l1 MINIMIZATION WITH NOISY DATA

Compressed sensing aims at recovering a sparse signal x is an element of R-N from few nonadaptive, linear measurements Phi(x) given by a measurement matrix Phi. One of the fundamental recovery algorithms is an l(1) minimization. In this paper we investigate the situation when our measurement Phi(x) is contaminated by arbitrary noise under the assumption that the matrix F satisfies the restricted isometry property. This complements results from [Candes, Romberg, and Tao, Comm. Pure Appl. Math., 59 (2006), pp. 1207-1223] and [DeVore, Petrova, and Wojtaszczyk, Appl. Comput. Harmon. Anal., 27 (2009), pp. 275-288].