the theory in fields such as image processing, video processing and compression, bio-sensing, medical imaging, machine vision and communications engineering. Expand
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A Wavelet Tour of Signal Processing, 2nd Edition
TLDR
Reading habit is not kind of something sold that you can take or not. Expand
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Multiresolution approximations and wavelet orthonormal bases of L^2(R)
A multiresolution approximation is a sequence of embedded vector spaces   V j  jmember Z for approximating L 2 (R) functions. We study the properties of a multiresolution approximation and proveExpand
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  • 135
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Group Invariant Scattering
  • S. Mallat
  • Mathematics, Computer Science
  • ArXiv
  • 11 January 2011
TLDR
This paper constructs translation-invariant operators on L 2 .R d /, which are Lipschitz-continuous to the action of diffeomorphisms. Expand
  • 582
  • 104
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Multifrequency channel decompositions of images and wavelet models
  • S. Mallat
  • Computer Science
  • IEEE Trans. Acoust. Speech Signal Process.
  • 1 December 1989
TLDR
The author reviews recent multichannel models developed in psychophysiology, computer vision, and image processing. Expand
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