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


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 like 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 spot the support of a sparse signal whereas maintaining the identical computational complexity. The performance guarantee of this modified OMP in recovering the support of a sparse signal is analysed within the framework of mutual (cross) coherence. Furthermore, they discuss the changed OMP within the case of bounded noise and Gaussian noise, and show that the performance of the changed OMP in the presence of noise relies on the mutual (cross) coherence and also the minimum magnitude of the non-zero components of the sparse signal. Finally, simulations are made to demonstrate the performance of the changed OMP.

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