Error analysis of a class of constrained iterative restoration algorithms

In this paper, we investigate the problem of noise stability in a class of iterative image restoration algorithms. The algorithm is a Gerchberg-Papoulis type algorithm that utilizes incomplete information and partial constraints to specify constraint operators for the iteration. The iteration, in the absence of noise, converges to a unique solution. In the presence of noise, the restoration is considered as an ill-posed problem. In this study, noise stability of the algorithm is investigated. A general error-analysis method is derived to predict the optimum number of iterations that minimizes the mean-square error between the ideal and the restored image. The tradeoff between signal reconstruction and noise amplification has been investigated, and it has been shown that by using prior knowledge of the signal and noise statistics, it is possible to achieve optimal restoration. Simulations have been performed to verify the theoretical results.