The transfer of distributions by LULU smoothers

Date
2008-12
Authors
Butler, Pieter-Willem
Journal Title
Journal ISSN
Volume Title
Publisher
Stellenbosch : Stellenbosch University
Abstract
LULU smoothers is a class of nonlinear smoothers and they are compositions of the maximum and minimum operators. By analogy to the discrete Fourier transform and the discrete wavelet transform, one can use LULU smoothers to create a nonlinear multiresolution analysis of a sequence with pulses. This tool is known as the Discrete Pulse Transform (DPT). Some research have been done into the distributional properties of the LULU smoothers. There exist results on the distribution transfers of the basic LULU smoothers, which are the building blocks of the discrete pulse transform. The output distributions of further smoothers used in the DPT, in terms of input distributions, has been a challenging problem. We motivate the use of these smoothers by first considering linear filters as well as the median smoother, which has been very popular in signal and image processing. We give an overview of the attractive properties of the LULU smoothers after which we tackle their output distributions. The main result is the proof of a recursive formula for the output distribution of compositions of LULU smoothers in terms of a given input distribution.
Description
Thesis (MSc (Mathematics))--Stellenbosch University, 2008.
Keywords
Discrete pulse transform, Distribution transfer, Median, Dissertations -- Mathematics, Theses -- Mathematics, Digital filters (Mathematics), Filters (Mathematics), Theory of distributions (Functional analysis), LULU smoothers, Nonlinear smoothers, Discrete pulse transorm, Distribution transfer
Citation