Denoising using multi-stage randomized orthogonal matching pursuit

Orthogonal Matching Pursuit (OMP) can denoise a signal by greedily approximating a least-squares (LS) estimate as a linear combination of elements (atoms) of a dictionary. OMP iteratively decomposes a signal through deterministic atom selections at each iteration step. Recently proposed randomized OMP algorithms employ random atom selections instead and have the potential to further improve denoising. Typically, the best approximation from these algorithms can be obtained only within a narrow range of iterations. In this paper, we propose a novel multi-stage randomized OMP (MS-ROMP) denoising approach that performs successive ROMP runs, each denoising the obtained estimate from the previous one. We show through simulations that, under certain conditions, this can significantly improve denoising performance by producing a good approximation after any number of iterations beyond the sparsity level.