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Iterative TV-regularization of grey-scale images. (English. Russian original) Zbl 1427.94013
J. Math. Sci., New York 242, No. 2, 323-336 (2019); translation from Probl. Mat. Anal. 99, 127-137 (2019).
Summary: The TV-regularization method due to L. I. Rudin et al. [Physica D 60, No. 1–4, 259–268 (1992; Zbl 0780.49028)] is widely used in mathematical image analysis. We consider a nonstationary and iterative variant of this approach and provide a mathematical theory that extends the results of E. Radmoser et al. to the BV setting [“Scale-space properties of nonstationary iterative regularization methods”, J. Vis. Commun. Image Represent. 11, No. 2, 96–114 (2000; doi:10.1006/jvci.1999.0437)]. While existence and uniqueness, a maximum-minimum principle, and preservation of the average grey value are not hard to prove, we also establish the convergence to a constant steady state and consider a large family of Lyapunov functionals. These properties allow us to interpret the iterated TV-regularization as a time-discrete scale-space representation of the original image.
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
68U10 Computing methodologies for image processing
49N60 Regularity of solutions in optimal control
Full Text: DOI
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