Multiresolution permutation filters based on decision trees

Abstract

Permutation filters are a broad class of nonlinear selection filters that utilize the complete spatial and rank order information of observation samples. The application of permutation filters is limited by the factorial growth in the number of spatial-rank orderings. Although M-permutation filters, which consider the spatial-rank ordering of a fixed sample subset, have been developed to address the growth in orderings, this method requires an a priori selection of samples that is uniformly applied. This uniform application is not appropriate in most cases. We develop a more general multiresolution approach based on decision trees. This implementation allows the level of ordering information utilized to automatically adjust to the problem at hand. Optimization procedures are developed for this method and simulation results illustrating its advantages are presented.