On the use of Lyapunov criteria to analyze the convergence of blind deconvolution algorithms

We present an approach to determine sufficient conditions for the global convergence of iterative blind deconvolution algorithms using finite impulse response (FIR) deconvolution filters. The novel technique, which incorporates Lyapunov’s direct method, is general, flexible, and can be easily adapted to analyze the behavior of many types of nonlinear iterative signal processing algorithms. Specifically, we find sufficient 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 tradeoff between the quality of the deconvolution result and the uniqueness of the solution. A procedure to determine the length of the deconvolution filter to guarantee a unique solution is established.