On the impact of prefiltering on compressed sensing in presence of invalid measurements

Abstract

We address the problem of sparse signal recovery in compressed sensing when a fraction of acquired measurements is invalid or damaged. This may occur due to some system malfunction or unreliable transmission medium. The current solution requires increasing the number of measurements to achieve accurate signal recovery, otherwise recovery performance is jeopardized. We study the performance impact of prefiltering the acquired measurements by detecting and omitting potentially invalid measurements prior to signal recovery. We demonstrate analytically and numerically that this approach significantly reduces the number of measurements required for accurate recovery, which leads to overall improvement of recovery performance, especially when a large fraction of measurements is invalid. Therefore, this approach enhances the ability of compressed sensing to tolerate realistic implementation challenges.