Statistical inference for block sparsity of complex signals

TL;DR

This paper introduces a novel statistical method to estimate the block sparsity of complex-valued signals, which is crucial for improving signal recovery in compressive sensing applications.

Contribution

It develops a new estimation technique for complex signals' block sparsity and analyzes its statistical properties, filling a gap in existing research.

Findings

The proposed estimator's statistical properties are validated through simulations.

Accurate block sparsity estimation significantly enhances signal recovery performance.

Sensitivity analysis shows the importance of precise sparsity estimation.

Abstract

Block sparsity is an important parameter in many algorithms to successfully recover block sparse signals under the framework of compressive sensing. However, it is often unknown and needs to be estimated. Recently there emerges a few research work about how to estimate block sparsity of real-valued signals, while there is, to the best of our knowledge, no investigation that has been conducted for complex-valued signals. In this paper, we propose a new method to estimate the block sparsity of complex-valued signal. Its statistical properties are obtained and verified by simulations. In addition, we demonstrate the importance of accurately estimating the block sparsity in signal recovery through a sensitivity analysis.