Recursive sparse recovery in large but correlated noise

In this work, we focus on the problem of recursively recovering a time sequence of sparse signals, with time-varying sparsity patterns, from highly undersampled measurements corrupted by very large but correlated noise. It is assumed that the noise is correlated enough to have an approximately low rank covariance matrix that is either constant, or changes slowly, with time. We show how our recently introduced Recursive Projected CS (ReProCS) and modifled-ReProCS ideas can be used to solve this problem very effectively. To the best of our knowledge, except for the recent work of dense error correction via i minimization, which can handle another kind of large but "structured" noise (the noise needs to be sparse), none of the other works in sparse recovery have studied the case of any other kind of large noise.