A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way

By S. Mallat. 2008

1,263 citations recorded by the source corpus.

Subfields: Numerical Methods & Scientific Computing, Signal Processing

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Numerical Methods & Scientific Computing

In Signal Processing

Citations in the corpus

Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network (2016, background): “This transform domain is usually a dictionary of image atoms [25, 10], which can be learnt through a training process that tries to discover the correspondence between LR and HR patches.”
Wavelet Scattering Regression of Quantum Chemical Energies (2016, background): “ted with the singular convolution kernel juj1. The Fourier spectrum 4ˇj!j2 is singular at != 0 and has a slow decay. Such homogeneous singular operators are better represented with wavelet transforms [15,33,34,30]. The following theorem proves that Coulomb potentials have a much more sparse regressi”
A Mathematical Motivation for Complex-Valued Convolutional Networks (2015, methodology): “A textbook treatment of all concepts and terms used above and below is given by Mallat (2008).”
The Cosparse Analysis Model and Algorithms (2011, positive): “In signal and image processing, discrete transforms such as wavelet, Gabor, curvelet, contourlet, shearlet, and others [33, 39, 13, 27], are of interest, and this empirical observation seems to give a good support for the sparse synthesis model.”
Dictionaries for Sparse Representation Modeling (2010, background): “Particularly frustrating, for instance, was the common knowledge that 2-D piecewisesmooth signals could be described much more efficiently using a simple piecewise-linear approximation over an adaptive triangle grid, than using any existing dictionary [5], [43].”
Sparse Modeling for Image and Vision Processing (2014, methodology): “When a signal f is “smooth” in a particular sense [see Mallat, 2008], it can be well approximated by a linear combination of a few wavelets.”
Pairs of frequency-based nonhomogeneous dual wavelet frames in the distribution space (2009, background): “For a function f : R → C, throughout the paper we shall use the following notation fλ;k,n(x) := |λ|1/2e−inλxf(λx− k) and fλ;k := fλ;k,0 = |λ|1/2f(λ · −k), x, λ, k, n ∈ R, (1.1) where i denotes the imaginary unit.”
Constant Q cepstral coefficients: A spoofing countermeasure for automatic speaker verification (2017, background): “) Wavelet techniques are, however, not well suited to this computation (Mallat, 2008).”
WiGest: A ubiquitous WiFi-based gesture recognition system (2014, background): “It has two main advantages: (a) an optimal resolution both in the time and the frequency domains; and (b) it achieves fine-grained multiscale analysis [39].”