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The transfer of distributions by LULU smoothers
Thesis (MSc (Mathematics))--Stellenbosch University, 2008.
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| Format: | Thesis |
| Language: | English |
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Stellenbosch : Stellenbosch University
2008
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| _version_ | 1867613981282140160 |
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| access_status_str | Open Access |
| author | Butler, Pieter-Willem |
| author2 | Rohwer, C. H. |
| author_browse | Butler, Pieter-Willem Rohwer, C. H. |
| author_facet | Rohwer, C. H. Butler, Pieter-Willem |
| author_sort | Butler, Pieter-Willem |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc (Mathematics))--Stellenbosch University, 2008. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/2962 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:44:46.833Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2008 |
| publishDateRange | 2008 |
| publishDateSort | 2008 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/2962 The transfer of distributions by LULU smoothers Butler, Pieter-Willem Rohwer, C. H. Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. 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 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. 2008-11-27T09:18:21Z 2010-06-01T09:02:37Z 2008-11-27T09:18:21Z 2010-06-01T09:02:37Z 2008-12 Thesis http://hdl.handle.net/10019.1/2962 en Stellenbosch University application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | 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 Butler, Pieter-Willem The transfer of distributions by LULU smoothers |
| title | The transfer of distributions by LULU smoothers |
| title_full | The transfer of distributions by LULU smoothers |
| title_fullStr | The transfer of distributions by LULU smoothers |
| title_full_unstemmed | The transfer of distributions by LULU smoothers |
| title_short | The transfer of distributions by LULU smoothers |
| title_sort | transfer of distributions by lulu smoothers |
| topic | 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 |
| url | http://hdl.handle.net/10019.1/2962 |
| work_keys_str_mv | AT butlerpieterwillem thetransferofdistributionsbylulusmoothers AT butlerpieterwillem transferofdistributionsbylulusmoothers |