BOOLEAN DERIVATIVES, WEIGHTED CHOW PARAMETERS, AND SELECTION PROBABILITIES OF STACK FILTERS

In the present paper, the theory of Boolean derivatives, the activitie s of the arguments of a BF, and Chow parameters are studied from the p oint of view of their application in the statistical analysis of a cla ss of nonlinear filters-stack filters, The connection between the part ial derivatives of a positive BF (PBF) and the selection probabilities of stack filters is established, The notions of the weighted activiti es of the variables of the PBF and weighted Chow parameters are introd uced for the analysis, the computation of the joint selection probabil ity matrix, and the sample selection probability vector of a continuou s stack filter, Spectral approaches to the selection probabilities of stack filters are derived, In particular, spectral algorithms with com putational complexity O(2(N)), where N is the number of input samples within an input window, are given for the computation of sample select ion probability vectors, The difference of the spectral algorithms pre sented here from the nonspectral ones is that spectral algorithms are universal, i.e., their complexities are independent of the PBF, which is used as the base for stack filtering. They are also straightforward to implement, and fast spectral transforms exist.