A Generalized Bidiagonal-Tikhonov Method Applied To Differential Phase Contrast Tomography

TL;DR

This paper introduces the Generalized Bidiagonal Tikhonov (GBiT) method for solving linear systems in phase contrast tomography, improving reconstruction quality by leveraging bidiagonal decomposition, validated through simulations and experiments.

Contribution

The paper presents the GBiT method, an adaptation of the Arnoldi-Tikhonov approach using bidiagonal decomposition, specifically tailored for phase contrast tomography reconstruction.

Findings

GBiT improves reconstruction accuracy in phase contrast tomography.

Finite difference approximation affects the quality of reconstructions.

Validated with both simulated and experimental data.

Abstract

Phase contrast tomography is an alternative to classic absorption contrast tomography that leads to higher contrast reconstructions in many applications. We review how phase contrast data can be acquired by using a combination of phase and absorption gratings. Using algebraic reconstruction techniques the object can be reconstructed from the measured data. In order to solve the resulting linear system we propose the Generalized Bidiagonal Tikhonov (GBiT) method, an adaptation of the generalized Arnoldi-Tikhonov method that uses the bidiagonal decomposition of the matrix instead of the Arnoldi decomposition. We also study the effect of the finite difference operator in the model by examining the reconstructions with either a forward difference or a central difference approximation. We validate our conclusions with simulated and experimental data.