| Paper: | SPTM-P9.9 | ||
| Session: | Signal Restoration, Reconstruction and Enhancement | ||
| Time: | Thursday, May 18, 14:00 - 16:00 | ||
| Presentation: | Poster | ||
| Topic: | Signal Processing Theory and Methods: Signal Restoration, Reconstruction, and Enhancement | ||
| Title: | Sparse Approximation via Iterative Thresholding | ||
| Authors: | Kyle Herrity, Anna Gilbert, Joel Tropp, University of Michigan, United States | ||
| 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. | ||
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