Uniqueness of Angular Velocity Reconstruction in Parallel-Beam and Diffraction Tomography

TL;DR

This paper investigates conditions for uniquely reconstructing rotational motion in parallel-beam and diffraction tomography, crucial for imaging biological samples manipulated by optical or acoustic tweezers, and provides explicit criteria ensuring uniqueness.

Contribution

It introduces explicit criteria for unique rotation reconstruction in tomography, analyzing the structural and motion conditions that guarantee this in biological imaging contexts.

Findings

Unique reconstruction conditions are established.

The set of objects with non-unique solutions is nowhere dense.

Explicit criteria for sample structure and motion are provided.

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.