| bibtype |
J -
Journal Article
|
| ARLID |
0571182 |
| utime |
20240402213828.0 |
| mtime |
20230426235959.9 |
| SCOPUS |
85142299302 |
| WOS |
000959169100009 |
| DOI |
10.1051/m2an/2022089 |
| title
(primary) (eng) |
Numerical approximation of probabilistically weak and strong solutions of the stochastic total variation flow |
| specification |
| page_count |
31 s. |
| media_type |
P |
|
| serial |
| ARLID |
cav_un_epca*0565235 |
| ISSN |
2822-7840 |
| title
|
ESAIM. Mathematical Modelling and Numerical Analysis |
| volume_id |
57 |
| volume |
2 (2023) |
| page_num |
785-815 |
|
| keyword |
stochastic total variation flow |
| keyword |
stochastic variational inequalities |
| keyword |
image processing |
| keyword |
finite element approximation |
| keyword |
tightness in BV spaces |
| author
(primary) |
| ARLID |
cav_un_auth*0260292 |
| name1 |
Ondreját |
| name2 |
Martin |
| institution |
UTIA-B |
| full_dept (cz) |
Stochastická informatika |
| full_dept (eng) |
Department of Stochastic Informatics |
| department (cz) |
SI |
| department (eng) |
SI |
| full_dept |
Department of Stochastic Informatics |
| country |
CZ |
| fullinstit |
Ústav teorie informace a automatizace AV ČR, v. v. i. |
|
| author
|
| ARLID |
cav_un_auth*0323271 |
| name1 |
Baňas |
| name2 |
L. |
| country |
DE |
|
| source |
|
| source |
|
| cas_special |
| project |
| project_id |
GA22-12790S |
| agency |
GA ČR |
| country |
CZ |
| ARLID |
cav_un_auth*0449240 |
|
| abstract
(eng) |
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. |
| result_subspec |
WOS |
| RIV |
BA |
| FORD0 |
10000 |
| FORD1 |
10100 |
| FORD2 |
10103 |
| reportyear |
2024 |
| num_of_auth |
2 |
| inst_support |
RVO:67985556 |
| permalink |
https://hdl.handle.net/11104/0342475 |
| confidential |
S |
| mrcbC91 |
A |
| mrcbT16-e |
MATHEMATICSAPPLIED |
| mrcbT16-j |
1.076 |
| mrcbT16-s |
1.247 |
| mrcbT16-D |
Q1 |
| mrcbT16-E |
Q1 |
| arlyear |
2023 |
| mrcbU14 |
85142299302 SCOPUS |
| mrcbU24 |
PUBMED |
| mrcbU34 |
000959169100009 WOS |
| mrcbU63 |
cav_un_epca*0565235 ESAIM. Mathematical Modelling and Numerical Analysis 57 2 2023 785 815 2822-7840 2804-7214 |
|