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Numerical analysis of oscillations in a nonconvex problem related to image selective smoothing


Chipot, M; March, R; Vitulano, D (2001). Numerical analysis of oscillations in a nonconvex problem related to image selective smoothing. Journal of Computational and Applied Mathematics, 136(1-2):123-133.

Abstract

We study some numerical properties of a nonconvex variational problem which arises as the continuous limit of a discrete optimization method designed for the smoothing of images with preservation of discontinuities. The functional that has to be minimized fails to attain a minimum value. Instead, minimizing sequences develop gradient oscillations which allow them to reduce the value of the functional. The oscillations of the gradient exhibit analogies with microstructures in ordered materials. The pattern of the oscillations is analysed numerically by using discrete parametrized measures.

We study some numerical properties of a nonconvex variational problem which arises as the continuous limit of a discrete optimization method designed for the smoothing of images with preservation of discontinuities. The functional that has to be minimized fails to attain a minimum value. Instead, minimizing sequences develop gradient oscillations which allow them to reduce the value of the functional. The oscillations of the gradient exhibit analogies with microstructures in ordered materials. The pattern of the oscillations is analysed numerically by using discrete parametrized measures.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:numerical examples; nonconvex variational problem; discrete optimization method; smoothing of images; preservation of discontinuities; gradient oscillations
Language:English
Date:2001
Deposited On:28 Jun 2010 14:56
Last Modified:05 Apr 2016 13:25
Publisher:Elsevier
ISSN:0377-0427
Publisher DOI:10.1016/S0377-0427(00)00579-3
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0989.65065

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