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On Backward p(x)-Parabolic Equations for Image Enhancement
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- Baravdish, George (author)
- Linköpings universitet,Kommunikations- och transportsystem,Tekniska högskolan
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- Svensson, Olof (author)
- Linköpings universitet,Kommunikations- och transportsystem,Tekniska högskolan
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- Åström, Freddie (author)
- Linköpings universitet,Datorseende,Tekniska högskolan,Centrum för medicinsk bildvetenskap och visualisering, CMIV
- (creator_code:org_t)
- 2014-12-10
- 2015
- English.
- In: Numerical Functional Analysis and Optimization. - : Taylor & Francis. - 0163-0563 .- 1532-2467. ; 36:2, s. 147-168
- Journal article (peer-reviewed)
Abstract
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
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- ref (subject category)
- art (subject category)
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