(untitled) (Journal of Computational Mathematics, 2023)
This paper considers a corrupted compressed sensing problem and is devoted to recover signals that are approximately sparse in some general dictionary but corrupted by a combination of interference having a sparse representation in a second general dictionary and measurement noise. We provide new restricted isometry property (RIP) analysis to achieve stable recovery of sparsely corrupted signals through Justice Pursuit De-Noising (JPDN) with an additional parameter. Our main tool is to adapt a crucial sparse decomposition technique to the analysis of the Justice Pursuit method. The proposed RIP condition improves the existing representative results. Numerical simulations are provided to verify the reliability of the JPDN model.