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A variational approach to the denoising of images based on different variants of the TV-regularization. (English) Zbl 1260.49074
The purpose of this short paper is to investigate the existence and the regularity of solutions for some variational problems related to varational partial differential methods used in image recovery. Loosely speaking, one has to reconstruct an original image from an observed pattern, and the technique to this end is to minimize a functional in the form of an integral which defines the quality of the data fitting. The authors consider successively nearly linear growth and linear growth and in each case they state some convergence properties for the approximation of the solution.

MSC:
49N90 Applications of optimal control and differential games
49N60 Regularity of solutions in optimal control
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
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