Original Articles

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

Published in: Quaestiones Mathematicae
Volume 38, issue 2, 2015 , pages: 297–305
DOI: 10.2989/16073606.2014.987903
Author(s): Dirk LaurieDepartment of Mathematical Sciences, South Africa, Carl RohwerDepartment of Mathematical Sciences, South Africa, Stephan WagnerDepartment of Mathematical Sciences, South Africa

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 .

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