## 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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### References:

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