Uniqueness of Angular Velocity Reconstruction in Parallel-Beam and Diffraction Tomography
Functional Analysis
2025-10-22 v1 Numerical Analysis
Mathematical Physics
math.MP
Numerical Analysis
Abstract
This work addresses the problem of uniquely determining a rotational motion from continuous time-dependent measurements within the frameworks of parallel-beam and diffraction tomography. The motivation stems from the challenge of imaging trapped biological samples manipulated and rotated using optical or acoustic tweezers. We analyze the conditions under which the rotation of the unknown sample can be uniquely recovered using the infinitesimal common line and circle method, respectively. We provide explicit criteria for the sample's structure and the induced motion that guarantee unique reconstruction of all rotation parameters. Moreover, we demonstrate that the set of objects for which uniqueness fails is nowhere dense.
Cite
@article{arxiv.2510.18829,
title = {Uniqueness of Angular Velocity Reconstruction in Parallel-Beam and Diffraction Tomography},
author = {Peter Elbau and Denise Schmutz},
journal= {arXiv preprint arXiv:2510.18829},
year = {2025}
}