Efficient Markov chain Monte Carlo sampling for electrical impedance tomography
Journal Title: Computer Assisted Methods in Engineering and Science - Year 2014, Vol 21, Issue 3
Abstract
This paper studies electrical impedance tomography (EIT) using Bayesian inference [1]. The resulting posterior distribution is sampled by Markov chain Monte Carlo (MCMC) [2]. This paper studies a toy model of EIT as the one presented in [3], and focuses on efficient MCMC sampling for this model. First, this paper analyses the computation of forward map of EIT which is the bottleneck of each MCMC update. The forward map is computed by the finite element method [4]. Here its exact computation was conducted up to five times more efficient, by updating the Cholesky factor of the stiffness matrix [5]. Since the forward map computation takes up nearly all the CPU time in each MCMC update, the overall efficiency of MCMC algorithms can be improved almost to the same amount. The forward map can also be computed approximately by local linearisation, and this approximate computation is much more efficient than the exact one. Without loss of efficiency, this approximate computation is more accurate here, after a log transformation is introduced into the local linearisation process. Later on, this improvement of accuracy will play an important role when the approximate computation of forward map will be employed for devising efficient MCMC algorithms. Second, the paper presents two novel MCMC algorithms for sampling the posterior distribution in the toy model of EIT. The two algorithms are made within the 'multiple prior update' [6] and 'the delayed-acceptance Metropolis-Hastings' [7] schemes respectively. Both of them have MCMC proposals that are made of localized updates, so that the forward map computation in each MCMC update can be made efficient by updating the Cholesky factor of the stiffness matrix. Both algorithms' performances are compared to that of the standard single-site Metropolis [8], which is considered hard to surpass [3]. The algorithm of 'multiple prior update' is found to be six times more efficient, while 'the delayed-acceptance Metropolis-Hastings' with single-site update is at least twice more efficient.
Authors and Affiliations
Erfang Ma
Keywords
Related Articles
- EP ID EP73497
- DOI -
- Views 194
- Downloads 0
Coupling of CFD and lumped parameter codes for thermal-hydraulic simulations of reactor containment
The work deals with thermal-hydraulic analyses of a pressurized water reactor containment response to accidents caused by a rupture of primary circuit. The in-house system computer code HEPCAL-AD and CFD ANSYS Fluent hav...
Computational mechanics of multiphase materials-modeling strategies at different scales
The paper addresses various scale-bridging modeling and discretization strategies for multiphase porous materials, starting with a micromechanics model for ion transport within the pore space to generate homogenized diff...
Mesh-free methods and time integrations for transient heat conduction
The paper deals with transient heat conduction in functionally gradient materials. The spatial variation of the temperature field is approximated by using alternatively two various mesh free approximations, while the tim...
Improved two-dimensional cracked finite element for crack fault diagnosis
In this paper the two-dimensional finite element with an embedded edge crack proposed by Potirniche et al. (2008) is improved further for crack depth ratios ranging up to 0.9 and for predicting the natural frequency of a...
MPCA for flight dynamics parameters determination
Aircraft have become increasingly costly and complex. Military and civil pilots and engineers have used flight simulators in order to increase safety of flight through the training of crew. It is necessary to calibrate t...