Comparative Analysis of Generalized Block Orthogonal Matching Pursuit Methods for Block Sparse Signal Recovery

This paper presents a comparative analysis of two Generalized Block Orthogonal Matching Pursuit (G-BOMP) techniques for recovering block sparse signals in noisy compressive sensing environments. While the conventional G-BOMP relies on maximum correlation for block selection, the proposed method integrates QR decomposition to enhance numerical stability and prevent redundant block selection. Through extensive MATLAB simulations, the improved G-BOMP with QR decomposition demonstrates a 31.31% higher noise reduction compared to the standard approach, achieving a recovery error reduction of 67.90% versus 36.59% under identical conditions. Complexity analysis reveals comparable computational costs, but the QR-based method exhibits superior robustness in ill-conditioned measurement matrices. The results underscore the efficacy of QR decomposition in mitigating noise propagation and improving reconstruction accuracy, particularly in high-noise scenarios.