Learning a microlocal prior for limited angle tomography
Tatiana Bubba - University of Bath
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 talk, I introduce a new method, 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 true form and extent of features. The method uses directional edge detection, implemented using complex wavelets and enhanced with morphological operations. By using machine learning, the visible part of the wavefront set is first extracted and then extended to the full domain, filling in the parts of the wavefront set that would otherwise be hidden due to the lack of measurement directions. This is a joint work with S. Rautio, R. Murthy, M. Lassas and S. Siltanen from the University of Helsinki.
Tatiana Bubba is an Assistant Professor in Applied Mathematics at the University of Bath, UK. After obtaining her PhD in 2016 from the University of Ferrara, Italy, she became postdoctoral researcher at the University of Helsinki, Finland, where she was an Academy Postdoc from 2020. In 2021 she relocated to UK, with a Royal Society Newton International Fellowship at the University of Cambridge, before taking her current post at the University of Bath in 2022. Her interest lies in computational inverse problems, especially in tomographic applications. Currently, her research revolves around combining sparse regularisation techniques based on multiresolution system like shearlets, with deep learning approaches.
June 27th 2022, 15:00
Room 706, UniGe DIMA, Via Dodecaneso 35, Genova, Italy