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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
  • Mathematics, Computer Science
  • IEEE Trans. Pattern Anal. Mach. Intell.
  • 1 July 1989
Multiresolution representations are effective for analyzing the information content of images. The properties of the operator which approximates a signal at a given resolution were studied. It isExpand
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Matching pursuits with time-frequency dictionaries
  • S. Mallat, Z. Zhang
  • Mathematics, Computer Science
  • IEEE Trans. Signal Process.
  • 1 August 1993
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. TheseExpand
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Characterization of Signals from Multiscale Edges
  • S. Mallat, S. Zhong
  • Computer Science, Mathematics
  • IEEE Trans. Pattern Anal. Mach. Intell.
  • 11 August 2011
A multiscale Canny edge detection is equivalent to finding the local maxima of a wavelet transform. The authors study the properties of multiscale edges through the wavelet theory. For patternExpand
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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 scales of theirExpand
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A Wavelet Tour of Signal Processing - The Sparse Way, 3rd Edition
Mallat's book is the undisputed reference in this field - it is the only one that covers the essential material in such breadth and depth. - Laurent Demanet, Stanford University The new edition ofExpand
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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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Group Invariant Scattering
  • S. Mallat
  • Computer Science, Mathematics
  • ArXiv
  • 11 January 2011
This paper constructs translation-invariant operators on L 2 .R d /, which are Lipschitz-continuous to the action of diffeomorphisms. A scattering propagator is a path-ordered product of nonlinearExpand
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A Wavelet Tour of Signal Processing, 2nd Edition
Bargaining with reading habit is no need. Reading is not kind of something sold that you can take or not. It is a thing that will change your life to life better. It is the thing that will give youExpand
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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
The author reviews recent multichannel models developed in psychophysiology, computer vision, and image processing. In psychophysiology, multichannel models have been particularly successful inExpand
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