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Sparse Approximation Via Iterative Thresholding

Herrity, Kyle K. and Gilbert, Anna C. and Tropp, Joel A. (2006) Sparse Approximation Via Iterative Thresholding. In: International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2006), Toulouse, France, 14-19 May 2006. Vol.III. IEEE , Piscataway, NJ, III-624. ISBN 1-4244-0469-X. https://resolver.caltech.edu/CaltechAUTHORS:HERicassp06

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Abstract

The well-known shrinkage technique is still relevant for contemporary signal processing problems over redundant dictionaries. We present theoretical and empirical analyses for two iterative algorithms for sparse approximation that use shrinkage. The GENERAL IT algorithm amounts to a Landweber iteration with nonlinear shrinkage at each iteration step. The BLOCK IT algorithm arises in morphological components analysis. A sufficient condition for which General IT exactly recovers a sparse signal is presented, in which the cumulative coherence function naturally arises. This analysis extends previous results concerning the Orthogonal Matching Pursuit (OMP) and Basis Pursuit (BP) algorithms to IT algorithms.


Item Type:Book Section
ORCID:
AuthorORCID
Tropp, Joel A.0000-0003-1024-1791
Additional Information:© Copyright 2006 IEEE. Reprinted with permission. [Posted online: 2006-07-24]
Record Number:CaltechAUTHORS:HERicassp06
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:HERicassp06
Alternative URL:http://dx.doi.org/10.1109/ICASSP.2006.1660731
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9067
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:25 Oct 2007
Last Modified:02 Oct 2019 23:56

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