Abstract
Practically, in the underdetermined model y=A x, where x is a K sparse vector (i.e., it has no more than K nonzero entries), both y and A could be totally perturbed. A more relaxed condition means less number of measurements are needed to ensure the sparse recovery from theoretical aspect. In this paper, based on restricted isometry property (RIP), for subspace pursuit (SP) and compressed sampling matching pursuit (CoSaMP), two relaxed sufficient conditions are presented under total perturbations to guarantee that the sparse vector x is recovered. Taking random matrix as measurement matrix, we also discuss the advantage of our condition. Numerical experiments validate that SP and CoSaMP can provide oracle-order recovery performance.
Highlights
Compressed sensing [1] has been attracted more and more attention since it has been proposed
The sparse signals can be accurately reconstructed from far less samples than those required in the classical Shannon-Nyquist theorem
The minimum of all constants δ satisfying (8) is called as the restricted isometry constant (RIC) δK
Summary
Compressed sensing [1] has been attracted more and more attention since it has been proposed. It is important to consider these perturbations since it can account for precision errors when applications call for physically implementing the matrix A in a sensor [9]. This case can be found in source separation [10]. The work of [14, 15] discussed the performance of SP and CoSaMP. They presented that oracle-order recovery performance of SP and CoSaMP is guaranteed. We denote vectors by boldface lowercase letters, e.g., x, and matrices as boldface uppercase letters, e.g., D. The minimum of all constants δ satisfying (8) is called as the restricted isometry constant (RIC) δK
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