Matrix recovery has find many applications in different areas, including video surveillance, face recognition and so on. The generic RPCA model though nonconvex, can well describe these applications, and under certain conditions, the convex relaxation problem can recover the solution of the RPCA model. In this talk, we study its application in moving target indication, where the problem enjoys its own sparse structure. Due to such special structure, there will be difficulties for the exact recovery of the original nonconvex model. This motivates our work in this talk where we discuss how to set up better models to solve the problem. We propose two models, the structured RPCA model and the row-modulus RPCA model, both of which will better fit the problem and take more use of the special structure of the sparse matrix. Simulation results confirm the improvement of the generic RPCA model.