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

R. K. Piña and R. C. Puetter
Publications of the Astronomical Society of the Pacific
Vol. 104, No. 681 (1992 November), pp. 1096-1103
Stable URL: http://www.jstor.org/stable/40679969
Page Count: 8
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Incorporation of Spatial Information in Bayesian Image Reconstruction: The Maximum Residual Likelihood Criterion
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Abstract

We have developed a new figure of merit, a "maximum-residual-likelihood" (MRL) statistic, for the goodness of fit for Bayesian image restoration which explicitly incorporates spatial information. The MRL constraint provides a natural means of incorporating the prior knowledge that the residuals contain no spatial structure through the autocorrelation function of the residuals. We demonstrate that this statistic follows a x² 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 the 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 overresolution in low signal-to-noise portions of the image.

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