ERROR ANALYSIS OF A CLASS OF CONSTRAINED ITERATIVE RESTORATION ALGORITHMS.

Abstract

The problem of noise stability in a class of iterative image restoration algorithms is investigated. 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 and noise stability of the algorithm is investigated. A general error-analysis method is derived to predict the optimal number of iterations that minimizes the mean-square error between the ideal and the reconstructed image. An investigation of the tradeoff between signal reconstruction and noise amplification shows that by using prior knowledge of the signal and noise statistics, it is possible to achieve optimal restoration. Simulations verify the theoretical results.