Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Theoretical Foundations of Anisotropic Diffusion in Image Processing
Proceedings of the 7th TFCV on Theoretical Foundations of Computer Vision
Stochastic Motion and the Level Set Method in Computer Vision: Stochastic Active Contours
International Journal of Computer Vision
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Smoothing, enhancing filters in terms of backward stochastic differential equations
ICCVG'10 Proceedings of the 2010 international conference on Computer vision and graphics: Part I
Stochastic differential equations and geometric flows
IEEE Transactions on Image Processing
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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.