Orthogonal Matching Pursuit under the Restricted Isometry Property
Abstract
This paper is concerned with the performance of Orthogonal Matching Pursuit (OMP) algorithms applied to a dictionary D in a Hilbert space H. Given an element f H, OMP generates a sequence of approximations fn, n = 1, 2, . . ., each of which is a linear combination of n dictionary elements chosen by a greedy criterion. It is studied whether the approximations fn are in some sense comparable to best n term approximation from the dictionary. One important result related to this question is a theorem of Zhang [8] in the context of sparse recovery of finite dimensional signals. This theorem shows that OMP exactly recovers n-sparse signal, whenever the dictionary D satisfies a Restricted Isometry Property (RIP) of order An for some constant A, and that the procedure is also stable in 2 under measurement noise. The main contribution of the present paper is to give a structurally simpler proof of Zhangs theorem, formulated in the general context of n term approximation from a dictionary in arbitrary Hilbert spaces H. Namely, it is shown that OMP generates near best n term approximations under a similar RIP condition.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 17, 2015
- Accession Number
- AD1002680
Entities
People
- Albert Cohen
- Ronald DeVore
- Wolfgang Dahmen
Organizations
- Texas A&M University