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.