Restoration of images via self-organizing feature map

S. Geman and D. Geman (1984) presented a basic statistical method for image restoration. In the method, the system searches an image X which makes a posterior probability p(X|Y) maximum, where Y is a noisy image given as an input. Using a Bayesian method, the posterior probability is rewritten as log p(X|Y)∝log p(X)+log p(Y|X), where p(X) and p(Y|X) are prior probability and likelihood of the image, respectively. The prior probability p(X) is usually represented by a heuristic function. S. Geman and D. Geman defined p(X) using the estimators to detect smoothness and edge. The prior probability greatly affects to the performance of the system so that it should be optimized to fit a class of images, which users want to restore. However, it is hard to optimize the estimator by hand. In this paper, we show a self-organizing feature map (SOM) proposed by Kohonen (1982) which approximately represents the prior probability of local features of images via learning. Therefore, the system can tune the estimator only by seeing original clean images. In the experiment section, we show that the new system using the SOM can restore actual images well