Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Advantage of Machine Learning over Maximum Likelihood in Limited-Angle Low-Photon X-Ray Tomography



Zhen Guo, Jungki Song, George Barbastathis, Michael Glinsky, Courtenay Vaughan, Kurt Larson, Bradley Alpert, Zachary H. Levine


Limited-angle X-ray tomography reconstruction is an ill-posed inverse problem in general. Especially when the projection angles are limited and the measurements are taken in a photon-limited condition, reconstructions from classical algorithms such as filtered backprojection may lose fidelity and acquire artifacts due to the missing-cone problem. To obtain satisfactory reconstruction results, prior assumptions, such as total variation minimization and nonlocal image similarity, are usually incorporated within the reconstruction algorithm. In this work, we introduce deep neural networks to determine and apply a prior distribution in the reconstruction process. Our neural networks learn the prior directly from the synthetic training samples. The neural nets thus obtain a prior distribution that is specific to the reconstructions we are interested in. In particular, we used deep generative models with 3D convolutional layers and 3D attention layers which are trained on 3D synthetic integrated circuit (IC) data from a model dubbed CircuitFaker. We demonstrate that the priors from our deep generative models can drastically improve the IC reconstruction quality on synthetic data compared with a maximum likelihood algorithm when the projection angles and photon budgets are limited. The advantages of using machine learning in limited angle X-ray tomography may further enable its applications in low-photon nanoscale imaging.
Proceedings Title
Machine Learning for Scientific Imaging 2022
Conference Dates
January 17-20, 2022
Conference Location
online (previously: San Francisco), CA, US
Conference Title
Machine Learning for Scientific Imaging 2022, at Imaging Science and Technology's Electronic Imaging 2022


limited angle X-ray tomography, machine learning, photon-limited imaging


Guo, Z. , Song, J. , Barbastathis, G. , Glinsky, M. , Vaughan, C. , Larson, K. , Alpert, B. and Levine, Z. (2022), Advantage of Machine Learning over Maximum Likelihood in Limited-Angle Low-Photon X-Ray Tomography, Machine Learning for Scientific Imaging 2022, online (previously: San Francisco), CA, US, [online],, (Accessed July 23, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created January 20, 2022, Updated May 7, 2023