Research On Optimization Theory And Algorithms Of Stack Filters

Stack filters which are a kind of nonlinear digital filters, have received considerable attention during recent years since 1986 when their theory was presented. Stack filters virtues lie in: applying the architecture of threshold decomposition, suitable to parallel processing and VLSI realization; including many kinds of nonlinear filters, being an important tool for nonlinear research. Therefore, researching on stack filters has important theoretical and practical values. Beginning with stack filters' fundamental theory, optimization algorithms and their application in image processing of stack filters are studied in this dissertation. The main contents and contributions of this paper are showed as following:A fast output signal restoration algorithm is presented according to the rule that the output signal satisfies stacking property. This algorithm can be used to restore output signal on a universal computer fast when parallel machine is unavailable.An algorithm for generating positive Boolean function (PBF) randomly is also presented in this paper based on the definition and representation methods of PBF. This algorithm makes using genetic algorithms to optimize stack filters possible. These two algorithms are simulated in Matlab environment. The experimental results show the fast output signal restoration algorithm restores output signal much faster on an ordinary computer than traditional algorithm.Using the algorithm for generating positive Boolean function randomly and the optimization model of stack filters based on MAE criteria, optimal stack filters are searched by simple genetic algorithms.The optimization speed of genetic algorithms is unacceptable, though it finds optimal stack filers effectively. In order to overcome this drawback, a fast adaptive algorithm for optimal stack filters is presented in this paper.Experimental results show that optimal stack filters based on MAE criteria, which are found by genetic algorithms preserve details of images perfectly and suppress noise passably. The fast algorithm has the same performance as the genetic algorithms but the time spending on optimizing is much less than genetic algorithms.The optimization model based on MSE criteria is presented in this paper because optimal stack filters base on MAE criterion cannot suppress noise of images perfectly. Adaptive genetic algorithms are used to optimize optimal stack filters based on MSE criterion. Computer simulated experiments show that the noise suppressing capability of this kind of optimal stack filters is better than the optimal stack filters based on MAE criterion but the detail preserving capability is little worse.For nonlinear filters, noise suppressing and detail preserving is a pair of contradictions. In order to calm down the confliction between them, a new kind of optimal stack filters-optimal stack filters based on detail detection is presented in this paper. The performance of stack filters is improved by this kind stack filters and get a good tradeoff between noise suppressing and detail preserving. Experimental results show that optimal stack filters based on detail detection can suppress noise perfectly as well as preserving details of an image effectively through processing the detail and smooth parts by different positive Boolean functions.Although optimal stack filters based on detail detection can reach a good tradeoff between noise suppressing and detail preservation, the processing procedure is more complicated. In order to overcome this drawback, a new kind of criterion-neighboring weighted mean absolute error criterion is presented as an optimality criterion of stack filters. Simulated experiments show that optimal stack filters based on neighboring weighted mean absolute criterion can also reach a good tradeoff between noise suppressing and detail preservation.