Recovery of Block-Structured Sparse Signal Using Block-Sparse Adaptive Algorithms via Dynamic Grouping

Abstract

A key point for the recovery of a block-sparse signal is how to treat the different sparsity distributed on the different parts of the considered signal. It has been shown recently that grouping the signal, i.e., partitioning the original signal into different groups or segments, and conducting the recovery for these groups separately provides an effective method to deal with the block-structured sparsity and can generate much better performance than the conventional sparse signal recovery (SSR) algorithms. In order to further improve the recovery performance, instead of the fixed grouping method used in the recent results, a novel dynamic grouping method will be first proposed in this paper, which classifies the segments due to the different levels of sparsity in a dynamic way. Then, by incorporating this technique into the block version of adaptive SSR algorithms. we developed recently, i.e., the block zero-attracting least-mean-square (BZA-LMS) algorithm and the block $\ell _{0}$ -norm LMS ( $\text{B}\ell _{0}$ -LMS) algorithm, the corresponding new algorithms, i.e., the BZA-LMS-D and $\text{B}\ell _{0}$ -LMS-D algorithms, will be established. The performance superiorities and the robustness against different block-sparsity and/or noise interference for the new algorithms based on dynamic grouping will be demonstrated by both analytic discussions and numerical simulations for a variety of scenarios.