Translation-Invariant Shrinkage/Thresholding of Group Sparse Signals

Abstract: 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 describes an approach, 'overlapping group shrinkage' (OGS), based on the minimization of a convex cost function incorporating a mixed norm. The groups are fully overlapping so as to avoid blocking artifacts. A simple minimization algorithm, based on successive substitution, is derived. A simple procedure for setting the regularization parameter, based on attenuating the noise to a specified level, is described in detail. 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 is free of musical noise.

Translation-invariant shrinkage/thresholding of group sparse signals.
P.-Y. Chen and I. W. Selesnick. Signal Processing. vol. 94, pp 476-489, January 2014.

Download paper: Chen_2014_OGS.pdf
Journal page
Download speech files: (linked from pdf file)
Earlier version: OGS_Sep07_2012.pdf

An explanatory remark on the derivation of the algorithm: OGS_equations_comment.pdf

Note: A newer algorithm based on non-convex regularization gives superior results: Non-Convex OGS

Matlab software

Download zip file:


Speech denoising using overlapping group shrinkage:

Noisy speech wav file
Denoised speech wav file
spectrograms of noisy and denoised speech


Po-Yu Chen and Ivan Selesnick
Electrical and Computer Engineering
NYU Polytechnic School of Engineering
New York University
Brooklyn, New York, United States


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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