Bayesian Image Restoration and Segmentationby Constrained

A constrained optimization method, called the Lagrange-Hoppeld (LH) method, is presented for solving Markov random eld (MRF) based Bayesian image estimation problems for restoration and segmentation. The method combines the augmented Lagrangian mul-tiplier technique with the Hoppeld network to solve a constrained optimization problem into which the original Bayesian estimation problem is reformulated. The LH method eeectively overcomes instabilities that are inherent in the penalty method (e.g. Hoppeld network) or the Lagrange multiplier method in constrained optimization. An additional advantage of the LH method is its suitability for neural-like analog implementation. Experimental results are presented which show that LH yields good quality solutions at reasonable computational costs.