Stable restoration and separation of approximately sparse signals

Christoph Studer, Richard G. Baraniuk

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse representation in a second general dictionary and measurement noise. The algorithms and analytical recovery conditions consider varying degrees of signal and interference support-set knowledge. Particular applications covered by the proposed framework include the restoration of signals impaired by impulse noise, narrowband interference, or saturation/clipping, as well as image in-painting, super-resolution, and signal separation. Two application examples for audio and image restoration demonstrate the efficacy of the approach.

Original languageEnglish (US)
Pages (from-to)12-35
Number of pages24
JournalApplied and Computational Harmonic Analysis
Issue number1
StatePublished - Jul 2014


  • Basis-pursuit denoising
  • Coherence
  • Deterministic recovery guarantees
  • Signal restoration
  • Signal separation
  • Sparse signal recovery

ASJC Scopus subject areas

  • Applied Mathematics


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