Geodesic
An alternative approach towards the higher order denoising of images. Analytical aspects
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 45, Tome 444 (2016), pp. 47-88

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We investigate theoretical aspects of a variational model for the denoising of images which can be interpreted as a substitute for a higher order approach. In this model, the smoothness term that usually involves the highest derivatives is replaced by a mixed expression for a second unknown function in which only derivatives of lower order occur. Our main results concern existence and uniqueness as well as the regularity properties of the solutions to this variational problem established under various assumptions imposed on the growth rates of the different parts of the energy functional. Bibliography: 56 titles. 
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     title = {An alternative approach towards the higher order denoising of images. {Analytical} aspects},
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M. Bildhauer; M. Fuchs; J. Weickert. An alternative approach towards the higher order denoising of images. Analytical aspects. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 45, Tome 444 (2016), pp. 47-88. http://geodesic.mathdoc.fr/item/ZNSL_2016_444_a2/