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LULU operators on multidimensional arrays and applications
Dissertation (MSc)--University of Pretoria, 2010.
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| Format: | Thesis |
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University of Pretoria
2013
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| _version_ | 1867613526502146048 |
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| access_status_str | Open Access |
| author2 | Anguelov, Roumen |
| author_browse | Anguelov, Roumen |
| author_facet | Anguelov, Roumen |
| collection | Thesis |
| dc_rights_str_mv | © 2009, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Dissertation (MSc)--University of Pretoria, 2010. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/27330 |
| institution | University of Pretoria (South Africa) |
| last_indexed | 2026-06-10T12:37:33.114Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2013 |
| publishDateRange | 2013 |
| publishDateSort | 2013 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/27330 LULU operators on multidimensional arrays and applications Anguelov, Roumen inger.fabris-rotelli@up.ac.za Fabris-Rotelli, Inger Nicolette Lulu operators Signal UCTD Dissertation (MSc)--University of Pretoria, 2010. The LULU operators, Ln and Un, are smoothers, that is they smooth data received as a signal. They are nonlinear and this nonlinearity makes them more robust but also more complicated to study since the projection theorem does not hold. Their smoothing action is aimed at removing the impulsive noise present in any received signal. A signal can be of one or two dimensions, or of any higher dimension. In one dimension a signal is represented as a sequence and in two dimensions as an image. Higher dimensions include video feed and other more complex data streams. Carl Rohwer developed the LULU smoothers for sequences over the last three decades and the need for an extension to higher dimensions became more and more obvious as the applications of these smoothers were investigated. Perhaps the most important application is that of the Discrete Pulse Transform which is obtained via recursive application of the smoothers. In this dissertation the extension to dimensions higher than one is presented. All the essential properties developed for the one dimensional smoothers are replicated in this work. In addition, the Discrete Pulse Transform is used to illustrate some simple applications to image smoothing and feature detection. Copyright Mathematics and Applied Mathematics unrestricted 2013-09-07T11:11:26Z 2010-08-17 2013-09-07T11:11:26Z 2010-04-16 2010-08-17 2010-08-17 Dissertation Fabris-Rotelli, IN 2009, LULU operators on multidimensional arrays and applications, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://hdl.handle.net/2263/27330 > E10/419/gm http://hdl.handle.net/2263/27330 http://upetd.up.ac.za/thesis/available/etd-08172010-183206/ © 2009, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | Lulu operators Signal UCTD LULU operators on multidimensional arrays and applications |
| title | LULU operators on multidimensional arrays and applications |
| title_full | LULU operators on multidimensional arrays and applications |
| title_fullStr | LULU operators on multidimensional arrays and applications |
| title_full_unstemmed | LULU operators on multidimensional arrays and applications |
| title_short | LULU operators on multidimensional arrays and applications |
| title_sort | lulu operators on multidimensional arrays and applications |
| topic | Lulu operators Signal UCTD |
| url | http://hdl.handle.net/2263/27330 http://upetd.up.ac.za/thesis/available/etd-08172010-183206/ |