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

Limited-angle X-ray tomography reconstruction is an ill-conditioned 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 synthetic training samples. The neural nets thus obtain a prior distribution that is specific to the class of objects we are interested in reconstructing. 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, when the projection angles and photon budgets are limited, the priors from our deep generative models can dramatically improve the IC reconstruction quality on synthetic data compared with maximum likelihood estimation. Training the deep generative models with synthetic IC data from CircuitFaker illustrates the capabilities of the learned prior from machine learning. We expect that if the process were reproduced with experimental data, the advantage of the machine learning would persist. The advantages of machine learning in limited angle X-ray tomography may further enable applications in low-photon nanoscale imaging.