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Signal Space CoSaMP for sparse recovery with partially known support

In this work, we extend the study of compressive sensing on Signal Space CoSaMP with redundant dictionaries by utilizing the partially known information. Under the assumption that the signal of interest, with some known locations of the nonzero coefficients, has a sparse representation under some redundant dictionaries, we modify the Signal Space CoSaMP algorithm by incorporating the partially known support into the recovery process. We then provide theoretical recovery guarantees of this proposed algorithm by using the well-known D-RIP condition. Numerical experiments are conducted to verify the improved performance, i.e., fewer measurements are needed to yield a good approximate reconstruction of the original signal.