A reconstruction algorithm for noisy compressed sensing; the UWB channel estimation test case

In the compressed sensing framework, reconstruction algorithms attempt to recover a signal from a collection of projections on randomly generated vectors. The Matching Pursuit algorithm is a greedy procedure that iteratively selects the current “best” match. We propose a modification to the Matching Pursuit algorithm that takes into account the effect of the projections on the noise. The new algorithm incorporates the colored statistics of the noise in the selection process of the best match. We apply the new algorithm in the context of estimating an UWB channel impulse response and compare its performance to that of Matching Pursuit. Finally, we investigate the effect of applying a block-wise compressed sensing approach to large-dimensions signals.