Phase Based Alignment and Improved Projection Matching of Parallel Beam Tomography Data

TL;DR

This paper introduces a novel phase-based method for aligning parallel beam tomography data by recovering phase shifts in the Fourier domain, improving reconstruction accuracy when data misalignment occurs.

Contribution

It presents a new phase recovery approach for data alignment in tomography, enhancing accuracy over traditional methods like cross-correlation.

Findings

The phase-based method accurately recovers misalignments in various scenarios.

Low pass filtering enhances the effectiveness of projection matching alignment.

The approach is flexible and robust across different parameters and settings.

Abstract

Tomography is an imaging technique that works by reconstructing a scene from acquired data in the form of line integrals of the imaging domain. A fundamental underlying assumption in the reconstruction procedure is the precise alignment of the data values, i.e. the relationship between the data values and the paths of the lines of integration is accurately known. In many applications, e.g. electron and X-ray tomography, it is necessary to establish this relationship using software alignment techniques or image registration due to misalignment when rotating the physical specimen. Unfortunately, highly accurate software alignment is still a challenge to achieve in many cases, and improper alignment results in severe loss in the imaging resolution. In this article, we develop a new approach that considers the alignment problem through a completely different lens, as a problem of recovering phase shifts in Fourier domain {within} the reconstruction algorithm. The recovery of these phase shifts serves as the data alignment, which is done by calculating discrepancies between the misaligned data and the current reconstruction. In the development of the approach, we investigate proper selection of parameters, and we show that it is fairly flexible and surprisingly accurate. Finally, the analysis of our approach provides insight into why projection matching alignment by cross-correlation can be improved through low pass filtering, which we demonstrate. Our methods are validated in a wide range of examples and settings.