Image restoration and edge detection using neural networks

This thesis is a combination of three inter-related research topics in image restoration and edge detection. More specifically: (i) A modified Hopfield network model is presented for regularized image restoration. The proposed network allows nonzero autoconnections in the interconnection matrix, and uses more efficient number representation scheme than the simple and binary sum schemes. A set of algorithms using the proposed network model are presented, with various updating modes. The sequential and the decoupled parallel algorithms are shown to converge to a local minimum of the energy (or the objective) function after a finite number of iterations. A partially asynchronous algorithm is presented, which allows a neuron to have a bounded time delay to communicate with others. The {dollar}lsb1{dollar} norm of the residual at the fixed point of this algorithm increases as the upper bound on the delay increases. The partially asynchronous algorithm can eliminate the synchronization overhead in synchronous algorithms, such as the proposed sequential and greedy algorithms. (ii) An edge detection algorithm using multistate adaptive linear neurons (ADALINES) is presented. The proposed edge detection algorithm performs better than Marr and Hildreth's LOG edge detector in terms of: (a) resulting edge quality and (b) computational efficiency due to the small window size. (iii) An adaptive image restoration algorithm is presented based on the greedy algorithm whose interconnection weights are adaptively trained by the output of the multistate ADALINES edge detector. By adaptively switching between the two different values of the regularization parameter, according to a measure of the spatial activity obtained by the edge information, the adaptive algorithm performs better than its nonadaptive counterpart, based both on the improvement in the mean squared error and on visual inspection. (Abstract shortened with permission of author.)...