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Adaptive Langevin Sampler for Separation of t-Distribution Modelled Astrophysical Maps

Adaptive Langevin Sampler for Separation of t-Distribution Modelled Astrophysical Maps,10.1109/TIP.2010.2048613,IEEE Transactions on Image Processing,

Adaptive Langevin Sampler for Separation of t-Distribution Modelled Astrophysical Maps   (Citations: 2)
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We propose to model the image differentials of astrophysical source maps by Student's t-distribution and to use them in the Bayesian source separation method as priors. We introduce an efficient Markov Chain Monte Carlo (MCMC) sampling scheme to unmix the astrophysical sources and describe the derivation details. In this scheme, we use the Langevin stochastic equation for transitions, which enables parallel drawing of random samples from the posterior, and reduces the computation time significantly (by two orders of magnitude). In addition, Student's t-distribution parameters are updated throughout the iterations. The results on astrophysical source separation are assessed with two performance criteria defined in the pixel and the frequency domains.
Journal: IEEE Transactions on Image Processing , vol. 19, no. 9, pp. 2357-2368, 2010
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    • ...First order derivative-based samplers have also been employed in [1] and in the recent work [2], but these approaches explore the Hamiltonian MH algorithm, whilst we have studied the Langevin MH. However, our contribution is more significant in the case of the second order derivative-based methods, where, in the present estimation problem, we have provided an improvement, by modifying the Hessian algorithm presented in [3] in the sense ...

    Cornelia Vacaret al. Langevin and hessian with fisher approximation stochastic sampling for...

    • ...The prior densities are constituted by modeling the image differentials in different directions as Multivariate Student’s t-distributions [9]...
    • ...We exploit the non-stationary image model in [10] to extend the method in [9]...
    • ...For estimation of the sources, we use an efficient Markov Chain Monte Carlo (MCMC) sampling method in which we resort to the Langevin stochastic equation [9]...
    • ...In this paper, we extend the stationary t-distribution image model previously proposed in [9] using the non-stationary model proposed in [10]...
    • ...The Maximum Likelihood (ML) estimations of the parameters αl,d, βl,d, δl,d,n, ¯ δl,d and νl,d are obtained using an EM method [9]...
    • ...The derivation details of the equation can be found in [9]...
    • ...The samples produced using (8) are applied to a Metropolis-Hastings scheme pixel-by-pixel as in [9]...

    Koray Kayabolandet al. Non-stationary t-Distribution Prior for Image Source Separation from B...

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