  In compressive sensing, one important parameter that characterizes the
various greedy recovery algorithms is the iteration bound which provides the
maximum number of iterations by which the algorithm is guaranteed to converge.
In this letter, we present a new iteration bound for CoSaMP by certain
mathematical manipulations including formulation of appropriate sufficient
conditions that ensure passage of a chosen support through the two selection
stages of CoSaMP, Augment and Update. Subsequently, we extend the treatment to
the subspace pursuit (SP) algorithm. The proposed iteration bounds for both
CoSaMP and SP algorithms are seen to be improvements over their existing
counterparts, revealing that both CoSaMP and SP algorithms converge in fewer
iterations than suggested by results available in literature.
