On the global asymptotic stability of the NAS-RIF algorithm for blind image restoration

In this paper, the authors present a convergence analysis for the NAS-RIF (nonnegativity and support constraints recursive inverse filtering) algorithm used in blind image restoration. A novel approach is presented to determine sufficient conditions for the global convergence of the technique. The approach is general to many signal processing algorithms and incorporates Lyapunov's direct method used commonly in nonlinear system analysis. The sufficient conditions for convergence are determined to be in the form of constraints on the blurred image pixels which can be tested for prior to the use of the NAS-RIF algorithm. An apparent trade-off between the quality of the restoration and the uniqueness of the solution is found.