We propose a fully practical numerical scheme for the simulation of the stochastic total variation flow (STFV). 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 to a solution that is defined in the sense of stochastic variational inequalities (SVIs). 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.

翻译：我们为模拟随机总变异流动(STFV)提出了一个完全实用的数值方案。近似值基于一个稳定的时隐性限元素空间时间近似值,一个常规的STVF方程式。近似值还涉及噪音的有限维分化,使该计划完全可以在物理硬件上实施。我们表明,拟议的数字方案与一个根据随机变异不平等(SVIs)定义的解决方案相融合。作为我们趋同分析的产物,我们为SVI的设置提供了一种一般化概念,即随机偏差部分差方程式(SPDEs)的概率薄弱解决方案概念。我们还证明,如果路径上的独特性存在的话,数字方案有可能与概率强的概率解决方案相融合。我们进行数字模拟,以说明拟议数字方案{及其非成型变方}在图像分解背景下的行为。