Bayesian-Based Iterative Method of Image Restoration*

It was assumed that the degraded image H was of the form H= W*S, where W is the original image, S is the point spread function, and * denotes the operation of convolution. It was also assumed that W, S, and H are discrete probability-frequency functions, not necessarily normalized. That is, the numerical value of a point of W, S, or H is considered as a measure of the frequency of the occurrence of an event at that point. S is usually in normalized form. Units of energy (which may be considered unique events) originating at a point in W are distributed at points in H according to the frequencies indicated by S. H then represents the resulting sums of the effects of the units of energy originating at all points of W. In what follows, each of the three letters has two uses when subscripted. For example, Wi indicates either the ith location in the array W or the value associated with the ith location. The unsubscripted letter refers to the entire array or the value associated with the array as in W = E i Wi. The doublesubscripted Wi j in two dimensions is interpreted similarly to Wi in one dimension. In the approximation formulas, a subscript r appears, which is the number of the iteration.