Noise Folding based on General Complete Perturbation in Compressed Sensing

TL;DR

This paper introduces a new perturbed compressed sensing model incorporating matrix perturbation and noise, analyzing its properties through whitening and exploring conditions like RIP and coherence.

Contribution

It proposes a comprehensive perturbed CS model with matrix and signal perturbations, and analyzes its properties using whitening techniques.

Findings

Model incorporates general matrix perturbation and noise.

Analyzes RIP and coherence of the perturbed system.

Provides theoretical foundations for stability under perturbations.

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 $y\in R^m,~u \in R^m,~u\neq 0,~e\in R^m$, $A\in R^{m\times n},~m\ll n$,~$E\in R^{m\times n}$ 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.