Learning a microlocal prior for limited-angle tomography

• Published in: IMA journal of applied mathematics Vol. 88; no. 6; pp. 888 - 916
• Main Authors: Rautio, Siiri, Murthy, Rashmi, Bubba, Tatiana A, Lassas, Matti, Siltanen, Samuli
• Format: Journal Article
• Language: English
• Published: 30-12-2023
• ISSN: 0272-4960; 1464-3634
• DOI: 10.1093/imamat/hxae005

Limited-angle tomography is a highly ill-posed linear inverse problem. It arises in many applications, such as digital breast tomosynthesis. Reconstructions from limited-angle data typically suffer from severe stretching of features along the central direction of projections, leading to poor separation between slices perpendicular to the central direction. In this paper, a new method is introduced, based on machine learning and geometry, producing an estimate for interfaces between regions of different X-ray attenuation. The estimate can be presented on top of the reconstruction, indicating more reliably the separation between features. The method uses directional edge detection, implemented using complex wavelets and enhanced with morphological operations. By using convolutional neural networks, the visible part of the singular support is first extracted and then extended to the full domain, filling in the parts of the singular support that would otherwise be hidden due to the lack of measurement directions.