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SIAM J. on Numerical Analysis / Volume 39 / Issue 2

SIAM J. Numer. Anal. 39, pp. 480-498 (19 pages)

New Methods of Controlled Total Variation Reduction for Digital Functions

Ronald R. Coifman and Artur Sowa

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We consider the functional of total variation for functions of either one or two discrete variables. We introduce a new principle for construction of evolution processes that gradually reduce the total variation of a function. The method is derived from analysis of relaxation of the functional along the directions given by the Haar wavelets---an approach that does not require regularization of either the functional or its singular gradient. We further present a rigorous analysis of the analytical properties of the resulting evolution schemes. The purely discrete theory grows out of universal observations about the relation between the total variation and the Haar functions. An additional advantage of the method is that it can be directly implemented as an effective numerical procedure. Moreover, it can be intertwined in a natural way with a nonlinear phase-space filtering which further increases control of the deformation of a signal. Finally, we report that the algorithms can be used as remarkable tools for signal processing and image enhancement.

© 2001 Society for Industrial and Applied Mathematics

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KEYWORDS

AMS Subject Headings

49M05, 68U10

PUBLICATION DATA

ISSN

0036-1429 (print)  
1095-7170 (online)

Publisher

$abstract.society.value is a Member of CrossRef Society for Industrial and Applied Mathematics

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1137/S0036142999362031

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