Radiation image reconstruction and uncertainty quantification using a Gaussian process prior

Lee, Jaewon; Joshi, Tenzing H.; Bandstra, Mark S.; Gunter, Donald L.; Quiter, Brian J.; Cooper, Reynold J.; Vetter, Kai

doi:10.1038/s41598-024-71336-z

Radiation image reconstruction and uncertainty quantification using a Gaussian process prior

Journal Article · Thu Oct 03 00:00:00 EDT 2024 · Scientific Reports

DOI:https://doi.org/10.1038/s41598-024-71336-z· OSTI ID:2479503

Lee, Jaewon ^[1]; Joshi, Tenzing H. ^[2]; Bandstra, Mark S. ^[2]; Gunter, Donald L. ^[3]; Quiter, Brian J. ^[2]; Cooper, Reynold J. ^[2]; Vetter, Kai ^[4]

University of California, Berkeley, CA (United States)
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Gunter Physics, Inc., Lisle, IL (United States)
University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

We propose a complete framework for Bayesian image reconstruction and uncertainty quantification based on a Gaussian process prior (GPP) to overcome limitations of maximum likelihood expectation maximization (ML-EM) image reconstruction algorithm. The prior distribution is constructed with a zero-mean Gaussian process (GP) with a choice of a covariance function, and a link function is used to map the Gaussian process to an image. Unlike many other maximum a posteriori approaches, our method offers highly interpretable hyperparamters that are selected automatically with the empirical Bayes method. Furthermore, the GP covariance function can be modified to incorporate a priori structural priors, enabling multi-modality imaging or contextual data fusion. Lastly, we illustrate that our approach lends itself to Bayesian uncertainty quantification techniques, such as the preconditioned Crank–Nicolson method and the Laplace approximation. The proposed framework is general and can be employed in most radiation image reconstruction problems, and we demonstrate it with simulated free-moving single detector radiation source imaging scenarios. We compare the reconstruction results from GPP and ML-EM, and show that the proposed method can significantly improve the image quality over ML-EM, all the while providing greater understanding of the source distribution via the uncertainty quantification capability. Furthermore, significant improvement of the image quality by incorporating a structural prior is illustrated.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 2479503

Journal Information:: Scientific Reports, Journal Name: Scientific Reports Journal Issue: 1 Vol. 14; ISSN 2045-2322

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

References (42)

The problem of diffusion in the lower atmosphere Sutton, O. G. Quarterly Journal of the Royal Meteorological Society, Vol. 73, Issue 317-318 https://doi.org/10.1002/qj.49707331704	journal	July 1947
Inverse problems: From regularization to Bayesian inference Calvetti, D.; Somersalo, E. WIREs Computational Statistics, Vol. 10, Issue 3 https://doi.org/10.1002/wics.1427	journal	January 2018
On the limited memory BFGS method for large scale optimization Liu, Dong C.; Nocedal, Jorge Mathematical Programming, Vol. 45, Issue 1-3 https://doi.org/10.1007/BF01589116	journal	August 1989
Scene data fusion: Real-time standoff volumetric gamma-ray imaging Barnowski, Ross; Haefner, Andrew; Mihailescu, Lucian Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 800 https://doi.org/10.1016/j.nima.2015.08.016	journal	November 2015
Gamma-Ray imaging for nuclear security and safety: Towards 3-D gamma-ray vision Vetter, Kai; Barnowksi, Ross; Haefner, Andrew Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 878 https://doi.org/10.1016/j.nima.2017.08.040	journal	January 2018
Coded-aperture imaging systems: Past, present and future development – A review Cieślak, Michał J.; Gamage, Kelum A. A.; Glover, Robert Radiation Measurements, Vol. 92 https://doi.org/10.1016/j.radmeas.2016.08.002	journal	September 2016
Asymptotic Statistics van der Vaart, A. W. Cambridge University Press https://doi.org/10.1017/CBO9780511802256	book	January 2012
Inverse problems: A Bayesian perspective Stuart, A. M. Acta Numerica, Vol. 19 https://doi.org/10.1017/S0962492910000061	journal	May 2010
Bayesian uncertainty quantification for machine-learned models in physics Gal, Yarin; Koumoutsakos, Petros; Lanusse, Francois Nature Reviews Physics, Vol. 4, Issue 9 https://doi.org/10.1038/s42254-022-00498-4	journal	August 2022
Dosimetry for Radiopharmaceutical Therapy Sgouros, George; Hobbs, Robert F. Seminars in Nuclear Medicine, Vol. 44, Issue 3 https://doi.org/10.1053/j.semnuclmed.2014.03.007	journal	May 2014
In vivo proton range verification: a review Knopf, Antje-Christin; Lomax, Antony Physics in Medicine and Biology, Vol. 58, Issue 15 https://doi.org/10.1088/0031-9155/58/15/R131	journal	July 2013
Regularization parameter selection methods for ill-posed Poisson maximum likelihood estimation Bardsley, Johnathan M.; Goldes, John Inverse Problems, Vol. 25, Issue 9 https://doi.org/10.1088/0266-5611/25/9/095005	journal	August 2009
LII. An essay towards solving a problem in the doctrine of chances. By the late Rev. Mr. Bayes, F. R. S. communicated by Mr. Price, in a letter to John Canton, A. M. F. R. S Bayes, Thomas Philosophical Transactions of the Royal Society of London, Vol. 53, p. 370-418 https://doi.org/10.1098/rstl.1763.0053	journal	January 1763
Incorporation of correlated structural images in PET image reconstruction No authors listed IEEE Transactions on Medical Imaging, Vol. 13, Issue 4, p. 627-640 https://doi.org/10.1109/42.363105	journal	January 1994
Maximum Likelihood Reconstruction for Emission Tomography Shepp, L. A.; Vardi, Y. IEEE Transactions on Medical Imaging, Vol. 1, Issue 2 https://doi.org/10.1109/TMI.1982.4307558	journal	October 1982
PET Image Reconstruction Using Kernel Method Wang, Guobao; Qi, Jinyi IEEE Transactions on Medical Imaging, Vol. 34, Issue 1 https://doi.org/10.1109/TMI.2014.2343916	journal	January 2015
A Maximum Likelihood Approach to Emission Image Reconstruction from Projections Rockmore, A. J.; Macovski, Albert IEEE Transactions on Nuclear Science, Vol. 23, Issue 4 https://doi.org/10.1109/TNS.1976.4328496	journal	January 1976
A Spherical Active Coded Aperture for $4\pi $ Gamma-Ray Imaging Hellfeld, Daniel; Barton, Paul; Gunter, Donald IEEE Transactions on Nuclear Science, Vol. 64, Issue 11 https://doi.org/10.1109/TNS.2017.2755982	journal	November 2017
Gamma-Ray Point-Source Localization and Sparse Image Reconstruction Using Poisson Likelihood Hellfeld, Daniel; Joshi, Tenzing H. Y.; Bandstra, Mark S. IEEE Transactions on Nuclear Science, Vol. 66, Issue 9 https://doi.org/10.1109/TNS.2019.2930294	journal	September 2019
Real-Time Free-Moving Active Coded Mask 3D Gamma-Ray Imaging Hellfeld, Daniel; Barton, Paul; Gunter, Donald IEEE Transactions on Nuclear Science, Vol. 66, Issue 10 https://doi.org/10.1109/TNS.2019.2939948	journal	October 2019
An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach: Link between Gaussian Fields and Gaussian Markov Random Fields Lindgren, Finn; Rue, Håvard; Lindström, Johan Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 73, Issue 4 https://doi.org/10.1111/j.1467-9868.2011.00777.x	journal	August 2011
Ongoing advancement of free-moving radiation imaging and mapping Quiter, Brian; Bandstra, Mark S.; Cates, Joshua W. Hard X-Ray, Gamma-Ray, and Neutron Detector Physics XXIV https://doi.org/10.1117/12.2635752	conference	October 2022
Practical Sketching Algorithms for Low-Rank Matrix Approximation Tropp, Joel A.; Yurtsever, Alp; Udell, Madeleine SIAM Journal on Matrix Analysis and Applications, Vol. 38, Issue 4 https://doi.org/10.1137/17M1111590	journal	January 2017
Bayesian Inference and Uncertainty Quantification for Medical Image Reconstruction with Poisson Data Zhou, Qingping; Yu, Tengchao; Zhang, Xiaoqun SIAM Journal on Imaging Sciences, Vol. 13, Issue 1 https://doi.org/10.1137/19M1248352	journal	January 2020
The Dawn of a New Era in Low-Dose PET Imaging Catana, Ciprian Radiology, Vol. 290, Issue 3 https://doi.org/10.1148/radiol.2018182573	journal	March 2019
Nonnegative Matrix Factorization with Gaussian Process Priors Schmidt, Mikkel N.; Laurberg, Hans Computational Intelligence and Neuroscience, Vol. 2008 https://doi.org/10.1155/2008/361705	journal	January 2008
Modern Diagnostic Imaging Technique Applications and Risk Factors in the Medical Field: A Review Hussain, Shah; Mubeen, Iqra; Ullah, Niamat BioMed Research International, Vol. 2022 https://doi.org/10.1155/2022/5164970	journal	June 2022
A Practical Bayesian Framework for Backpropagation Networks MacKay, David J. C. Neural Computation, Vol. 4, Issue 3 https://doi.org/10.1162/neco.1992.4.3.448	journal	May 1992
Non-destructive testing and evaluation of composite materials/structures: A state-of-the-art review Wang, Bing; Zhong, Shuncong; Lee, Tung-Lik Advances in Mechanical Engineering, Vol. 12, Issue 4 https://doi.org/10.1177/1687814020913761	journal	April 2020
Bayesian Data Analysis Gelman, Andrew; Carlin, John B.; Stern, Hal S. https://doi.org/10.1201/b16018	book	November 2013
MCMC Methods for Functions: Modifying Old Algorithms to Make Them Faster Cotter, S. L.; Roberts, G. O.; Stuart, A. M. Statistical Science, Vol. 28, Issue 3 https://doi.org/10.1214/13-STS421	journal	August 2013
Bayesian approach to limited-angle reconstruction in computed tomography Hanson, Kenneth M.; Wecksung, George W. Journal of the Optical Society of America, Vol. 73, Issue 11 https://doi.org/10.1364/JOSA.73.001501	journal	November 1983
List-mode likelihood Barrett, Harrison H.; White, Timothy; Parra, Lucas C. Journal of the Optical Society of America A, Vol. 14, Issue 11 https://doi.org/10.1364/JOSAA.14.002914	journal	January 1997
Efficient Computer Manipulation of Tensor Products with Applications to Multidimensional Approximation Pereyra, V.; Scherer, G. Mathematics of Computation, Vol. 27, Issue 123 https://doi.org/10.2307/2005663	journal	July 1973
Advances in Nuclear Radiation Sensing: Enabling 3-D Gamma-Ray Vision Vetter, Kai; Barnowski, Ross; Cates, Joshua W. Sensors, Vol. 19, Issue 11 https://doi.org/10.3390/s19112541	journal	June 2019
Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions Halko, Nathan; Martinsson, Per-Gunnar; Tropp, Joel A. arXiv https://doi.org/10.48550/arXiv.0909.4061	text	January 2009
Gaussian Process Kernels for Pattern Discovery and Extrapolation Wilson, Andrew Gordon; Adams, Ryan Prescott arXiv https://doi.org/10.48550/arXiv.1302.4245	text	January 2013
Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP) Wilson, Andrew Gordon; Nickisch, Hannes arXiv https://doi.org/10.48550/arXiv.1503.01057	preprint	January 2015
Deep Kernel Learning Wilson, Andrew Gordon; Hu, Zhiting; Salakhutdinov, Ruslan arXiv https://doi.org/10.48550/arXiv.1511.02222	preprint	January 2015
A Conceptual Introduction to Markov Chain Monte Carlo Methods Speagle, Joshua S. arXiv https://doi.org/10.48550/arXiv.1909.12313	preprint	January 2019
Plug-and-Play Image Restoration with Deep Denoiser Prior Zhang, Kai; Li, Yawei; Zuo, Wangmeng arXiv https://doi.org/10.48550/arXiv.2008.13751	preprint	January 2020
Laplace Redux -- Effortless Bayesian Deep Learning Daxberger, Erik; Kristiadi, Agustinus; Immer, Alexander arXiv https://doi.org/10.48550/arXiv.2106.14806	preprint	January 2021

Similar Records

Bayesian reconstruction of functional images using anatomical information as priors

Journal Article · Tue Nov 30 23:00:00 EST 1993 · IEEE Transactions on Medical Imaging (Institute of Electrical and Electronics Engineers); (United States) · OSTI ID:5043048

Combining Poisson singular integral and total variation prior models in image restoration

Journal Article · Mon Oct 14 00:00:00 EDT 2013 · Signal Processing · OSTI ID:1488405

Bayesian image reconstruction in SPECT using higher order mechanical models as priors

Journal Article · Thu Nov 30 23:00:00 EST 1995 · IEEE Transactions on Medical Imaging · OSTI ID:182939

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Radiation image reconstruction and uncertainty quantification using a Gaussian process prior

Citation Formats

References (42)

Similar Records

Related Subjects