Group-Sparse Signal Denoising: Non-Convex Regularization, Convex Optimization

Abstract: Convex optimization with sparsity-promoting convex regularization is a standard approach for estimating sparse signals in noise. In order to promote sparsity more strongly than convex regularization, it is also standard practice to employ non-convex optimization. In this paper, we take a third approach. We utilize a non-convex regularization term chosen such that the total cost function (consisting of data consistency and regularization terms) is convex. Therefore, sparsity is more strongly promoted than in the standard convex formulation, but without sacrificing the attractive aspects of convex optimization (unique minimum, robust algorithms, etc.). We use this idea to improve the recently developed 'overlapping group shrinkage' (OGS) algorithm for the denoising of group-sparse signals. The algorithm is applied to the problem of speech enhancement with favorable results in terms of both SNR and perceptual quality.

Group-sparse signal denoising: Non-convex regularization, convex optimization.
P.-Y. Chen and I. W. Selesnick. IEEE Trans. on Signal Processing, 62(13):3464-3478, July 1, 2014.
Preprint: Chen_2014_TSP_NCOGS.pdf
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Po-Yu Chen and Ivan W. Selesnick
Electrical and Computer Engineering
NYU Tandon School of Engineering
New York University
Brooklyn, New York


This material is based upon work supported by the National Science Foundation under Grant No. 1018020.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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