  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.
