Dariusz Borkowski

Smoothing, enhancing filters in terms of backward stochastic differential equations

In this paper we propose a novel approach for reconstruction of images with additive Gaussian noise. In order to solve this inverse problem we use backward stochastic differential equations. Model of the image reconstruction is driven by two stochastic processes. One process has values in domain of the image, and second one in codomain. Appropriate construction of these processes leads to smoothing (anisotropic diffusion) and enhancing filters. Our numerical experiments show that the new algorithm gives very good results and compares favourably with classical Perona-Malik method.

Modified diffusion to Image Denoising

In this paper a novel approach for image denoising using stochastic differential equations (SDEs) is presented. In proposed method a controlled parameter to Euler’s approximations of solutions to SDEs with reflecting boundary is added. It is shown that modified diffusion gives very good results for Gaussian noise source models and compares favourably with other image denoising filters.

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 Eulers 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 Eulers scheme. Our numerical experiments show that the new algorithm gives very good results and compares favourably with other image denoising filters.

Application of backward stochastic differential equations to reconstruction of vector-valued images

In this paper we explore the problem of reconstruction of vector-valued images with additive Gaussian noise. In order to solve this problem we use backward stochastic differential equations. Our numerical experiments show that the new approach gives very good results and compares favourably with deterministic partial differential equation methods.

Stochastic Approximation to Reconstruction of Vector-Valued Images

In this paper we present a new method of reconstruction of vector-valued images with additive Gaussian noise. In order to solve this inverse problem we use stochastic differential equations with reflecting boundary. The reconstruction algorithm is based on Euler’s approximations of solutions of such equations. We consider Euler scheme with random terminal time and controlled parameter of diffusion which is driven by geometry of \(\mathbf R^n\)- valued noisy image. Our numerical experiments show that the new approach gives very good results and compares favourably with deterministic partial differential equation methods.

Image Restoration Using Anisotropic Stochastic Diffusion Collaborated with Non Local Means

In this paper we explore the problem of the reconstruction of images with additive Gaussian noise. In order to solve this inverse problem we use stochastic differential equations with reflecting boundary and famous non local means algorithm. Expressing anisotropic diffusion in terms of stochastic equations allows us to adapt the concept of similarity patches used in non local means. This novel look on the reconstruction problem is fruitful, gives encouraging results and compares favourably with other image denoising filters.

Image Denoising Using Backward Stochastic Differential Equations

In this paper we explore the problem of reconstruction of RGB images with additive Gaussian noise. In order to solve this problem we use backward stochastic differential equations. The reconstructed image is characterized by smoothing noisy pixels and at the same time enhancing and sharpening edges. This novel look on the reconstruction is fruitful, gives encouraging results and can be successfully applied to denoising of high ISO images.

Random NL-Means to Restoration of Colour Images

In this paper we propose a new method of denoising of colour images. We use non local means algorithm considered on non square searching window which is driven by anisotropic stochastic process. This modification allow us to adapt the idea from famous non local means and anisotropic diffusion approaches. Experimental results show that this new method gives encouraging results and can be successfully applied to denoising of high ISO images.

Feynman-Kac Formula and Restoration of High ISO Images

In this paper we explore the problem of reconstruction of RGB images with additive Gaussian noise. In order to solve this problem we use Feynman-Kac formula and non local means algorithm. Expressing the problem in stochastic terms allows us to adapt to anisotropic diffusion the concept of similarity patches used in non local means. This novel look on the reconstruction is fruitful, gives encouraging results and can be successfully applied to denoising of high ISO images.