In previous work [1], the authors introduced a cost function to define reconstruction as an optimization problem. In this paper, a procedure is presented for the optimal reconstruction of images from blurred data. The procedure employs a Bayesian approach for the use of available information. This information comes from knowledge of the set of possible edge locations. Data processing provides an estimate of the jump size, while available gray level data supports identification of smooth, internal regions. The authors also discuss the use of their procedure for a discretized model. Examples are presented for both simulated and real data.