Stopping Condition for Greedy Block Sparse Signal Recovery

TL;DR

This paper proposes a probabilistic stopping condition for greedy block sparse recovery algorithms, specifically BOMP and ICBOMP, which improves efficiency by reducing unnecessary iterations while maintaining high recovery accuracy.

Contribution

The paper introduces a novel probabilistic stopping criterion for BOMP that effectively detects the last supporting block, enhancing recovery efficiency and accuracy.

Findings

The stopping condition reduces unnecessary iterations in BOMP and ICBOMP.

Simulation results demonstrate improved recovery accuracy.

The approach is effective for both BOMP and interference cancellation based BOMP.

Abstract

For greedy block sparse recovery where the sparsity level is unknown, we derive a stopping condition to stop the iteration process. Focused on the block orthogonal matching pursuit (BOMP) algorithm, we model the energy of residual signals at each iteration from a probabilistic perspective. At the iteration when the last supporting block is detected, the resulting energy of residual signals is supposed to suffer an obvious decrease. Based on this, we stop the iteration process when the energy of residual signals is below a given threshold. Compared with other approaches, our derived condition works well for the BOMP recovery. What is more, we promote our approach to the interference cancellation based BOMP (ICBOMP) recovery in paper [1]. Simulation results show that our derived condition can save many unnecessary iterations and at the same time guarantees a favorable recovery accuracy, both for the BOMP and ICBOMP recoveries.