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We propose a fully practical numerical scheme for the simulation of thestochastic total variation flow (STFV). The approximation is based on a stabletime-implicit finite element space-time approximation of a regularized STVFequation. The approximation also involves a finite dimensional discretizationof the noise that makes the scheme fully implementable on physical hardware. Weshow that the proposed numerical scheme converges to a solution that is definedin the sense of stochastic variational inequalities (SVIs). As a by product ofour convergence analysis we provide a generalization of the concept ofprobabilistically weak solutions of stochastic partial differential equation(SPDEs) to the setting of SVIs. We also prove convergence of the numericalscheme to a probabilistically strong solution in probability if pathwiseuniqueness holds. We perform numerical simulations to illustrate the behaviorof the proposed numerical scheme {as well as its non-conforming variant} in thecontext of image denoising.

Numerical approximation of probabilistically weak and strong solutions of the stochastic total variation flow