Signal Recovery From Incomplete and Inaccurate Measurements Via Regularized Orthogonal Matching Pursuit
Year: 2010
Type: article
Abstract: We demonstrate a simple greedy algorithm that can reliably recover a vectorv¿ ¿dfrom incomplete and inaccurate measurementsx= ¿v+e. Here, ¿ is aNxdmeasurement matrix withNeis an error vector. Our algorithm, Regularized Orthogonal Matching Pursuit (ROMP), seeks to provide the benefits of the two major approaches to sparse recovery. It combines the speed and ease of implementation of the greedy methods with the strong guarantees of the convex programming methods. For any measurement matrix ¿ that satisfies a quantitative restricted isometry principle, ROMP recovers a signalvwithO(n) nonzeros from its inaccurate measurementsxin at mostniterations, where each iteration amounts to solving a least squares problem. The noise level of the recovery is proportional to ¿{logn} ||e||2. In particular, if the error termevanishes the reconstruction is exact.
Authors: Deanna Needell, Roman Vershynin
Institutions: University of California, Davis, University of Michigan
Language: English
Subfield: Signal Processing
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2095978736