A parameter-controlled relaxation algorithm for Bayesian restoration of images using the maximum entropy method (design, analysis, Mach band simulation and parallelization)

A relaxation scheme is developed for the maximum entropy method and applied to the Bayesian restoration of images. The scheme involves optimizing a system by controlling its states in sequence, using specific parameter strategies. The results evolve directly from the functional analysis of a stationary point equation derived from the Bayesian-based entropy optimization functional. The convergence behaviour of the system is characterized in terms of its state-entropy. Given a degraded input image and the degradation parameter(s), the relaxation scheme performs restoration using a numerical algorithm. For inputs degraded by Gaussian noise, it is shown that the specification of noise variance is not necessary. Using a set of criteria, the algorithm estimates the control parameters adaptively to minimize the influence of the strength of the external constraints upon the system. The algorithm also allows the user to specify a parameter to control the speed of convergence. Test studies with worst case examples demonstrate an expected behaviour of the algorithm along with the performance figures showing an improvement between 58% and 87% over the constrained lease squares approach. In a specific test study, the ME relaxation algorithm is observed to simulate the psycho-physical characteristics of Mach bands in biological visual systems. Analytical studies reveal the underlying mechanism similar to Mach's non-linear biological visual model but differs by its response-dependent basis. Test studies show new prospects for the ME method in edge detection and enhancement applications. Motivated by the results, parallelization of the restoration algorithm is attempted using two concepts of parallelism: instruction and image domain partitioning. The domain partitioning parallelism is approached with the aim of realizing a VLSI implementation based on dedicated parallel architectures. Initial implementation studies have been conducted using Myrias parallel computers, which are general purpose, MIMD (multiple instruction and multiple data stream) computers. The performance studies show optimum efficiencies of 91% with 16 processors for convolution algorithm and 78.4% with 8 processors for the maximum entropy deconvolution algorithm using the relaxation scheme.