Thesis (MSc (Mathematics))--Stellenbosch University, 2008. / 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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/2962 |
| Date | 12 1900 |
| Creators | Butler, Pieter-Willem |
| Contributors | Rohwer, C. H., Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Rights | Stellenbosch University |
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