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In compressive sensing, one important parameter that characterizes thevarious greedy recovery algorithms is the iteration bound which provides themaximum number of iterations by which the algorithm is guaranteed to converge.In this letter, we present a new iteration bound for CoSaMP by certainmathematical manipulations including formulation of appropriate sufficientconditions that ensure passage of a chosen support through the two selectionstages of CoSaMP, Augment and Update. Subsequently, we extend the treatment tothe subspace pursuit (SP) algorithm. The proposed iteration bounds for bothCoSaMP and SP algorithms are seen to be improvements over their existingcounterparts, revealing that both CoSaMP and SP algorithms converge in feweriterations than suggested by results available in literature.

On the Number of Iterations for Convergence of CoSaMP and Subspace Pursuit Algorithms