Bayesian image restoration and segmentation by constrained optimization

A constrained optimization method, called the Lagrange-Hopfield (LH) method, is presented for solving Markov random field (MRF) based Bayesian image estimation problems for restoration and segmentation. The method combines the augmented Lagrangian multiplier technique with the Hopfield network to solve a constrained optimization problem into which the original Bayesian estimation problem is reformulated. The LH method effectively overcomes instabilities that are inherent in the penalty method (e.g. Hopfield 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.