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Compressive sampling (CoSa) is a new methodology which demonstrates thatsparse signals can be recovered from a small number of linear measurements.Greedy algorithms like CoSaMP have been designed for this recovery, andvariants of these methods have been adapted to the case where sparsity is withrespect to some arbitrary dictionary rather than an orthonormal basis. In thiswork we present an analysis of the so-called Signal Space CoSaMP method whenthe measurements are corrupted with mean-zero white Gaussian noise. Weestablish near-oracle performance for recovery of signals sparse in somearbitrary dictionary. In addition, we analyze the block variant of the methodfor signals whose supports obey a block structure, extending the method intothe model-based compressed sensing framework. Numerical experiments confirmthat the block method significantly outperforms the standard method in thesesettings.

Near Oracle Performance and Block Analysis of Signal Space Greedy Methods