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Functions of bounded variation, wavelets, and applications to image processing

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Functions of bounded variation, wavelets, and applications to image processing

Morgante, Anthony (2006) Functions of bounded variation, wavelets, and applications to image processing. Masters thesis, Concordia University.

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Abstract

A common problem in image processing is to decompose an observed image f into a sum u + v , where u represents the more vital features of the image, i.e. the objects, and v represents the textured areas and any noise that may be present. The benefit of such a decomposition is that the " u " component represents a compressed and noise reduced version of the original image f . The space BV of functions of bounded variation has been known to work very well as a model space for the objects in an image because indicator functions of sets whose boundary is finite in length belong to BV . This thesis is aimed at investigating the mathematical properties of the space BV while looking at a very well known "u+v" model, called the ROF model, in which it is assumed that u ✹ BV . More recent work has shown that the optimal pair ( u,v ) to many decomposition problems can be obtained by expanding a given image f into a wavelet basis and performing simple operations on the wavelet coefficients. This thesis will provide a detailed introduction to the theory of orthonormal wavelets, giving some important examples of their effectiveness, as well as showing comparisons of wavelet bases with classical Fourier series

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Morgante, Anthony
Pagination:vi, 69 leaves : ill. ; 29 cm.
Institution:Concordia University
Degree Name:M. Sc.
Program:Mathematics and Statistics
Date:2006
Thesis Supervisor(s):Dafni, Galia
ID Code:8994
Deposited By:Concordia University Libraries
Deposited On:18 Aug 2011 14:41
Last Modified:18 Aug 2011 14:59
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