On the use of Lyapunov Criteria to Analyze the Convergence of Blind Deconvolution Algorithms1

We present an approach to determine su cient conditions for the global convergence of iterative blind deconvolution algorithms using nite impulse response (FIR) deconvolution lters. The novel technique, which incorporates Lyapunov's direct method, is general, exible and can be easily adapted to analyze the behaviour of many types of nonlinear iterative signal processing algorithms. Speci cally, we nd su cient conditions to guarantee a unique solution for the NAS-RIF algorithm used for blind image restoration. We determine that in many cases there exists a trade-o between the quality of the deconvolution result and the uniqueness of the solution. A procedure to determine the length of the deconvolution lter to guarantee a unique solution is established. This work was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. 1