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A shape-derivative approach to some PDE model in image restoration. (English) Zbl 1397.49055

This paper is devoted to the analysis of shape derivative of certain functionals arising in image restoration, whose main feature is that it involves a variable exponent. A detailed introduction is given. Preliminaries on variable exponent Lebesgue and Sobolev spaces are collected in Section 2. The main result, Theorem 3.9 on the differentiability of the cost functional, is proved in Section 3. The second main result, Theorem 4.6, on the improvement of the formula for the derivative of the functional, is proved in Section 4. An appendix on some \(\Gamma\)-convergence results is given at the end as Section 5.

MSC:

49Q10 Optimization of shapes other than minimal surfaces
49J45 Methods involving semicontinuity and convergence; relaxation
68U10 Computing methodologies for image processing
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
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References:

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