Bayesian image reconstruction - The pixon and optimal image modeling

Publications of the Astronomical Society of the Pacific1993Vol. 105, pp. 630–630

Citations Over TimeTop 10% of 1993 papers

Abstract

In this paper we describe the Optimal Image Model, Maximum Residual LIkelihood method (OptMRL) for image reconstruction. OptMRL, like maximum entropy mehtods (ME), is a Bayesian image reconstruction technique for removing point spread function blurring. Like ME, OptMRL uses both a goodness of fit criterion (GOF) and an "image prior," i.e., a function which quantifies the a priori probability of the image. However, unlike standard ME techniques which typically reconstruce the image on the data pixel grid, OptMRL varies the image model in order to find the optimal functional basis with which to represent the iage. In this regard, our method is similar to the multi-channel ME methods proposed by Weir. In this paper, we show how an optimal basis for image representation can be selected and in doing so, develop the concept of the "pixon" which is a generalized image cell from which this basis is constructed. By allowing both the image and the image representation to be variable, the OptMRL method greatly increases the volume of solution space over which the image is optimized. Hence the likelihood of the final reconstructed image is greatly increased. For the goodness of fit criterion, OptMRL uses the Maximum Residual Likelihood probability distribution introduced previously by Pina and Puetter. This GOF probability distribution, which is based on the spatial autocorrelation of the residuals, has the advantage that it ensures spatially uncorrelated image reconstruction residuals.

Citations Over TimeTop 10% of 1993 papers

Abstract

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