SNR Spectra as a Quantitative Model for Image Quality in Polychromatic X-Ray Imaging

In polychromatic x-ray imaging for nondestructive testing, material science or medical applications, image quality is usually a problem of detecting sample structure in noisy data. This problem is typically stated this way: As many photons as possible need to be detected to get a good image quality. We instead propose to use the concept of signal detection, which is more universal. In signal detection, it is the sample properties which are detected. Photons play the role of information carriers for the signal. Signal detection for example allows modeling the effects which polychromaticity has on image quality. $\mathit{SNR}$ spectra (= spatial $\mathit{SNR}$) are used as a quantity to describe if reliable signal detection is possible. They include modulation transfer and phase contrast in addition to noisiness effects. $\mathit{SNR}$ spectra can also be directly measured, which means that theoretical predictions can easily be tested. We investigate the effects of signal and noise superposition on the $\mathit{SNR}$ spectrum and show how selectively not detecting photons can increase the image quality

Comparing Image Quality in Phase Contrast subμ\mu X-Ray Tomography -- A Round-Robin Study

How to evaluate and compare image quality from different sub-micrometer (sub$\mu$) CT scans? A simple test phantom made of polymer microbeads is used for recording projection images as well as 13 CT scans in a number of commercial and non-commercial scanners. From the resulting CT images, signal and noise power spectra are modeled for estimating volume signal-to-noise ratios (3D SNR spectra). Using the same CT images, a time- and shape-independent transfer function (MTF) is computed for each scan, including phase contrast effects and image blur ($\mathrm{MTF_{blur}}$). The SNR spectra and MTF of the CT scans are compared to 2D SNR spectra of the projection images. In contrary to 2D SNR, volume SNR can be normalized with respect to the object's power spectrum, yielding detection effectiveness (DE) a new measure which reveals how technical differences as well as operator-choices strongly influence scan quality for a given measurement time. Using DE, both source-based and detector-based sub$\mu$ CT scanners can be studied and their scan quality can be compared. Future application of this work requires a particular scan acquisition scheme which will allow for measuring 3D signal-to-noise ratios, making the model fit for 3D noise power spectra obsolete

Optimierung von Bildqualität in der hochauflösenden Röntgenbildgebung

The SNR spectra model and measurement method developed in this work yield reliable application-specific optima for image quality. This optimization can either be used to understand image quality, find out how to build a good imaging device or to (automatically) optimize the parameters of an existing setup. SNR spectra are here defined as a fraction of power spectra instead of a product of device properties. In combination with the newly developed measurement method for this definition, a close correspondence be- tween theory and measurement is achieved. Prior approaches suffer from a focus on theoretical definitions without fully considering if the defined quantities can be measured correctly. Additionally, discrepancies between assumptions and reality are common. The new approach is more reliable and complete, but also more difficult to evaluate and interpret. The signal power spectrum in the numerator of this fraction allows to model the image quality of different contrast mechanisms that are used in high-resolution x-ray imaging. Superposition equations derived for signal and noise enable understanding how polychromaticity (or superposition in general) affects the image quality. For the concept of detection energy weighting, a quantitative model for how it affects im- age quality was found. It was shown that—depending on sample properties—not detecting x-ray photons can increase image quality. For optimal computational energy weighting, more general formula for the optimal weight was found. In addition to the signal strength, it includes noise and modulation transfer. The novel method for measuring SNR spectra makes it possible to experimentally optimize image quality for different contrast mechanisms. This method uses one simple measurement to obtain a measure for im- age quality for a specific experimental setup. Comparable measurement methods typically require at least three more complex measurements, where the combination may then give a false result. SNR spectra measurements can be used to: • Test theoretical predictions about image quality optima. • Optimize image quality for a specific application. • Find new mechanisms to improve image quality. The last item reveals an important limitation of x- ray imaging in general: The achievable image quality is limited by the amount of x-ray photons interacting with the sample, not by the amount incident per detector area (see section 3.6). If the rest of the imaging geometry is fixed, moving the detector only changes the field of view, not the image quality. A practical consequence is that moving the sample closer to the x-ray source increases image quality quadratically. The results of a SNR spectra measurement represent the image quality only on a relative scale, but very reliable. This relative scale is sufficient for an optimization problem. Physical effects are often already clearly identifiable by the shape of the functional relationship between input parameter and measurement result. SNR spectra as a quantity are not well suited for standardization, but instead allow a reliable optimization. Not satisfying the requirements of standardization allows to use methods which have other advantages. In this case, the SNR spectra method describes the image quality for a specific application. Consequently, additional physical effects can be taken into account. Additionally, the measurement method can be used to automate the setting of optimal machine parameters. The newly proposed image quality measure detection effectiveness is better suited for standardization or setup comparison. This quantity is very similar to measures from other publications (e.g. CNR(u)), when interpreted monochromatically. Polychromatic effects can only be modeled fully by the DE(u). The measurement processes of both are different and the DE(u) is fundamentally more reliable. Information technology and digital data processing make it possible to determine SNR spectra from a mea- sured image series. This measurement process was designed from the ground up to use these technical capabilities. Often, information technology is only used to make processes easier and more exact. Here, the whole measurement method would be infeasible without it. As this example shows, using the capabilities of digital data processing much more extensively opens many new possibilities. Information technology can be used to extract information from measured data in ways that analog data processing simply cannot. The original purpose of the SNR spectra optimization theory and methods was to optimize high resolution x-ray imaging only. During the course of this work, it has become clear that some of the results of this work affect x-ray imaging in general. In the future, these results could be applied to MI and NDT x-ray imaging. Future work on the same topic will also need to consider the relationship between SNR spectra or DE(u) and sufficient image quality.This question is about the minimal image quality required for a specific measurement task.Das in dieser Arbeit entwickelte Modell und die Messmethode für SNR Spektren ergeben zuverlässige anwendungsspezifische Optima für die Bildqualität. Diese Optimierung kann verwendet werden, entweder um Bildqualität zu verstehen, um herauszufinden wie ein gutes Bildgebungsgerät gebaut werden kann oder um die Parameter eines existierenden Aufbaus (automatisch) festzulegen. ..

Correcting multi material artifacts from single material phase retrieved holo-tomograms with a simple 3D Fourier method

Here we present a method for the removal of multi-material artifacts which occur during the application of a single material phase retrieval procedure to X-ray tomographic data sets. For the phase retrieval we chose the most common method which is the single material filter. The correction method which we describe in the following has been designed for samples consisting of three distinct materials, hence effectively two different material interfaces. Furthermore the material phase with the strongest X-ray interaction needs to show sufficient absorption in order to allow for segmenting this phase through application of a grey value threshold. If these conditions are fulfilled the method is easy to apply through post processing as is shown for the volume images of two sample types

Robust Image Reconstruction Strategy for Multiscalar Holotomography

Holotomography is an extension of computed tomography where samples with low X-ray absorption can be investigated with higher contrast. In order to achieve this, the imaging system must yield an optical resolution of a few micrometers or less, which reduces the measurement area (field of view = FOV) to a few mm at most. If the sample size, however, exceeds the field of view (called local tomography or region of interest = ROI CT), filter problems arise during the CT reconstruction and phase retrieval in holotomography. In this paper, we will first investigate the practical impact of these filter problems and discuss approximate solutions. Secondly, we will investigate the effectiveness of a technique we call “multiscalar holotomography”, where, in addition to the ROI CT, a lower resolution non-ROI CT measurement is recorded. This is used to avoid the filter problems while simultaneously reconstructing a larger part of the sample, albeit with a lower resolution in the additional area