Diffusions for global optimizations
SIAM Journal on Control and Optimization
Diffusion for global optimization in Rn
SIAM Journal on Control and Optimization
Cooling schedules for optimal annealing
Mathematics of Operations Research
Constrained Restoration and the Recovery of Discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: A Mathematical Introduction (Stochastic Modelling and Applied Probability)
Global optimization by adapted diffusion
IEEE Transactions on Signal Processing
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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.