Numerical methods for CT reconstruction with unknown geometry parameters

• Type of Material: Article
• Authors: Chang Meng, Emory University; James Nagy, Emory University
• Language: English
• Date: 2022-12-19
• Publisher: Springer Verlag
• Publication Version: Final Published Version
• Copyright Statement: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022, Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
• Final Published Version (URL): http://dx.doi.org/10.1007/s11075-022-01451-3
• Title of Journal or Parent Work: NUMERICAL ALGORITHMS
• Volume: 92
• Issue: 1
• Start Page: 831
• End Page: 847
• Grant/Funding Information: This work was supported in part by the US National Science Foundation grants DMS-2038118 and DMS-2208294.
• Keywords: Machine learning; Computed tomography; Optimization
• Research Categories: Mathematics

Abstract

Computed tomography (CT) techniques are well known for their ability to produce high-quality images needed for medical diagnostic purposes. Unfortunately, standard CT machines are extremely large, heavy, require careful and regular calibration, and are expensive, which can limit their availability in point-of-care situations. An alternative approach is to use portable machines, but parameters related to the geometry of these devices (e.g., distance between source and detector, orientation of source to detector) cannot always be precisely calibrated, and these parameters may change slightly when the machine is adjusted during the image acquisition process. In this work, we describe the non-linear inverse problem that models this situation, and discuss algorithms that can jointly estimate the geometry parameters and compute a reconstructed image. In particular, we propose a hybrid machine learning and block coordinate descent (ML-BCD) approach that uses an ML model to calibrate geometry parameters, and uses BCD to refine the predicted parameters and reconstruct the imaged object simultaneously. We show using numerical experiments that our new method can efficiently improve the accuracy of both the image and geometry parameters.