Efficient Recovery of Block Sparse Signals via Zero-point Attracting Projection

TL;DR

This paper introduces an extended zero-point attracting projection (ZAP) algorithm tailored for block-sparse signals in compressed sensing, demonstrating improved stability and reconstruction accuracy over existing methods.

Contribution

The paper develops a block version of the ZAP algorithm using an approximate l_{2,0} norm, enhancing recovery stability and accuracy for block-sparse signals in noisy environments.

Findings

Outperforms state-of-the-art methods in block sparse recovery

Offers improved stability under noisy conditions

Provides theoretical analysis of local minimum stability

Abstract

In this paper, we consider compressed sensing (CS) of block-sparse signals, i.e., sparse signals that have nonzero coefficients occurring in clusters. An efficient algorithm, called zero-point attracting projection (ZAP) algorithm, is extended to the scenario of block CS. The block version of ZAP algorithm employs an approximate $l_{2,0}$ norm as the cost function, and finds its minimum in the solution space via iterations. For block sparse signals, an analysis of the stability of the local minimums of this cost function under the perturbation of noise reveals an advantage of the proposed algorithm over its original non-block version in terms of reconstruction error. Finally, numerical experiments show that the proposed algorithm outperforms other state of the art methods for the block sparse problem in various respects, especially the stability under noise.