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arXiv · 2310.16557

TILT: topological interface recovery in limited-angle tomography

Elli Karvonen·Matti Lassas·Pekka Pankka·Samuli Siltanen
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Abstract

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.

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Elli Karvonen, Matti Lassas, Pekka Pankka, Samuli Siltanen. 2023-10-25. TILT: topological interface recovery in limited-angle tomography. https://arxiv.org/abs/2310.16557

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