Online performance guarantees for sparse recovery

Raja Giryes*, Volkan Cevher

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

A K*-sparse vector x* ∈ ℝN produces measurements via linear dimensionality reduction as u = Φx* + n, where Φ ∈ ℝM×N (M < N), and n ∈ ℝM consists of independent and identically distributed, zero mean Gaussian entries with variance σ2. An algorithm, after its execution, determines a vector x̂ that has K-nonzero entries, and satisfies ∥u - Φx̂∥ ≤ ∈. How far can x̂ be from x*? When the measurement matrix Φ provides stable embedding to 2K-sparse signals (the so-called restricted isometry property), they must be very close. This paper therefore establishes worst-case bounds to characterize the distance ∥x̂ - x*∥ based on the online meta-information. These bounds improve the pre-run algorithmic recovery guarantees, and are quite useful in exploring various data error and solution sparsity trade-offs. We also evaluate the performance of some sparse recovery algorithms in the context of our bound.

Original languageEnglish
Title of host publication2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings
Pages2020-2023
Number of pages4
DOIs
StatePublished - 2011
Externally publishedYes
Event36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Prague, Czech Republic
Duration: 22 May 201127 May 2011

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Conference

Conference36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011
Country/TerritoryCzech Republic
CityPrague
Period22/05/1127/05/11

Keywords

  • compressive sensing
  • near-oracle performance guarantees
  • restricted isometry property

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