Stable Recovery of Sparsely Corrupted Signals Through Justice Pursuit De-Noising (Journal of Computational Mathematics, 2023)
This paper considers a corrupted compressed sensing problem and is devoted to recoversignals that are approximately sparse in some general dictionary but corrupted by a combination of interference having a sparse representation in a second general dictionary andmeasurement noise. We provide new restricted isometry property (RIP) analysis to achievestable recovery of sparsely corrupted signals through Justice Pursuit De-Noising (JPDN)with an additional parameter. Our main tool is to adapt a crucial sparse decompositiontechnique to the analysis of the Justice Pursuit method. The proposed RIP conditionimproves the existing representative results. Numerical simulations are provided to verifythe reliability of the JPDN model.
Keywords: Justice Pursuit De-Noising; Restricted isometry property; Corrupted compressed sensing; Signal recovery.