Document Type Master's Dissertation Author Fabris-Rotelli, Inger Nicolette firstname.lastname@example.org URN etd-08172010-183206 Document Title LULU operators on multidimensional arrays and applications Degree MSc Department Mathematics and Applied Mathematics Supervisor
Advisor Name Title Prof R Anguelov Supervisor Keywords
- LULU operators
Date 2010-04-16 Availability unrestricted AbstractThe 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.
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Please cite as follows:
Fabris-Rotelli, IN 2009, LULU operators on multidimensional arrays and applications, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://upetd.up.ac.za/thesis/available/etd-08172010-183206/ >
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