Overlapping Thresholding for Group-Sparse Signal Denoising

Group-Sparse Signal Denoising: Non-Convex Regularization, Convex Optimization
Po-Yu Chen and Ivan Selesnick
IEEE Transactions on Signal Processing, vol.62, no.13, pp. 3464-3478, July 1, 2014.
Preprint: http://arxiv.org/abs/1308.5038
Web: http://eeweb.poly.edu/iselesni/ncogs/

Software version: 6.2

This algorithm performs group-sparse thresholding. The algorithm is intended for denoising signals that posses a group sparse structure. The approach is based on overlapping group sparsity (OGS). Although the regularizer is non-convex, it is designed such that the total cost function is convex. The comparison to convex-regularized OGS demonstrates the improvement obtained by non-convex regularization.

Matlab programs for non-convex OGS

• ogs1.m OGS for 1D signals
• ogs2.m OGS for 2D signals
• ogs3.m OGS for 3D signals

Demos in Matlab

• demo 1 Group-sparse thresholding using 1D OGS
• demo 2 Group-sparse thresholding using 2D OGS
• demo 3 Group-sparse thresholding using 3D OGS

Examples from paper

• Example 1 Signal denoising using 1D OGS (example from the paper)
• Example 2 Speech enhancement using 2D OGS in time-frequency (spectrogram) domain.

Notes

• The recommended regularizers are 'atan' and 'mcp'. The 'mcp' regularizer is described in the paper: C.-H. Zhang, 'Nearly unbiased variable selection under minimax concave penalty,' The Annals of Statistics, pages 894-942, 2010.

Acknowledgment

This research was supported by the NSF under Grant No. CCF-1018020.