Incorporation of Spatial Information in Bayesian Image Reconstruction: The Maximum Residual Likelihood Criterion

Abstract

We have developed a new figure of merit, a "Maximum-Residual-Likelihood" (MRL) statistic, for the goodness of fit for Bayesian image resotration which explicitly incorporates spatial information. The MRL constraint provides a natural means of incorporating the prior knowledge that the residuals contal no spatial structure through teh autocorrelation function of the residuals. We demonstrate that this statistic follows a Chi-2-distribution and that forcing this statistic to have its most probable value leads to a restored image whose residuals are consistent with the noise model. Our numerical experiments suggest that image restoration using hte MRL statistic alone (without an "image prior", e.g., an entropy function) is numerically robust and produces results which are independent of the initial guess for the restored image. However, we caution that using the MRL statistic without an image prior can result in over-resolution in low signal-to-noise portions of the image.