The number of cones generated by a multiresolution analysis with a sequence of LULU operators

Abstract

LULU operators provide a simple yet effective nonlinear algorithm, with many desired attributes, to decompose a sequence into unit pulses at ascending resolution levels. This decomposition is however linear on the cone generated by the constituent pulses, with important consequences for image analysis. It is therefore a natural problem to study the number of possible cones that can arise for sequences of a given length. We provide an answer to this combinatorial question, proving that the number of different cones associated with sequences of length n is the central binomial coefficient .