Hopfield neural network based algorithms for image restoration and reconstruction. I. Algorithms and simulations

In our previous work, the eliminating-highest error (EHE) criterion was proposed for the modified Hopfield (1982) neural network (MHNN) for image restoration and reconstruction. The performance of the MHNN is considerably improved by the EHE criterion as shown in many simulations. In inspiration of revealing the insight of the EHE criterion, in this paper, we first present a generalized updating rule (GUR) of the MHNN for gray image recovery. The stability properties of the GUR are given. It is shown that the neural threshold set up in this GUR is necessary and sufficient for energy decrease with probability one at each update. The new fastest-energy-descent (FED) criterion is then proposed parallel to the EHE criterion. While the EHE criterion is shown to achieve the highest probability of correct transition, the FED criterion achieves the largest amount of energy descent. In image restoration, the EHE and FED criteria are equivalent. A group of new algorithms based on the EHE and FED criteria is set up. A new measure, the correct transition rate (CTR), is proposed for the performance of iterative algorithms. Simulation results for gray image restoration show that the EHE (FED) based algorithms obtained the best visual quality and highest SNR of recovered images, took much smaller number of iterations, and had higher CTR. The CTR is shown to be a rational performance measure of iterative algorithms and predict quality of recovered images.