Euler's Approximations to Image Reconstruction

In this paper we present a new method to reconstruction of images with additive Gaussian noise. In order to solve this inverse problem we use stochastic differential equations with reflecting boundary (in short reflected SDEs). The continuous model of the image denoising is expressed in terms of such equations. The reconstruction algorithm is based on Euler's approximations of solutions to reflected SDEs. We consider a classical Euler scheme with random terminal time and controlled parameter of diffusion. The reconstruction time of our method is substantially reduced in comparison with classical Euler's scheme. Our numerical experiments show that the new algorithm gives very good results and compares favourably with other image denoising filters.