This article is cited in 3 papers

Pattern Recognition

Application of Gibbs Random Fields Methods to Image Denoising Problems

X. Decombes^a, E. A. Zhizhina<sup>b

a</sup> French National Institute for Research in Computer Science and Automatic Control (INRIA), IRISA
^b Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: In this paper, we address the problem of image denoising using a stochastic differential equation approach. Proposed stochastic dynamics schemes are based on the property of diffusion dynamics to converge to a distribution on global minima of the energy function of the model, under a special cooling schedule (the annealing procedure). To derive algorithms for computer simulations, we consider discrete-time approximations of the stochastic differential equation. We study convergence of the corresponding Markov chains to the diffusion process. We give conditions for the ergodicity of the Euler approximation scheme. In the conclusion, we compare results of computer simulations using the diffusion dynamics algorithms and the standard Metropolis–Hasting algorithm. Results are shown on synthetic and real data.

UDC: 621.391.1:519.2

Received: 06.05.2003
Revised: 06.05.2004

 English version: Problems of Information Transmission, 2004, 40:3, 279–295

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