Fast algorithms for analyzing and designing weighted median filters

Abstract

In this paper, two fast algorithms are developed to compute a set of parameters, called M i 's, of weighted median filters for integer weights and real weights, respectively. The M i 's, which characterize the statistical properties of weighted median filters and are the critical parameters in designing optimal weighted median filters, are defined as the cardinality of the positive subsets of weighted median filters. The first algorithm, which is for integer weights, is about four times faster than the existing algorithm. The second algorithm, which applies for real weights, reduces the computational complexity significantly for many applications where the symmetric weight structures are assumed. Applications of these new algorithms include design of optimal weighted filters, computations of the output distributions, the output moments, and the rank selection probabilities, and evaluation of noise attenuation for weighted median filters.