RIP-Based Near-Oracle Performance Guarantees for SP, CoSaMP, and IHT

This correspondence presents an average case denoising performance analysis for SP, CoSaMP, and IHT algorithms. This analysis considers the recovery of a noisy signal, with the assumptions that it is corrupted by an additive random zero-mean white Gaussian noise and has a K-sparse representation with respect to a known dictionary D . The proposed analysis is based on the RIP, establishing a near-oracle performance guarantee for each of these algorithms. Beyond bounds for the reconstruction error that hold with high probability, in this work we also provide a bound for the average error.