In this paper we propose a novel approach for reduction of JPEG artifacts using advanced techniques of stochastic calculus. In order to solve this problem we use backward stochastic differential equations (in short BSDEs) and the non local means method. In our algorithm we consider two processes. One of them has values in the image domain and determines pixels that will be involved in the reconstruction, the second one has values in the image codomain and gives weight to values of pixels. To

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... culate the weights, we use the idea of the patches similarity used in the non local means. Our experiments show that the new approach gives very good results and compares favourably with other methods.