title: Image Processing for Talbot-Lau X-ray Imaging
Creators: name: Käppler, Sebastian
Publisher: name: Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
Year: 2024

description: X-ray imaging is a standard modality for medical imaging and non-destructive testing. Conventional X-ray systems measure the attenuation of radiation. During the last few years, several principles that also allow measuring the refraction of X-rays have been proposed. One of these measuring principles is the Talbot-Lau interferometer, which has the advantage that it can be integrated into multiple types of existing X-ray devices. A typical Talbot-Lau interferometer consists of three periodic gratings containing micrometer-sized structures, which are placed in the X-ray beam path. Besides refraction, the Talbot-Lau interferometer also measures a so-called dark-field signal, which can be used as a measure for the homogeneity of the imaged object. Imaging with a Talbot-Lau interferometer is, however, much more complex than with a standard X-ray system. The goal of this thesis was to improve the image quality of Talbot-Lau interferometers through image processing. The contributions of the thesis are split into two parts. The first part of this thesis mainly considers the correction of artifacts that arise from uncontrolled motion of the gratings. Correction algorithms were developed for two types of motion. An optimization-based approach was developed to correct for motion during acquisitions. Additionally, a second approach was developed for the special case of slit-scanning acquisitions. For the second type of motion, i.e. motion occurring after a calibration scan, two distinct approaches were presented and compared. These methods are based on either spatial or temporal correlation. The method based on temporal correlation utilizes an efficient numerical optimization scheme. An extension of this approach, which does not require a previous interferometer calibration, was additionally proposed. The correction algorithms enable the operation of a Talbot-Lau interferometer even in challenging mechanical conditions. Besides artifact correction methods, improvements to the interferometer-specific preprocessing steps were also developed. These improvements can, under certain conditions, reduce the image noise, as well as improve the quantitative accuracy of the dark-field signal when the X-ray dose is low. The second part of this thesis concerns the postprocessing of the measured refraction images. The Talbot-Lau interferometer measures refraction perpendicular to the bar structures in the gratings. In order to obtain the actual refractive index, it is necessary to compute integrals over the measured data, which leads to a strong amplification of image noise. To this end, an efficient numerical optimization framework was developed. This framework was used to combine and evaluate multiple approaches for noise suppression. Noise behavior in tomographic reconstructions of refraction data is largely influenced by the orientation of the grating structures. This relationship was theoretically investigated. Based on these investigations, a method for deriving noise-suppressing filters was developed and experimentally evaluated.