Efficient tensor tomography in fan-beam coordinates. II: Attenuated transforms

TL;DR

This paper develops a stable and explicit method for reconstructing complex-valued attenuated tensor fields in fan-beam coordinates, extending previous work to more general attenuation models in tensor tomography.

Contribution

It introduces a constructive approach for the unique and stable reconstruction of arbitrary order tensors from their attenuated transforms in the Euclidean unit disc.

Findings

Provides an explicit reconstruction procedure for complex-valued attenuated tensors.

Ensures stability and uniqueness in tensor reconstruction from attenuated X-ray data.

Extends tensor tomography theory to include complex attenuation in fan-beam coordinates.

Abstract

This article extends the author's past work [Inv. Probl. Imaging, 10:2 (2016), 433--459] to attenuated X-ray transforms, where the attenuation is complex-valued and only depends on position. We give a positive and constructive answer to the attenuated tensor tomography problem on the Euclidean unit disc in fan-beam coordinates. For a tensor of arbitrary order, we propose an equivalent tensor of the same order which can be uniquely and stably reconstructed from its attenuated transform, as well as an explicit and efficient procedure to do so.