RIP-based near-oracle performance guarantees for SP, CoSaMP, and IHT

Raja Giryes*, Michael Elad

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 bf 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.

Original languageEnglish
Article number6071013
Pages (from-to)1465-1468
Number of pages4
JournalIEEE Transactions on Signal Processing
Issue number3
StatePublished - Mar 2012
Externally publishedYes


  • Additive white noise
  • Gaussian noise
  • compressed sensing
  • signal denoising
  • signal reconstruction
  • signal representations


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