Bayesian inference and uncertainty quantification for image reconstruction with Poisson data



Zhou, Qingping, Yu, Tengchao, Zhang, Xiaoqun and Li, Jinglai ORCID: 0000-0001-7980-6901
(2019) Bayesian inference and uncertainty quantification for image reconstruction with Poisson data. SIAM Journal on Imaging Sciences, 13 (1). pp. 29-52.

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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 MCMC 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.

Item Type: Article
Uncontrolled Keywords: math.NA, math.NA, cs.NA, stat.CO
Depositing User: Symplectic Admin
Date Deposited: 22 Jul 2019 08:29
Last Modified: 17 Mar 2024 03:15
DOI: 10.1137/19m1248352
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3050151