The transfer of distributions by LULU smoothers

Simple item page
dc.contributor.advisorRohwer, C. H.
dc.contributor.authorButler, Pieter-Willem
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.
dc.date.accessioned2008-11-27T09:18:21Zen_ZA
dc.date.accessioned2010-06-01T09:02:37Z
dc.date.available2008-11-27T09:18:21Zen_ZA
dc.date.available2010-06-01T09:02:37Z
dc.date.issued2008-12
dc.descriptionThesis (MSc (Mathematics))--Stellenbosch University, 2008.
dc.description.abstractLULU 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.en
dc.identifier.urihttp://hdl.handle.net/10019.1/2962
dc.language.isoen
dc.publisherStellenbosch : Stellenbosch University
dc.rights.holderStellenbosch University
dc.subjectDiscrete pulse transformen
dc.subjectDistribution transferen
dc.subjectMedianen
dc.subjectDissertations -- Mathematicsen
dc.subjectTheses -- Mathematicsen
dc.subjectDigital filters (Mathematics)en
dc.subjectFilters (Mathematics)en
dc.subjectTheory of distributions (Functional analysis)en
dc.subjectLULU smoothersen
dc.subjectNonlinear smoothersen
dc.subjectDiscrete pulse transormen
dc.subjectDistribution transferen
dc.titleThe transfer of distributions by LULU smoothersen
dc.typeThesis
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
butler_transfer_2008.pdf
Size:
630.24 KB
Format:
Adobe Portable Document Format
Description:
Download
Collections
Masters Degrees (Mathematical Sciences)