caa a22 4500 60552226X CHVBK 20210128105158.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s10958-015-2237-4 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2237-4 On Some Perturbations of the total variation image inpainting method. Part II: Relaxation and Dual Variational Formulation [Elektronische Daten] [M. Bildhauer, M. Fuchs] We continue the analysis of some strongly elliptic modifications of the total variation image inpainting model formulated in the space BV(Ω) and investigate the corresponding dual variational problems. Remarkable features are the uniqueness of the dual solution and the uniqueness of the absolutely continuous part ∇ a u of the gradient of BV-solutions u on the whole domain. Additionally, any BV-minimizer u automatically satisfies the inequality 0 ≤ u ≤ 1, which means that u measures the intensity of the grey level. Outside of the damaged region we even have the uniqueness of BV-solutions, whereas on the damaged domain the L 2-deviation u − υ L 2 $$ {\left\Vert u-\upsilon \right\Vert}_{L^2} $$ of different solutions is governed by the total variation of the singular part ∇ s (u − υ) of the vector measure ∇(u − υ). Moreover, the dual solution is related to the BV-solutions through an equation of stress-strain type. Bibliography: 23 titles. Springer Science+Business Media New York, 2015 Bildhauer M. Universität des Saarlandes, Fachbereich 6.1 Mathematik Postfach 15 11 50, D-66041, Saarbrücken, Germany aut Fuchs M. Universität des Saarlandes, Fachbereich 6.1 Mathematik Postfach 15 11 50, D-66041, Saarbrücken, Germany aut Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 205/2(2015-02-01), 121-140 1072-3374 205:2<121 2015 205 10958 https://doi.org/10.1007/s10958-015-2237-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2237-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bildhauer M. Universität des Saarlandes, Fachbereich 6.1 Mathematik Postfach 15 11 50, D-66041, Saarbrücken, Germany aut NATIONALLICENCE 700 1- Fuchs M. Universität des Saarlandes, Fachbereich 6.1 Mathematik Postfach 15 11 50, D-66041, Saarbrücken, Germany aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 205/2(2015-02-01), 121-140 1072-3374 205:2<121 2015 205 10958 SWISSBIB 560502303