Low-Rank Tensor Regression for X-Ray Tomography

TL;DR

This paper introduces a low-rank tensor regression method for X-ray tomography that efficiently reconstructs 3D structures by exploiting tensor structures, reducing dimensionality, and handling ill-posed inverse problems.

Contribution

It proposes a novel tensor-based regression approach with low-rank constraints for improved tomographic reconstruction, especially under limited data conditions.

Findings

Effective in synthetic noise-free data

Robust to Gaussian noise

Reduces dimensionality of unknowns

Abstract

Tomographic imaging is useful for revealing the internal structure of a 3D sample. Classical reconstruction methods treat the object of interest as a vector to estimate its value. Such an approach, however, can be inefficient in analyzing high-dimensional data because of the underexploration of the underlying structure. In this work, we propose to apply a tensor-based regression model to perform tomographic reconstruction. Furthermore, we explore the low-rank structure embedded in the corresponding tensor form. As a result, our proposed method efficiently reduces the dimensionality of the unknown parameters, which is particularly beneficial for ill-posed inverse problem suffering from insufficient data. We demonstrate the robustness of our proposed approach on synthetic noise-free data as well as on Gaussian noise-added data.