Coherence‐based analysis of modified orthogonal matching pursuit using sensing dictionary

Abstract

Compressed sensing (CS) has attracted considerable attention in signal processing because of its advantage of recovering sparse signals with lower sampling rates than the Nyquist rates. Greedy pursuit algorithms such as orthogonal matching pursuit (OMP) are well-known recovery algorithms in CS. In this study, the authors study a modified OMP proposed by Schnass et al., which uses a special sensing dictionary to identify the support of a sparse signal while maintaining the same computational complexity. The performance guarantee of this modified OMP in recovering the support of a sparse signal is analysed in the framework of mutual (cross) coherence. Furthermore, they discuss the modified OMP in the case of bounded noise and Gaussian noise, and show that the performance of the modified OMP in the presence of noise relies on the mutual (cross) coherence and the minimum magnitude of the non-zero elements of the sparse signal. Finally, simulations are constructed to demonstrate the performance of the modified OMP.