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Image inpainting with energies of linear growth. A collection of proposals. (English. Russian original) Zbl 1302.49004
J. Math. Sci., New York 196, No. 4, 490-497 (2014); translation from Probl. Mat. Anal. 74, 45-50 (2013).
Summary: We discuss different variants of the so-called total variation image inpainting method collecting existence and regularity results related to the proposed techniques. As a new feature we give an interpretation of a boundary value problem in the class of \(L^\infty\)-data. We use an averaging process and pass to the limit.

MSC:
49J20 Existence theories for optimal control problems involving partial differential equations
49N60 Regularity of solutions in optimal control
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
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