The Stability of Regularized Orthogonal Matching Pursuit Algorithm
نویسندگان
چکیده
This paper studies a fundamental problem that arises in sparse representation and compressed sensing community: can greedy algorithms give us a stable recovery from incomplete and contaminated observations ? Using the Regularized Orthogonal Matching Pursuit (ROMP) algorithm, a modified version of Orthogonal Matching Pursuit (OMP) [1], which was recently introduced by D.Needell and R.Vershynin [2], we assert that ROMP is stable and guarantees approximate recovery of non-sparse signals, as good as the Basis Pursuit algorithm [16]. We also will set up criterions at which the algorithm halts, and the upper bounds for the reconstructed error. It will be proved in the paper that these upper bounds are proportional to the noise energy.
منابع مشابه
Algorithm: Regularized Orthogonal Matching Pursuit (ROMP)
This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements – L1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized version of the Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of t...
متن کامل8 Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit
This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements – L1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized version of Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of L1-mi...
متن کاملSignal Recovery from Inaccurate and Incomplete Measurements via Regularized Orthogonal Matching Pursuit
We demonstrate a simple greedy algorithm that can reliably recover a vector v ∈ R from incomplete and inaccurate measurements x = Φv + e. Here Φ is a N × d measurement matrix with N ≪ d, and e is an error vector. 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 ...
متن کاملUniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit
This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements – L1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized version of Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of L1-mi...
متن کاملGreedy type algorithms for RIP matrices. A study of two selection rules
On [24] some consequences of the Restricted Isometry Property (RIP) of matrices have been applied to develop a greedy algorithm called “ROMP” (Regularized Orthogonal Matching Pursuit) to recover sparse signals and to approximate non-sparse ones. These consequences were subsequently applied to other greedy and thresholding algorithms like “SThresh”, “CoSaMP”, “StOMP” and “SWCGP”. In this paper, ...
متن کامل