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Kim, Yunho
Mathematical Imaging Lab
Research Interests
  • Optimization, inverse problems, convex analysis, calculus of variations, partial differential equations, computational mathematics, medical/biomedical imaging

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IMAGE RECOVERY USING FUNCTIONS OF BOUNDED VARIATION AND SOBOLEV SPACES OF NEGATIVE DIFFERENTIABILITY

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Title
IMAGE RECOVERY USING FUNCTIONS OF BOUNDED VARIATION AND SOBOLEV SPACES OF NEGATIVE DIFFERENTIABILITY
Author
Kim, YunhoVese, Luminita A.
Issue Date
2009-02
Publisher
AMER INST MATHEMATICAL SCIENCES
Citation
INVERSE PROBLEMS AND IMAGING, v.3, no.1, pp.43 - 68
Abstract
In this work we wish to recover an unknown image from a blurry, or noisy-blurry version. We solve this inverse problem by energy minimization and regularization. We seek a solution of the form u + v, where u is a function of bounded variation (cartoon component), while v is an oscillatory component (texture), modeled by a Sobolev function with negative degree of differentiability. We give several results of existence and characterization of minimizers of the proposed optimization problem. Experimental results show that this cartoon + texture model better recovers textured details in natural images, by comparison with the more standard models where the unknown is restricted only to the space of functions of bounded variation.
URI
https://scholarworks.unist.ac.kr/handle/201301/8932
DOI
10.3934/ipi.2009.3.43
ISSN
1930-8337
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