Bayesian inference and uncertainty quantification for medical image reconstruction with Poisson data

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Bayesian inference and uncertainty quantification for medical image reconstruction with Poisson data. / Zhou, Qingping; Yu, Tengchao; Zhang, Xiaoqun; Li, Jinglai.

In: SIAM Journal on Imaging Sciences, Vol. 13, No. 1, 07.01.2020, p. 29–52.

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@article{650946967ceb4d78a7431b6bacf7292d,
title = "Bayesian inference and uncertainty quantification for medical image reconstruction with Poisson data",
abstract = "We provide a complete framework for performing infinite dimensional Bayesian inference and uncertainty quantification for image reconstruction with Poisson data. In particular, we address the following issues to make the Bayesian framework applicable in practice. We first introduce a positivity-preserving reparametrization, and we prove that under the reparametrization and a hybrid prior, the posterior distribution is well-posed in the infinite dimensional setting. Second, we provide a dimension-independent Markov chain Monte Carlo algorithm, based on the preconditioned Crank--Nicolson Langevin method, in which we use a primal-dual scheme to compute the offset direction. Third, we give a method combining the model discrepancy method and maximum likelihood estimation to determine the regularization parameter in the hybrid prior. Finally we propose to use the obtained posterior distribution to detect artifacts in a recovered image. We provide an example to demonstrate the effectiveness of the proposed method.",
keywords = "Poisson distribution, Bayesian inference, image reconstruction, uncertainty quantification, Markov chain Monte Carlo, positron emission tomography",
author = "Qingping Zhou and Tengchao Yu and Xiaoqun Zhang and Jinglai Li",
year = "2020",
month = jan,
day = "7",
doi = "10.1137/19M1248352",
language = "English",
volume = "13",
pages = "29–52",
journal = "SIAM Journal on Imaging Sciences",
issn = "1936-4954",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",

}

RIS

TY - JOUR

T1 - Bayesian inference and uncertainty quantification for medical image reconstruction with Poisson data

AU - Zhou, Qingping

AU - Yu, Tengchao

AU - Zhang, Xiaoqun

AU - Li, Jinglai

PY - 2020/1/7

Y1 - 2020/1/7

N2 - We provide a complete framework for performing infinite dimensional Bayesian inference and uncertainty quantification for image reconstruction with Poisson data. In particular, we address the following issues to make the Bayesian framework applicable in practice. We first introduce a positivity-preserving reparametrization, and we prove that under the reparametrization and a hybrid prior, the posterior distribution is well-posed in the infinite dimensional setting. Second, we provide a dimension-independent Markov chain Monte Carlo algorithm, based on the preconditioned Crank--Nicolson Langevin method, in which we use a primal-dual scheme to compute the offset direction. Third, we give a method combining the model discrepancy method and maximum likelihood estimation to determine the regularization parameter in the hybrid prior. Finally we propose to use the obtained posterior distribution to detect artifacts in a recovered image. We provide an example to demonstrate the effectiveness of the proposed method.

AB - We provide a complete framework for performing infinite dimensional Bayesian inference and uncertainty quantification for image reconstruction with Poisson data. In particular, we address the following issues to make the Bayesian framework applicable in practice. We first introduce a positivity-preserving reparametrization, and we prove that under the reparametrization and a hybrid prior, the posterior distribution is well-posed in the infinite dimensional setting. Second, we provide a dimension-independent Markov chain Monte Carlo algorithm, based on the preconditioned Crank--Nicolson Langevin method, in which we use a primal-dual scheme to compute the offset direction. Third, we give a method combining the model discrepancy method and maximum likelihood estimation to determine the regularization parameter in the hybrid prior. Finally we propose to use the obtained posterior distribution to detect artifacts in a recovered image. We provide an example to demonstrate the effectiveness of the proposed method.

KW - Poisson distribution

KW - Bayesian inference

KW - image reconstruction

KW - uncertainty quantification

KW - Markov chain Monte Carlo

KW - positron emission tomography

UR - https://doi.org/10.1137/19M1248352

U2 - 10.1137/19M1248352

DO - 10.1137/19M1248352

M3 - Article

VL - 13

SP - 29

EP - 52

JO - SIAM Journal on Imaging Sciences

JF - SIAM Journal on Imaging Sciences

SN - 1936-4954

IS - 1

ER -