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

被引:192
作者
Chen, Po-Yu [1 ]
Selesnick, Ivan W. [1 ]
机构
[1] NYU, Polytech Sch Engn, Dept Elect & Comp Engn, Brooklyn, NY 11201 USA
基金
美国国家科学基金会;
关键词
Convex optimization; denoising; group sparse model; non-convex optimization; sparse optimization; speech enhancement; translation-invariant denoising; VARIABLE SELECTION; MIXED NORMS; RECONSTRUCTION; SHRINKAGE; RECOVERY; RESTORATION; ALGORITHMS; IMAGES;
D O I
10.1109/TSP.2014.2329274
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
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.
引用
收藏
页码:3464 / 3478
页数:15
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