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Cite Details

Sergey Voronin and Rick Chartrand, "A new generalized thresholding algorithm for inverse problems with sparsity constraints", in IEEE International Conference on Acoustics, Speech, and Signal Processing, 2013

Abstract

We propose a new generalized thresholding algorithm useful for inverse problems with sparsity constraints. The algorithm uses a thresholding function with a parameter p. When p = 1, the thresholding function is equivalent to classical soft thresholding. For values of p below 1, the thresholding penalizes small coefficients over a wider range and applies less bias to the larger coefficients, much like hard thresholding but without discontinuities. The functional that the new thresholding minimizes is non-convex for p < 1. We state an algorithm similar to the Iterative Soft Thresholding Algorithm (ISTA). We show that the new thresholding performs better in numerical examples than soft thresholding.

BibTeX Entry

@inproceedings{voronin-2013-new,
author = {Sergey Voronin and Rick Chartrand},
title = {A new generalized thresholding algorithm for inverse problems with sparsity constraints},
year = {2013},
urlpdf = {http://math.lanl.gov/Research/Publications/Docs/voronin-2013-new.pdf},
booktitle = {IEEE International Conference on Acoustics, Speech, and Signal Processing}
}