DENOISING WITH GREEDY-LIKE PURSUIT ALGORITHMS

摘要

This paper provides theoretical guarantees for denoising performancernof greedy-like methods. Those include CompressivernSampling Matching Pursuit (CoSaMP), Subspace Pursuitrn(SP), and Iterative Hard Thresholding (IHT). Our resultsrnshow that the denoising obtained with these algorithms isrna constant and a log-factor away from the oracle’s performance,rnif the signal’s representation is sufficiently sparse.rnTurning to practice, we show how to convert these algorithmsrnto work without knowing the target cardinality, and insteadrnconstrain the solution to an error-budget. Denoising tests onrnsynthetic data and image patches show the potential in thisrnstagewise technique as a replacement of the classical OMP.