摘要
Compressive sensing(CS)is an emerging methodology in computational signal processing that has recently attracted intensive research activities.At present,the basic CS theory includes recoverability and stability:the former quantifies the central fact that a sparse signal of length n can be exactly recovered from far fewer than n measurements via l1-minimization or other recovery techniques,while the latter specifies the stability of a recovery technique in the presence of measurement errors and inexact sparsity.So far,most analyses in CS rely heavily on the Restricted Isometry Property(RIP)for matrices.In this paper,we present an alternative,non-RIP analysis for CS via l1-minimization.Our purpose is three-fold:(a)to introduce an elementary and RIP-free treatment of the basic CS theory;(b)to extend the current recoverability and stability results so that prior knowledge can be utilized to enhance recovery via l1-minimization;and(c)to substantiate a property called uniform recoverability of l1-minimization;that is,for almost all random measurement matrices recoverability is asymptotically identical.With the aid of two classic results,the non-RIP approach enables us to quickly derive from scratch all basic results for the extended theory.
