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On Backward p(x)-Parabolic Equations for Image Enhancement
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-3324-2298
Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
2015 (English)In: Numerical Functional Analysis and Optimization, ISSN 0163-0563, E-ISSN 1532-2467, Vol. 36, no 2, 147-168 p.Article in journal (Refereed) Published
Abstract [en]

In this study, we investigate the backward p(x)-parabolic equation as a new methodology to enhance images. We propose a novel iterative regularization procedure for the backward p(x)-parabolic equation based on the nonlinear Landweber method for inverse problems. The proposed scheme can also be extended to the family of iterative regularization methods involving the nonlinear Landweber method. We also investigate the connection between the variable exponent p(x) in the proposed energy functional and the diffusivity function in the corresponding Euler-Lagrange equation. It is well known that the forward problems converges to a constant solution destroying the image. The purpose of the approach of the backward problems is twofold. First, solving the backward problem by a sequence of forward problems we obtain a smooth image which is denoised. Second, by choosing the initial data properly we try to reduce the blurriness of the image. The numerical results for denoising appear to give improvement over standard methods as shown by preliminary results.

Place, publisher, year, edition, pages
Taylor & Francis, 2015. Vol. 36, no 2, 147-168 p.
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-111581DOI: 10.1080/01630563.2014.970643ISI: 000346249200002OAI: oai:DiVA.org:liu-111581DiVA: diva2:758277
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VIDI
Available from: 2014-10-26 Created: 2014-10-26 Last updated: 2017-12-05

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Baravdish, GeorgeSvensson, OlofÅström, Freddie

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Baravdish, GeorgeSvensson, OlofÅström, Freddie
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Communications and Transport SystemsThe Institute of TechnologyComputer VisionCenter for Medical Image Science and Visualization (CMIV)
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Numerical Functional Analysis and Optimization
Mathematical Analysis

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