Research Of Optimization Theory And Algorithms Of Mirrored Stack Filters

In order to satisfy the demand of people requiring higher ability of signal processing, nonlinear signal processing is gradually developing, nonlinear filters are widely studied which are the main means of nonlinear signal processing. Stack filters are a class of nonlinear digital filters which posess threshold decomposition and stacking properties. According the different ways of threshold decomposition stack filters include traditional threshold decomposition stack filters(referred to as traditional stack filters) and mirrored threshold decomposition stack filters(referred to as mirrored stack filters). Compared with traditional stack filters, mirrored stack filters not only are provided with low-pass characteristic, but also band-pass and high-pass characteristics. This paper focuses on the optimization theory and algorithms of mirrored stack filters, the study includes the following aspects:Firstly, stack filtering theory is studied which includes definition, properties and generating algorithm of positive boolean function, definition and fast reconstruction of the output signals of mirrored stack filter, optimization model of mirrored stack filters, relative optimization algorithms are introduced.Secondly, in order to reduce the calculation of constraints of mirrored threshold decomposition, a two small windows cascade recursive filtering structure is introduced, the filtering effect of cascade windows is extended comparing with single window of same size; recursive structure saves the computing space and improves filtering effect. The optimum shape and sizes of the two small windows are ensured through experiments.Thirdly, for poor optimizing shortcomings of discrete particle swarm algorithm, an improved discrete particle swarm algorithm is proposed. The elite group and adaptive mutation strategies are introduced to enhance the optimizing capability of the algorithm, the elite group is made up of several high-fitness particles; mutation probabilities are adaptive and ensured by the particles' concentration. Experiments show that comparing with single genetic algorithm and discrete particle swarm algorithm the mirrored stack filters optimizing by the improved digital particle swarm algorithm do well in keeping the details of the original images.Fourthly, considering the effect of the initial swarm to the searching capability of algorithm, genetic algorithm which demands less of initial swarm is explored, the crossover operation which is the main effective factor of the algorithm is improved: new particles are generated by crossing fine particles and poor particles which are with larger similarity and with lower fitness compared with the fine particles, the similarities of particles are measured by Hamming distances. Experiments show that comparing with improved discrete particle swarm algorithm the mirrored stack filters optimizing by the improved genetic algorithm pose higher capability of ereasing the noise of the original images.Finally, in order to increase diversity of swarm and effectively enhance the global optimization performance, clonal selection algorithm is studied. The improvement is as follow: polyclonal operator is introduced to memory group, the reorganization of the polyclonal operator adopts the thought of crossover operator in improved genetic algorithm; monoclonal operator is introduced to reservation group and the mutation of the monoclonal operator adopts the adaptive mutation strategy in the improved discrete particle swarm optimization algorithm, in addition there are exchanges of information between the two groups to avoid late evolutionary stagnation. Experiments show that comparing with improved genetic algorithm and improved discrete particle swarm algorithm capabilities of ereasing noise and keeping details of original images of stack filters optimizing by improved clonal selection algorithm are balanced.