7 research outputs found
Group-Sparse Signal Denoising: Non-Convex Regularization, Convex Optimization
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.Comment: 14 pages, 11 figure
Translation-Invariant Shrinkage/Thresholding of Group Sparse Signals
This paper addresses signal denoising when large-amplitude coefficients form
clusters (groups). The L1-norm and other separable sparsity models do not
capture the tendency of coefficients to cluster (group sparsity). This work
develops an algorithm, called 'overlapping group shrinkage' (OGS), based on the
minimization of a convex cost function involving a group-sparsity promoting
penalty function. The groups are fully overlapping so the denoising method is
translation-invariant and blocking artifacts are avoided. Based on the
principle of majorization-minimization (MM), we derive a simple iterative
minimization algorithm that reduces the cost function monotonically. A
procedure for setting the regularization parameter, based on attenuating the
noise to a specified level, is also described. The proposed approach is
illustrated on speech enhancement, wherein the OGS approach is applied in the
short-time Fourier transform (STFT) domain. The denoised speech produced by OGS
does not suffer from musical noise.Comment: 33 pages, 7 figures, 5 table