Translation-Invariant Shrinkage/Thresholding of Group Sparse Signals
This addresses denoising for group-sparse signals like speech, but it is incremental as it builds on existing sparsity models.
The paper tackles signal denoising for clustered coefficients by developing an overlapping group shrinkage (OGS) algorithm based on convex optimization, which avoids blocking artifacts and musical noise in speech enhancement.
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.