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

Research output: Contribution to journal › Article › peer-review

Standard

Nonlocal TV-gaussian prior for bayesian inverse problems with applications to limited CT reconstruction. / Lv, Didi; Zhou, Qingping; Choi, Jae Kyu; Li, Jinglai; Zhang, Xiaoqun.

In: Inverse Problems and Imaging, Vol. 14, No. 1, 02.2020, p. 117-132.

Research output: Contribution to journal › Article › peer-review

Harvard

Lv, D, Zhou, Q, Choi, JK, Li, J & Zhang, X 2020, 'Nonlocal TV-gaussian prior for bayesian inverse problems with applications to limited CT reconstruction', Inverse Problems and Imaging, vol. 14, no. 1, pp. 117-132. https://doi.org/10.3934/ipi.2019066

APA

Lv, D., Zhou, Q., Choi, J. K., Li, J., & Zhang, X. (2020). Nonlocal TV-gaussian prior for bayesian inverse problems with applications to limited CT reconstruction. Inverse Problems and Imaging, 14(1), 117-132. https://doi.org/10.3934/ipi.2019066

Vancouver

Lv D, Zhou Q, Choi JK, Li J, Zhang X. Nonlocal TV-gaussian prior for bayesian inverse problems with applications to limited CT reconstruction. Inverse Problems and Imaging. 2020 Feb;14(1):117-132. https://doi.org/10.3934/ipi.2019066

Author

Lv, Didi ; Zhou, Qingping ; Choi, Jae Kyu ; Li, Jinglai ; Zhang, Xiaoqun. / Nonlocal TV-gaussian prior for bayesian inverse problems with applications to limited CT reconstruction. In: Inverse Problems and Imaging. 2020 ; Vol. 14, No. 1. pp. 117-132.

Bibtex

@article{30d6f75e040541288ad15b907bc8d3f3,
title = "Nonlocal TV-gaussian prior for bayesian inverse problems with applications to limited CT reconstruction",
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.",
keywords = "Bayesian inverse problems, Gaussian measure, Limited tomography, Nonlocal total variation, Uncertainty quantification",
author = "Didi Lv and Qingping Zhou and Choi, {Jae Kyu} and Jinglai Li and Xiaoqun Zhang",
year = "2020",
month = feb,
doi = "10.3934/ipi.2019066",
language = "English",
volume = "14",
pages = "117--132",
journal = "Inverse Problems and Imaging",
issn = "1930-8337",
publisher = "American Institute of Mathematical Sciences",
number = "1",

}

RIS

TY - JOUR

T1 - Nonlocal TV-gaussian prior for bayesian inverse problems with applications to limited CT reconstruction

AU - Lv, Didi

AU - Zhou, Qingping

AU - Choi, Jae Kyu

AU - Li, Jinglai

AU - Zhang, Xiaoqun

PY - 2020/2

Y1 - 2020/2

N2 - 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.

AB - 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.

KW - Bayesian inverse problems

KW - Gaussian measure

KW - Limited tomography

KW - Nonlocal total variation

KW - Uncertainty quantification

UR - http://www.scopus.com/inward/record.url?scp=85077213887&partnerID=8YFLogxK

U2 - 10.3934/ipi.2019066

DO - 10.3934/ipi.2019066

M3 - Article

AN - SCOPUS:85077213887

VL - 14

SP - 117

EP - 132

JO - Inverse Problems and Imaging

JF - Inverse Problems and Imaging

SN - 1930-8337

IS - 1

ER -