A Robust Method for Sparse Signal Recovery under Multiplicative Perturbation

In this paper, we address the problem of sparse signal reconstruction using compressive sampling (CS) in the presence of unknown multiplicative perturbations. Such perturbations cause mismatch between the true signal basis and that in the measurements. We propose an algorithm which iteratively determines active bases, estimates the mismatch in the identified active bases, and adjusts the CS reconstruction equation according to compensated bases. We apply our technique to sparse signal acquisition and CS reconstruction in wireless fading channels with high Doppler frequencies, which are the source of multiplicative perturbations, and verify the effectiveness of our algorithm in suppressing reconstruction noise and accurate signal recovery.