an:07139975
Zbl 1427.94013
Fuchs, M.; Weickert, J.
Iterative TV-regularization of grey-scale images
EN
J. Math. Sci., New York 242, No. 2, 323-336 (2019); translation from Probl. Mat. Anal. 99, 127-137 (2019).
1072-3374 1573-8795
2019
j
94A08 68U10 49N60
Summary: The TV-regularization method due to \textit{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 \textit{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; \url{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.
0780.49028