A novel reconstruction method is introduced for the severely ill-posed inverse problem of limited-angle tomography. It is well known that, depending on the available measurement, angles specify a subset of the wavefront set of the unknown target, while some oriented singularities remain invisible in the data. Topological Interface recovery for Limited-angle Tomography, or TILT, is based on lifting the visible part of the wavefront set under a universal covering map. In the space provided, it is possible to connect the appropriate pieces of the lifted wavefront set correctly using dual-tree complex wavelets, a dedicated metric, and persistent homology. The result is not only a suggested invisible boundary but also a computational representation for all interfaces in the target.
@article{arxiv.2310.16557,
title = {TILT: topological interface recovery in limited-angle tomography},
author = {Elli Karvonen and Matti Lassas and Pekka Pankka and Samuli Siltanen},
journal= {arXiv preprint arXiv:2310.16557},
year = {2023}
}