Restoration of Blurred Images when Blur is Incompletely Specified

Work in restoration of blurred images often assumes the form and extent of blurring to be known. In practice it may not be known or may not be easily quantified. Chan and Gray (1996) and Gray and Chan (1995) studied the effects of misspecifying the degree and/or form of blur in image regularization. This paper will consider the situation where these are not assumed known but are estimated as part of a restoration procedure. We describe several different simultaneous estimation-restoration algorithms, namely an extension of Green’s application of his One Step Late (OSL) approximation, for penalized maximum likelihood estimation, to the EM algorithm (Green 1990, 1993), an extension of quadratic image regularization, and an extension of a Bayesian method of Archer and Titterington (1995) which can be optimized either directly or by simulated annealing using the Gibbs sampler (Geman and Geman, 1984). Performance will be compared empirically by means of a simulation study.