Statistical Reconstruction For Anisotropic X-ray Dark-Field Tomography

TL;DR

This paper introduces a new statistical reconstruction method for anisotropic X-ray dark-field tomography that improves noise performance and computational efficiency, enabling more accurate and accessible fiber structure imaging.

Contribution

It provides numerically stable implementations, validates advanced statistical models, and introduces a new efficient formulation that retains noise assumptions for AXDT.

Findings

Statistical reconstruction outperforms previous models in noise performance.

The new formulation is highly efficient with identical accuracy.

Analysis of optimization behavior guides future algorithm development.

Abstract

Anisotropic X-ray Dark-Field Tomography (AXDT) is a novel imaging technology that enables the extraction of fiber structures on the micrometer scale, far smaller than standard X-ray Computed Tomography (CT) setups. Directional and structural information is relevant in medical diagnostics and material testing. Compared to existing solutions, AXDT could prove a viable alternative. Reconstruction methods in AXDT have so far been driven by practicality. Improved methods could make AXDT more accessible. We contribute numerically stable implementations and validation of advanced statistical reconstruction methods that incorporate the statistical noise behavior of the imaging system. We further provide a new statistical reconstruction formulation that retains the advanced noise assumptions of the imaging setup while being efficient and easy to optimize. Finally, we provide a detailed analysis of the optimization behavior for all models regarding AXDT. Our experiments show that statistical reconstruction outperforms the previously used model, and particularly the noise performance is superior. While the previously proposed statistical method is effective, it is computationally expensive, and our newly proposed formulation proves highly efficient with identical performance. Our theoretical analysis opens the possibility to new and more advanced reconstruction algorithms, which in turn enable future research in AXDT.