  Applications of compressed sensing motivate the possibility of using
different operators to encode and decode a signal of interest. Since it is
clear that the operators cannot be too different, we can view the discrepancy
between the two matrices as a perturbation. The stability of L1-minimization
and greedy algorithms to recover the signal in the presence of additive noise
is by now well-known. Recently however, work has been done to analyze these
methods with noise in the measurement matrix, which generates a multiplicative
noise term. This new framework of generalized perturbations (i.e., both
additive and multiplicative noise) extends the prior work on stable signal
recovery from incomplete and inaccurate measurements of Candes, Romberg and Tao
using Basis Pursuit (BP), and of Needell and Tropp using Compressive Sampling
Matching Pursuit (CoSaMP). We show, under reasonable assumptions, that the
stability of the reconstructed signal by both BP and CoSaMP is limited by the
noise level in the observation. Our analysis extends easily to arbitrary greedy
methods.

Numerical Analysis