Some approximation methods for Bayesian inversion of electrical impedance tomography

Electrical impedance tomography (EIT) is a non-invasive imaging technique where the conductivity of an object is inferred through measurements on electrodes attached to its surface. EIT is well-known as a highly ill-posed nonlinear inverse problem, where the forward problem is modelled by an ellipti...

Full description

Bibliographic Details
Main Author: Pham, Quang Huy
Other Authors: Hoang Viet Ha
Format: Thesis-Doctor of Philosophy
Language:English
Published: Nanyang Technological University 2024
Subjects:
Online Access:https://hdl.handle.net/10356/173918
_version_ 1826109932560187392
author Pham, Quang Huy
author2 Hoang Viet Ha
author_facet Hoang Viet Ha
Pham, Quang Huy
author_sort Pham, Quang Huy
collection NTU
description Electrical impedance tomography (EIT) is a non-invasive imaging technique where the conductivity of an object is inferred through measurements on electrodes attached to its surface. EIT is well-known as a highly ill-posed nonlinear inverse problem, where the forward problem is modelled by an elliptic partial differential equation (PDE). Bayesian inferences using Markov chain Monte Carlo (MCMC) are computationally expensive because, for each iteration of MCMC, we need to solve a PDE. We propose and analyse the convergence rate of some approximation methods to reduce the computational cost of Bayesian computation in EIT. 1) Using multivariate Lagrange interpolation, we approximate the PDE forward solver by a polynomial surrogate. The set of interpolating nodes is chosen adaptively based on the importance of parameters. 2) We use a multi-level MCMC algorithm to approximate the posterior expectation. 3) We approximate the posterior distribution using adaptive mesh refinement to solve forward PDEs.
first_indexed 2024-10-01T02:26:31Z
format Thesis-Doctor of Philosophy
id ntu-10356/173918
institution Nanyang Technological University
language English
last_indexed 2024-10-01T02:26:31Z
publishDate 2024
publisher Nanyang Technological University
record_format dspace
spelling ntu-10356/1739182024-04-09T03:58:57Z Some approximation methods for Bayesian inversion of electrical impedance tomography Pham, Quang Huy Hoang Viet Ha School of Physical and Mathematical Sciences VHHOANG@ntu.edu.sg Mathematical Sciences Electrical impedance tomography (EIT) is a non-invasive imaging technique where the conductivity of an object is inferred through measurements on electrodes attached to its surface. EIT is well-known as a highly ill-posed nonlinear inverse problem, where the forward problem is modelled by an elliptic partial differential equation (PDE). Bayesian inferences using Markov chain Monte Carlo (MCMC) are computationally expensive because, for each iteration of MCMC, we need to solve a PDE. We propose and analyse the convergence rate of some approximation methods to reduce the computational cost of Bayesian computation in EIT. 1) Using multivariate Lagrange interpolation, we approximate the PDE forward solver by a polynomial surrogate. The set of interpolating nodes is chosen adaptively based on the importance of parameters. 2) We use a multi-level MCMC algorithm to approximate the posterior expectation. 3) We approximate the posterior distribution using adaptive mesh refinement to solve forward PDEs. Doctor of Philosophy 2024-03-06T08:10:24Z 2024-03-06T08:10:24Z 2023 Thesis-Doctor of Philosophy Pham, Q. H. (2023). Some approximation methods for Bayesian inversion of electrical impedance tomography. Doctoral thesis, Nanyang Technological University, Singapore. https://hdl.handle.net/10356/173918 https://hdl.handle.net/10356/173918 10.32657/10356/173918 en This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). application/pdf Nanyang Technological University
spellingShingle Mathematical Sciences
Pham, Quang Huy
Some approximation methods for Bayesian inversion of electrical impedance tomography
title Some approximation methods for Bayesian inversion of electrical impedance tomography
title_full Some approximation methods for Bayesian inversion of electrical impedance tomography
title_fullStr Some approximation methods for Bayesian inversion of electrical impedance tomography
title_full_unstemmed Some approximation methods for Bayesian inversion of electrical impedance tomography
title_short Some approximation methods for Bayesian inversion of electrical impedance tomography
title_sort some approximation methods for bayesian inversion of electrical impedance tomography
topic Mathematical Sciences
url https://hdl.handle.net/10356/173918
work_keys_str_mv AT phamquanghuy someapproximationmethodsforbayesianinversionofelectricalimpedancetomography