Genetic algorithm implementation of stack filter design for image restoration

Abstract
Stack filters are a class of nonlinear spatial operators used for noise suppression. Their design is formulated as an optimisation problem and genetic algorithms (GAs) are used to perform the configuration. Applying the mean absolute error (MAE) as the basis of an objective function, the stack filter is used to restore magnetic resonance (MR) images corrupted with uncorrelated additive noise from 10% and 50%. The filter is trained on corresponding patches of the original and noisy image and then applied to the whole image. The outcomes are compared with the median filter and return a smaller MAE for all noise levels. The dependency of MAE on training window size and GA early termination is examined, showing that a reduction of 75% in computational complexity can be achieved by a 10% relaxation in MAE. The design is then extended from 9-point to 13-point filters and by training on Poisson noise, the filter is applied to nuclear medicine bone scans where no absolute truth exists. Surface topology, image profiles and the measurement of relative contrast show its value in reducing noise whilst preserving contrast. Because of its computational complexity the process has been implemented as a distributed GA using the parallel virtual machine (PVM) software.

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