Penalty and Threshold Functions for Sparse Signal Processing

This tutorial describes the use of penalty functions for sparse signal processing. Several penalty functions are illustrated, both convex and non-convex. It is shown how a nonlinear threshold function can be derived from the penalty function and vice versa. An algorithm for solving a linear inverse problem with a sparse penalty function is derived using majorization-minimization (MM). As an example, the algorithm is applied to deconvolution of a sparse spike signal. Two penalty functions are used in the examlple to show the influence of the penalty function.

Download tutorial: sparse_penalties.pdf (pdf file)

Download Matlab demo software: (zip file)

Sparse deconvolution in MATLAB: Example (link)

This tutorial is also a CNX module (link)


Ivan W. Selesnick
Polytechnic Institute of New York University
Electrical and Computer Engineering
Brooklyn, New York, United States

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