Noise Folding based on General Complete Perturbation in Compressed Sensing

Abstract

This paper first present a new general completely perturbed compressed sensing (CS) model y=(A+E)(x+u)+e,called \emph{noise folding based on general completely perturbed CS system},~where $y\in R^m,u\in R^m,u\ne 0,e\in R^m$, $A\in R^{m\times n},m\ll n$,~$E\in R^{m\times n}$ with incorporating general nonzero perturbation E to sensing matrix A and noise u into signal x simultaneously based on the standard CS model y=Ax+e.~Our constructions mainly will whiten the new proposed CS model and explore into RIP,~coherence for A+E of the new CS model after being whitened.

This paper has been withdrawn by the author due to lack of numerical experiment