0571182 20240402213828.020230426235959.9 85142299302 000959169100009 10.1051/m2an/2022089 31 s. P cav_un_epca*05652352822-7840572 (2023)785-815 stochastic total variation flow stochastic variational inequalities image processing finite element approximation tightness in BV spaces cav_un_auth*0260292 Ondreját Martin UTIA-B Stochastická informatika Department of Stochastic Informatics SI SI Department of Stochastic Informatics CZ Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0323271 Baňas L. DE http://library.utia.cas.cz/separaty/2023/SI/ondrejat-0571182.pdf https://www.esaim-m2an.org/articles/m2an/abs/2023/02/m2an220087/m2an220087.html GA22-12790S GA ČR CZ cav_un_auth*0449240 We propose a fully practical numerical scheme for the simulation of the stochastic total variation flow (STVF). The approximation is based on a stable time-implicit finite element space-time approximation of a regularized STVF equation. The approximation also involves a finite dimensional discretization of the noise that makes the scheme fully implementable on physical hardware. We show that the proposed numerical scheme converges in law to a solution that is defined in the sense of stochastic variational inequalities (SVIs). Under strengthened assumptions the convergence can be show to holds even in probability. As a by product of our convergence analysis we provide a generalization of the concept of probabilistically weak solutions of stochastic partial differential equation (SPDEs) to the setting of SVIs. We also prove convergence of the numerical scheme to a probabilistically strong solution in probability if pathwise uniqueness holds. We perform numerical simulations to illustrate the behavior of the proposed numerical scheme as well as its non-conforming variant in the context of image denoising. WOS BA 10000 10100 10103 2024 2 RVO:67985556 https://hdl.handle.net/11104/0342475 S Article Mathematics Applied A MATHEMATICS.APPLIED 2 0.5 9 0.00407 1.076 2906 85 1.247 41.28 1.86 576 Q1 2.000 116 Q1 84.2 Q1 Q1 1 Q2 84.2 2023 85142299302 SCOPUS PUBMED 000959169100009 WOS cav_un_epca*0565235 ESAIM. Mathematical Modelling and Numerical Analysis 57 2 2023 785 815 2822-7840 2804-7214