Optimality Analysis and Block Sparse Algorithm for Complex Compressed Sensing

TL;DR

This paper introduces a novel block Newton hard-thresholding pursuit algorithm for complex compressed sensing with block sparse constraints, demonstrating improved accuracy and efficiency over classical methods.

Contribution

The paper develops a new model and algorithm specifically for complex block sparse compressed sensing, including theoretical analysis and practical performance improvements.

Findings

BNHTP outperforms AMP in recovery accuracy

BNHTP reduces calculation time

Theoretical analysis confirms algorithm's effectiveness

Abstract

Recently, many new challenges in Compressed Sensing (CS), such as block sparsity, arose. In this paper, we present a new algorithm for solving CS with block sparse constraints (BSC) in complex fields. Firstly, based on block sparsity characteristics, we propose a new model to deal with CS with BSC and analyze the properties of the functions involved in this model. We then present a new $\tau$-stationary point and analyze corresponding first-order sufficient and necessary conditions. That ensures we to further develop a block Newton hard-thresholding pursuit (BNHTP) algorithm for efficiently solving CS with BSC. Finally, preliminary numerical experiments demonstrate that the BNHTP algorithm has superior performance in terms of recovery accuracy and calculation time when compared with the classical AMP algorithm.