Signal Recovery from Incomplete and Inaccurate Measurements via Regularized Orthogonal Matching Pursuit
Skip to main content
eScholarship
Open Access Publications from the University of California

Department of Mathematics

Faculty bannerUC Davis

Signal Recovery from Incomplete and Inaccurate Measurements via Regularized Orthogonal Matching Pursuit

Published Web Location

https://arxiv.org/pdf/0712.1360.pdf
No data is associated with this publication.
Abstract

We demonstrate a simple greedy algorithm that can reliably recover a d-dimensional vector v from incomplete and inaccurate measurements x. Here our measurement matrix is an N by d matrix with N much smaller than d. Our algorithm, Regularized Orthogonal Matching Pursuit (ROMP), seeks to close the gap between 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 Uniform Uncertainty Principle, ROMP recovers a signal with O(n) nonzeros from its inaccurate measurements x in at most n iterations, where each iteration amounts to solving a Least Squares Problem. The noise level of the recovery is proportional to the norm of the error, up to a log factor. In particular, if the error vanishes the reconstruction is exact. This stability result extends naturally to the very accurate recovery of approximately sparse signals.

Item not freely available? Link broken?
Report a problem accessing this item