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Keywords = splitting Gibbs measure

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12 pages, 288 KiB  
Article
Extremality of Disordered Phase of λ-Model on Cayley Trees
by Farrukh Mukhamedov
Algorithms 2022, 15(1), 18; https://doi.org/10.3390/a15010018 - 3 Jan 2022
Cited by 14 | Viewed by 2382
Abstract
In this paper, we consider the λ-model for an arbitrary-order Cayley tree that has a disordered phase. Such a phase corresponds to a splitting Gibbs measure with free boundary conditions. In communication theory, such a measure appears naturally, and its extremality is [...] Read more.
In this paper, we consider the λ-model for an arbitrary-order Cayley tree that has a disordered phase. Such a phase corresponds to a splitting Gibbs measure with free boundary conditions. In communication theory, such a measure appears naturally, and its extremality is related to the solvability of the non-reconstruction problem. In general, the disordered phase is not extreme; hence, it is natural to find a condition for their extremality. In the present paper, we present certain conditions for the extremality of the disordered phase of the λ-model. Full article
27 pages, 9722 KiB  
Article
Bayesian Activity Estimation and Uncertainty Quantification of Spent Nuclear Fuel Using Passive Gamma Emission Tomography
by Ahmed Karam Eldaly, Ming Fang, Angela Di Fulvio, Stephen McLaughlin, Mike E. Davies, Yoann Altmann and Yves Wiaux
J. Imaging 2021, 7(10), 212; https://doi.org/10.3390/jimaging7100212 - 14 Oct 2021
Cited by 4 | Viewed by 2869
Abstract
In this paper, we address the problem of activity estimation in passive gamma emission tomography (PGET) of spent nuclear fuel. Two different noise models are considered and compared, namely, the isotropic Gaussian and the Poisson noise models. The problem is formulated within a [...] Read more.
In this paper, we address the problem of activity estimation in passive gamma emission tomography (PGET) of spent nuclear fuel. Two different noise models are considered and compared, namely, the isotropic Gaussian and the Poisson noise models. The problem is formulated within a Bayesian framework as a linear inverse problem and prior distributions are assigned to the unknown model parameters. In particular, a Bernoulli-truncated Gaussian prior model is considered to promote sparse pin configurations. A Markov chain Monte Carlo (MCMC) method, based on a split and augmented Gibbs sampler, is then used to sample the posterior distribution of the unknown parameters. The proposed algorithm is first validated by simulations conducted using synthetic data, generated using the nominal models. We then consider more realistic data simulated using a bespoke simulator, whose forward model is non-linear and not available analytically. In that case, the linear models used are mis-specified and we analyse their robustness for activity estimation. The results demonstrate superior performance of the proposed approach in estimating the pin activities in different assembly patterns, in addition to being able to quantify their uncertainty measures, in comparison with existing methods. Full article
(This article belongs to the Special Issue Inverse Problems and Imaging)
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