1,844 research outputs found
A Hierarchical Bayesian Model for Frame Representation
In many signal processing problems, it may be fruitful to represent the
signal under study in a frame. If a probabilistic approach is adopted, it
becomes then necessary to estimate the hyper-parameters characterizing the
probability distribution of the frame coefficients. This problem is difficult
since in general the frame synthesis operator is not bijective. Consequently,
the frame coefficients are not directly observable. This paper introduces a
hierarchical Bayesian model for frame representation. The posterior
distribution of the frame coefficients and model hyper-parameters is derived.
Hybrid Markov Chain Monte Carlo algorithms are subsequently proposed to sample
from this posterior distribution. The generated samples are then exploited to
estimate the hyper-parameters and the frame coefficients of the target signal.
Validation experiments show that the proposed algorithms provide an accurate
estimation of the frame coefficients and hyper-parameters. Application to
practical problems of image denoising show the impact of the resulting Bayesian
estimation on the recovered signal quality
Adaptive Langevin Sampler for Separation of t-Distribution Modelled Astrophysical Maps
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.Comment: 12 pages, 6 figure
Loopy belief propagation and probabilistic image processing
Estimation of hyperparameters by maximization of the marginal likelihood in probabilistic image processing is investigated by using the cluster variation method. The algorithms are substantially equivalent to generalized loopy belief propagation
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