Nonlocal TV-gaussian prior for bayesian inverse problems with applications to limited CT reconstruction

Research output: Contribution to journalArticlepeer-review

Authors

  • Didi Lv
  • Qingping Zhou
  • Jae Kyu Choi
  • Jinglai Li
  • Xiaoqun Zhang

Colleges, School and Institutes

External organisations

  • Shanghai Jiao Tong University
  • Tongji University

Abstract

Bayesian inference methods have been widely applied in inverse problems due to the ability of uncertainty characterization of the estimation. The prior distribution of the unknown plays an essential role in the Bayesian inference, and a good prior distribution can significantly improve the inference results. In this paper, we propose a hybrid prior distribution on combining the nonlocal total variation regularization (NLTV) and the Gaussian distribution, namely NLTG prior. The advantage of this hybrid prior is two-fold. The proposed prior models both texture and geometric structures present in images through the NLTV. The Gaussian reference measure also provides a flexibility of incorporating structure information from a reference image. Some theoretical properties are established for the hybrid prior. We apply the proposed prior to limited tomography reconstruction problem that is difficult due to severe data missing. Both maximum a posteriori and conditional mean estimates are computed through two efficient methods and the numerical experiments validate the advantages and feasibility of the proposed NLTG prior.

Details

Original languageEnglish
Pages (from-to)117-132
Number of pages16
JournalInverse Problems and Imaging
Volume14
Issue number1
Early online date30 Nov 2019
Publication statusPublished - Feb 2020

Keywords

  • Bayesian inverse problems, Gaussian measure, Limited tomography, Nonlocal total variation, Uncertainty quantification