Hopfield neural network based algorithms for image restoration and reconstruction. II. Performance analysis

In this paper, we analyze four typical sequential Hopfield neural network (HNN) based algorithms for image restoration and reconstruction, which are the modified HNN (PK) algorithm, the HNN (ZCVJ) algorithm with energy checking, the eliminating-highest-error (EHE) algorithm, and the simulated annealing (SA) algorithm. A new measure, the correct transition probability (CTP), is proposed for performance of iterative algorithms and is used in this analysis. The CTP measures the correct transition probability for a neuron transition at a particular time and reveals the insight of the performance at each iteration. The general properties of the CTP are discussed. Derived are the CTP formulas of these four algorithms. The analysis shows that the EHE algorithm has the highest CTP in all conditions of the severity of blurring, the signal-to-noise ratio (SNR) of a blurred noisy image, and the regularization term. This confirms the result in many previous simulations that the EHE algorithms can converge to more accurate images with much fewer iterations, have much higher correct transition rates than other HNN algorithms, and suppress streaks in restored images. The analysis also shows that the CTP’s of all these algorithms decrease with the severity of blurring, the severity of noise, and the degree of regularization, which also confirms the results in previous simulations. This in return suggests that the correct transition probability be a rational performance measure.