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Keywords
(8)
Distributed Modelling
Frequency Domain
Indexing Terms
Markov Chain Monte Carlo
Random Sampling
Source Separation
Stochastic Equation
Metropolis Hastings
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Adaptive Langevin Sampler for Separation of tDistribution Modelled Astrophysical Maps
Adaptive Langevin Sampler for Separation of tDistribution Modelled Astrophysical Maps,10.1109/TIP.2010.2048613,IEEE Transactions on Image Processing,
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Adaptive Langevin Sampler for Separation of tDistribution Modelled Astrophysical Maps
(
Citations: 2
)
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Koray Kayabol
,
Ercan E. Kuruoglu
,
José Luis Sanz
,
Bülent Sankur
,
Emanuele Salerno
,
Diego Herranz
We propose to model the image differentials of astrophysical source maps by Student's tdistribution 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 tdistribution 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. 23572368, 2010
DOI:
10.1109/TIP.2010.2048613
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Citation Context
(2)
...First order derivativebased 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 derivativebased methods, where, in the present estimation problem, we have provided an improvement, by modifying the Hessian algorithm presented in [3] in the sense ...
Cornelia Vacar
,
et 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 tdistributions [
9
]...
...We exploit the nonstationary 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 tdistribution image model previously proposed in [
9
] using the nonstationary 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 MetropolisHastings scheme pixelbypixel as in [
9
]...
Koray Kayaboland
,
et al.
Nonstationary tDistribution Prior for Image Source Separation from B...
References
(31)
Bayesian Separation of Images Modeled With MRFs Using MCMC
(
Citations: 8
)
Koray Kayabol
,
Ercan E. Kuruoglu
,
Bülent Sankur
Journal:
IEEE Transactions on Image Processing
, vol. 18, no. 5, pp. 982994, 2009
THE THREE EASY ROUTES TO INDEPENDENT COMPONENT ANALYSIS; CONTRASTS AND GEOMETRY
(
Citations: 40
)
JeanFrancois Cardoso
Conference:
Independent Component Analysis  ICA
, 2001
On the probable error of a mean
(
Citations: 103
)
Willeam Sealy Gosset
Spatial applications of Markov chain Monte Carlo for Bayesian inference
(
Citations: 10
)
D. Higdon
Published in 1994.
Variational Bayesian Image Restoration Based on a Product of tDistributions Image Prior
(
Citations: 17
)
Giannis K. Chantas
,
Nikolaos Galatsanos
,
Aristidis Likas
,
Michael Saunders
Journal:
IEEE Transactions on Image Processing
, vol. 17, no. 10, pp. 17951805, 2008
Sort by:
Citations
(2)
Langevin and hessian with fisher approximation stochastic sampling for parameter estimation of structured covariance
(
Citations: 1
)
Cornelia Vacar
,
JeanFrancois Giovannelli
,
Yannick Berthoumieu
Conference:
International Conference on Acoustics, Speech, and Signal Processing  ICASSP
, pp. 39643967, 2011
Nonstationary tDistribution Prior for Image Source Separation from Blurred Observations
Koray Kayaboland
,
Ercan E. Kuruoglu
Conference:
Independent Component Analysis  ICA
, pp. 506513, 2010