Numerical Approximation of the Stochastic Total Variation Flow

Explore a 43-minute conference talk on the numerical approximation of the stochastic total variation flow (STVF), presented by Martin Ondreját at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the proposed fully practical numerical schemes for simulating STVF, based on joint work with L. Baňas. Discover the stable time-implicit finite element space-time approximation of a regularized STVF equation and the finite dimensional discretization of noise for implementable solutions. Learn about the convergence of the numerical scheme to solutions defined by stochastic variational inequalities (SVIs) and the generalization of probabilistically weak solutions of stochastic partial differential equations (SPDEs) to SVIs. Examine the conditions for convergence to probabilistically strong solutions and witness numerical simulations illustrating the behavior of the proposed scheme and its non-conforming variant in image denoising applications.