<title>Model adaptive optimal image restoration</title>

Abstract

This work addresses the problem of restoring blurred and noise corrupted images when typical deterministic methods (least squares, max entropy, etc.) are not known to be optimal. The proposed approach is to adapt, based on observed image data only, the optimization criterion used in the restoration to one most suited to the statistical properties of the observed image. This is done without prior knowledge or restriction assumptions about the data. Maximum likelihood (ML) image restoration is considered where the noise distribution is not known ar-priori, but is modeled by a general family of parametric distributions whose widely varying shapes are controlled by a small set of parameters. It is shown that the generalized p-Gaussian (gpG) distribution family can match a surprisingly wide range of typical noise distributions (uniform, Gaussian, exponential, Cauchy, etc.) by varying a single shape parameter p. Restoration is accomplished by adapting the noise model through adjusting p as part of the estimation problem. Once p is found, the ML estimate is simply the associated lp norm minimization solution. The optimization criterion is thus adapted to suit the observation. Examples of improved reconstruction using this method, as compared with least squares and maximum entropy, are presented. The extension of model adaptive restoration to maximum a-posteriori (MAP) estimation is discussed. The potential applicability of another more general parametric distribution, the generalized beta of the second kind (GB2), is discussed.