Distribution-aware Block-sparse Recovery via Convex Optimization

TL;DR

This paper introduces a convex optimization approach for block-sparse signal recovery that incorporates prior support probability information, optimizing measurement efficiency through conic integral geometry.

Contribution

It proposes a novel weighted optimization method that leverages prior support probabilities to improve block-sparse recovery, minimizing measurement requirements.

Findings

Weights significantly reduce sample complexity

Method outperforms traditional algorithms in simulations

Applicable to synthetic and real data

Abstract

We study the problem of reconstructing a block-sparse signal from compressively sampled measurements. In certain applications, in addition to the inherent block-sparse structure of the signal, some prior information about the block support, i.e. blocks containing non-zero elements, might be available. Although many block-sparse recovery algorithms have been investigated in Bayesian framework, it is still unclear how to incorporate the information about the probability of occurrence into regularization-based block-sparse recovery in an optimal sense. In this work, we bridge between these fields by the aid of a new concept in conic integral geometry. Specifically, we solve a weighted optimization problem when the prior distribution about the block support is available. Moreover, we obtain the unique weights that minimize the expected required number of measurements. Our simulations on both synthetic and real data confirm that these weights considerably decrease the required sample complexity.