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6. A new point of view: the "parsimonious path".
Since the advent of Hilbertian signal decomposition methods, and more particularly wavelet decomposition methods, a new approach has gradually emerged, based on the following empirical observation: a good representation for a signal or a class of signals tends to concentrate information on a small number of coefficients. This is known as the parsimony property, on which we'll focus below.
6.1 Notion of parsimony
Given a signal x, and a representation of it by a sequence of coefficients α k (which can be either samples or the coefficients of its decomposition on any basis, Fourier or otherwise), this representation is said to be parsimonious if the proportion of non-zero, or numerically significant, coefficients is...
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A new point of view: the "parsimonious path".
Appendices
Bibliography
Software tools
Peter Söndergaard. Ltfat, the linear time-frequency analysis toolbox (matlab/octave, freeware), 2009
The Mathworks. Matlab, 2009
Multiple authors. Mathtools.net,...
Websites
Rice University DSP group. Compressed sensing resources, 2009
http://www.dsp.ece.rice.edu/cs
Thomas Ströhmer. A first guided tour on the irregular sampling problem, 2000
http://www.math.ucdavis.edu/~strohmer/research/sampling/irsampl.html
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