Deep-learning-based denoising of X-ray differential phase and dark-field images

PURPOSE

Statistical photon noise has always been a common problem in X-ray multi-contrast imaging and significantly influenced the quality of retrieved differential phase and dark-field images. We intend to develop a deep learning-based denoising algorithm to reduce the noise of retrieved X-ray differential phase and dark-field images.

METHODS

A novel deep learning based image noise suppression algorithm (named DnCNN-P) is presented. We proposed two different denoising modes: Retrieval-Denoising mode (R-D mode) and Denoising-Retrieval mode (D-R mode). While the R-D mode denoises the retrieved images, the D-R mode denoises the raw phase stepping data. The two denoising modes are evaluated under different photon counts and visibilities.

RESULTS

Experimental results show that with the algorithm DnCNN-P used, the D-R mode always exhibits a better noise reduction under diverse experimental conditions, even in the case of a low photon count and/or a low visibility. With a detected photon count of 1800 and a visibility of 0.3, compared to the differential phase images without denoising, the standard deviation is reduced by 89.1% and 16.4% in the D-R and R-D modes. Compared to the dark-field images without denoising, the standard deviation is reduced by 83.7% and 12.6% in the D-R and R-D modes, respectively.

CONCLUSIONS

The novel supervised DnCNN-P algorithm can significantly reduce the noise in retrieved X-ray differential phase and dark-field images. We believe this novel algorithm can be a promising approach to improve the quality of X-ray differential phase and dark-field images, and therefore dose efficiency in future biomedical applications.

Initial Characterization of Dark-Field CT on a Clinical Gantry

X-ray computed tomography (CT) is an important non-destructive imaging technique, particularly in clinical diagnostics. Even with the latest innovations like dual-energy and photon-counting CT, the image contrast is solely generated from attenuation in the tissue. An extension - fully compatible with these novelties - is dark-field CT, which retrieves an additional, so-called dark-field contrast. Unlike the attenuation channel, the dark-field channel is sensitive to tissue microstructure and porosity below the resolution of the imaging system, which allows additional insights into the health of the lung tissue or the structure of calcifications. The potential clinical value has been demonstrated in several preclinical studies and recently also in radiography patient studies. Just recently the first dark-field CT for the human body was established at the Technical University of Munich and in this paper, we discuss the performance of this prototype. We evaluate the interferometer components and the imposed challenges that the integration into the CT gantry brings by comparing the results to simulations and measurements at a laboratory setup. The influence of the clinical X-ray source on the Talbot-Lau interferometer and the impact of vibrations, which are immanent on the clinical CT gantry, are analyzed in detail to reveal their characteristic frequencies and origin. A beam hardening correction is introduced as an important step to adapt to the poly-chromatic spectrum and make quantitative dark-field imaging possible. We close with an analysis of the image resolution and the applied patient dose, and conclude that the performance is sufficient to suggest initial patient studies using the presented dark-field CT system.

Modeling Vibrations of a Tiled Talbot-Lau Interferometer on a Clinical CT

X-ray computed tomography (CT) is an invaluable imaging technique for non-invasive medical diagnosis. However, for soft tissue in the human body the difference in attenuation is inherently small. Grating-based X-ray phase-contrast is a relatively novel imaging method which detects additional interaction mechanisms between photons and matter, namely refraction and small-angle scattering, to generate additional images with different contrast. The experimental setup involves a Talbot-Lau interferometer whose susceptibility to mechanical vibrations hindered acquisition schemes suitable for clinical routine in the past. We present a processing pipeline to identify spatially and temporally variable fluctuations occurring in an interferometer installed on a continuously rotating clinical CT gantry. The correlations of the vibrations in the modular grating setup are exploited to identify a small number of relevant fluctuation modes, allowing for a sample reconstruction free of vibration artifacts.

Technical Design Considerations of a Human-Scale Talbot-Lau Interferometer for Dark-Field CT

Computed tomography (CT) as an important clinical diagnostics method can profit from extension with dark-field imaging, as it is currently restricted to X-rays' attenuation contrast only. Dark-field imaging allows access to more tissue properties, such as micro-structural texture or porosity. The up-scaling process to clinical scale is complex because several design constraints must be considered. The two most important ones are that the finest grating is limited by current manufacturing technology to a [Formula: see text] period and that the interferometer should fit into the CT gantry with minimal modifications only. In this work we discuss why an inverse interferometer and a triangular G1 profile are advantageous and make a compact and sensitive interferometer implementation feasible. Our evaluation of the triangular grating profile reveals a deviation in the interference pattern compared to standard grating profiles, which must be considered in the subsequent data processing. An analysis of the grating orientation demonstrates that currently only a vertical layout can be combined with cylindrical bending of the gratings. We also provide an in-depth discussion, including a new simulation approach, of the impact of the extended X-ray source spot which can lead to large performance loss and present supporting experimental results. This analysis reveals a vastly increased sensitivity to geometry and grating period deviations, which must be considered early in the system design process.

Single-exposure X-ray phase imaging microscopy with a grating interferometer

The advent of hard X-ray free-electron lasers enables nanoscopic X-ray imaging with sub-picosecond temporal resolution. X-ray grating interferometry offers a phase-sensitive full-field imaging technique where the phase retrieval can be carried out from a single exposure alone. Thus, the method is attractive for imaging applications at X-ray free-electron lasers where intrinsic pulse-to-pulse fluctuations pose a major challenge. In this work, the single-exposure phase imaging capabilities of grating interferometry are characterized by an implementation at the I13-1 beamline of Diamond Light Source (Oxfordshire, UK). For comparison purposes, propagation-based phase contrast imaging was also performed at the same instrument. The characterization is carried out in terms of the quantitativeness and the contrast-to-noise ratio of the phase reconstructions as well as via the achievable spatial resolution. By using a statistical image reconstruction scheme, previous limitations of grating interferometry regarding the spatial resolution can be mitigated as well as the experimental applicability of the technique.

Noise Reduction for Single-Shot Grating-Based Phase-Contrast Imaging at an X-ray Backlighter

X-ray backlighters allow the capture of sharp images of fast dynamic processes due to extremely short exposure times. Moiré imaging enables simultaneously measuring the absorption and differential phase-contrast (DPC) of these processes. Acquiring images with one single shot limits the X-ray photon flux, which can result in noisy images. Increasing the photon statistics by repeating the experiment to gain the same image is not possible if the investigated processes are dynamic and chaotic. Furthermore, to reconstruct the DPC and transmission image, an additional measurement captured in absence of the object is required. For these reference measurements, shot-to-shot fluctuations in X-ray spectra and a source position complicate the averaging of several reference images for noise reduction. Here, two approaches of processing multiple reference images in combination with one single object image are evaluated regarding the image quality. We found that with only five reference images, the contrast-to-noise ratio can be improved by approximately 13% in the DPC image. This promises improvements for short-exposure single-shot acquisitions of rapid processes, such as laser-produced plasma shock-waves in high-energy density experiments at backlighter X-ray sources such as the PHELIX high-power laser facility.

Fourier-based interpretation and noise analysis of the moments of small-angle x-ray scattering in grating-based x-ray phase contrast imaging

In grating-based x-ray phase contrast imaging, Fourier component analysis (FCA) is usually recognized as a gold standard to retrieve the contrasts including attenuation, phase and dark-field, since it is well-established on wave optics and is of high computational efficiency. Meanwhile, an alternative approach basing on the particle scattering theory is being developed and can provide similar contrasts with FCA by calculating multi-order moments of deconvolved small-angle x-ray scattering, so called as multi-order moment analysis (MMA). Although originated from quite different physics theories, the high consistency between the contrasts retrieved by FCA and MMA implies us that there may be some intrinsic connections between them, which has not been fully revealed to the best of our knowledge. In this work, we present a Fourier-based interpretation of MMA and conclude that the contrasts retrieved by MMA are actually the weighted compositions of Fourier coefficients, which means MMA delivers similar physical information as FCA. Based on the recognized cosine model, we also provide a truncated analytic MMA method, and its computational efficiency can be hundreds of times faster than the original deconvolution-based MMA method. Moreover, a noise analysis for our proposed truncated method is also conducted to further evaluate its performances. The results of numerical simulation and physical experiments support our analyses and conclusions.

Fabrication of X-ray Gratings for Interferometric Imaging by Conformal Seedless Gold Electroplating

We present a method to produce small pitch gratings for X-ray interferometric imaging applications, allowing the phase sensitivity to be increased and/or the length of the laboratory setup to be minimized. The method is based on fabrication of high aspect ratio silicon microstructures using deep reactive ion etching (Bosch technique) of dense grating arrays and followed by conformal electroplating of Au. We demonstrated that low resistivity Si substrates (<0.01 Ohm·cm) enable the metal seeding layer deposition step to be avoided, which is normally required to initiate the electroplating process. Etching conditions were optimized to realize Si recess structures with a slight bottom tapering, which ensured the void-free Au filling of the trenches. Vapor HF was used to remove the native oxide layer from the Si grating surface prior to electroplating in the cyanide-based Au electrolyte. Fabrication of Au gratings with pitch in the range 1.2-3.0 µm was successfully realized. A substantial improved aspect ratio of 45:1 for a pitch size of 1.2 µm was achieved with respect to the prior art on 4-inch wafer-based technology. The fabricated Au gratings were tested with X-ray interferometers in Talbot-Laue configuration with measured visibility of 13% at an X-ray design energy of 26 keV.

X-ray phase contrast simulation for grating-based interferometry using GATE

The overall importance of x-ray phase contrast (XPC) imaging has grown substantially in the last decades, in particular with the recent advent of compact lab-based XPC systems. For optimizing the experimental XPC setup, as well as benchmarking and testing new acquisition and reconstruction techniques, Monte Carlo (MC) simulations are a valuable tool. GATE, an open source application layer on top of the Geant4 simulation software, is a versatile MC tool primarily intended for various types of medical imaging simulations. To our knowledge, however, there is no GATE-based academic simulation software available for XPC imaging. In this paper, we extend the GATE framework with new physics-based tools for accurate XPC simulations. Our approach combines Monte Carlo simulations in GATE for modelling the x-ray interactions in the sample with subsequent numerical wave propagation, starting from the GATE output.

Enhancing the X-Ray Differential Phase Contrast Image Quality With Deep Learning Technique

OBJECTIVE

The purpose of this work is to investigate the feasibility of using deep convolutional neural network (CNN) to improve the image quality of a grating-based X-ray differential phase contrast imaging (XPCI) system.

METHODS

In this work, a novel deep CNN based phase signal extraction and image noise suppression algorithm (named as XP-NET) is developed. The numerical phase phantom, the ex vivo biological specimen and the ACR breast phantom are evaluated via the numerical simulations and experimental studies, separately. Moreover, images are also evaluated under different low radiation levels to verify its dose reduction capability.

RESULTS

Compared with the conventional analytical method, the novel XP-NET algorithm is able to reduce the bias of large DPC signals and hence increasing the DPC signal accuracy by more than 15%. Additionally, the XP-NET is able to reduce DPC image noise by about 50% for low dose DPC imaging tasks.

CONCLUSION

This proposed novel end-to-end supervised XP-NET has a great potential to improve the DPC signal accuracy, reduce image noise, and preserve object details.

SIGNIFICANCE

We demonstrate that the deep CNN technique provides a promising approach to improve the grating-based XPCI performance and its dose efficiency in future biomedical applications.

A theoretical framework for comparing noise characteristics of spectral, differential phase-contrast and spectral differential phase-contrast x-ray imaging

Spectral and grating-based differential phase-contrast (DPC) x-ray imaging are two emerging technologies that offer additional information compared with conventional attenuation-based x-ray imaging. In the case of spectral imaging, energy-resolved measurements allow the generation of material-specific images by exploiting differences in the energy-dependent attenuation. DPC imaging uses the phase shift that an x-ray wave exhibits when traversing an object as contrast generation mechanism. Recently, we have investigated the combination of these two imaging techniques (spectral DPC imaging) and demonstrated potential advantages compared with spectral imaging. In this work, we present a noise analysis framework that allows the prediction of (co-) variances and noise power spectra for all three imaging methods. Moreover, the optimum acquisition parameters for a particular imaging task can be determined. We use this framework for a performance comparison of all three imaging methods. The comparison is focused on (projected) electron density images since they can be calculated with all three imaging methods. Our study shows that spectral DPC imaging enables the calculation of electron density images with strongly reduced noise levels compared with the other two imaging methods for a large range of clinically relevant pixel sizes. In contrast to conventional DPC imaging, there are no long-range noise correlations for spectral DPC imaging. This means that excessive low frequency noise can be avoided. We confirm the analytical predictions by numerical simulations.

Spectral Differential Phase Contrast X-Ray Radiography

We investigate the combination of two emerging X-ray imaging technologies, namely spectral imaging and differential phase contrast imaging. By acquiring spatially and temporally registered images with several different X-ray spectra, spectral imaging can exploit differences in the energy-dependent attenuation to generate material selective images. Differential phase contrast imaging uses an entirely different contrast generation mechanism: The phase shift that an X-ray wave exhibits when traversing an object. As both methods can determine the (projected) electron density, we propose a novel material decomposition algorithm that uses the spectral and the phase contrast information simultaneously. Numerical experiments show that the combination of these two imaging techniques benefits from the strengths of the individual methods while the weaknesses are mitigated: Quantitatively accurate basis material images are obtained and the noise level is strongly reduced, compared to conventional spectral X-ray imaging.

Transmission, refraction and dark-field retrieval in hard X-ray grating interferometry

A three-image algorithm is proposed to retrieve the sample's transmission, refraction and dark-field information in hard X-ray grating interferometry. Analytical formulae of the three-image algorithm are theoretically derived and presented, and evaluated by proof-of-principle synchrotron radiation experiments. The results confirm the feasibility of the proposed algorithm. The novelty of the proposed algorithm is that it allows versatile and tunable multimodal X-ray imaging by substantially relaxing the existing limitations on the lateral grating position. Furthermore, this algorithm can also be adapted for samples with negligible refraction, reducing the number of required sample measurements to two. Furthermore, the noise properties of the retrieved images are investigated in terms of the standard deviations. Theoretical models are presented and verified by synchrotron radiation measurements. It is shown that the noise standard deviations exhibit strong dependence on the lateral grating position, especially in the case of refraction and dark-field images. Further noise reduction and dose reduction can thus be possible by optimizing the lateral grating position for a selected region of interest. Those results can serve as general guidelines to optimize the data acquisition scheme for specific applications and problems.

The trigonometric orthogonality of phase-stepping curves in grating-based x-ray phase-contrast imaging: Integral property and its implications for noise optimization

PURPOSE

Grating-based x-ray phase-contrast imaging (GPCI) is a promising technique for clinical applications as it can provide two newly emerging imaging modalities (differential phase-contrast and dark-field contrast) in addition to the conventional absorption contrast. As far, phase-stepping strategy is the most commonly used approach in GPCI to indirectly acquire differential phase-contrast and dark-field contrast. It is known that the obtained phase-stepping curves (PSCs) have the cosine property and the convolution property, leading to two types of information retrieval approaches in literature: the Fourier component analysis and the multi-order moment analysis. The purpose of this paper is to derive a new property of PSCs and apply the property to noise optimization for information retrieval.

METHODS

Based on the cosine expression of the flat PSC without the sample and the well-established convolution relationship between the flat PSC and the sample PSC, we reveal an important integral property of PSCs: the inner product of PSCs and an arbitrary function contains only zero-order and first-order components in the Fourier series. Furthermore, we apply the property to the direct multi-order moment analysis and propose a set of generalized forms including an optimal one in the presence of noise.

RESULTS

To validate the effectiveness of our analysis, we compared the simulated and real experiment results retrieved by the original direct multi-order moment analysis with the ones retrieved by our proposed noise-optimal form. A significant improvement of noise performance by our method is observed and the improvement ratio in differential phase-contrast is consistent with our theoretical calculation (39.2%).

CONCLUSIONS

In this paper, we reveal a new integral property of the acquired PSCs with and without samples in GPCI, which can be applied to information retrieval approaches like the direct multi-order moment analysis. Then we optimize these approaches to improve the noise performance, offering great potentials of dose reduction in practical applications.

Is high sensitivity always desirable for a grating-based differential phase contrast imaging system?

PURPOSE

In grating-based x-ray differential phase contrast (DPC) imaging, the measured signal amplitude of the phase shift induced by an image object is proportional to the so-called system sensitivity. Therefore, to achieve a better signal-to-noise (SNR) for improved imaging performance, it is generally believed that one should increase the system sensitivity by reducing the period of the analyzer grating or increasing the distance between the phase grating and analyzer grating. The purpose of this work is to theoretically and experimentally demonstrate that there is an optimal system sensitivity to attain the highest SNR for a given task provided that the standard phase-stepping acquisition and phase retrieval methods are used. When system sensitivity goes beyond this optimal value, SNR decreases and the imaging performance deteriorates.

METHODS

Due to the fundamental fact that the measured phase signal is a cyclic variable, the phase wrapping effect is inevitable in DPC imaging when the system sensitivity increases. The phase wrapping effect appears in both signal and noise measurements. The effect in the signal measurement is manifested in the so-called signal statistical bias and such effect often impacts the accuracy of the measurement. The phase wrapping effect also appears in the noise variance measurement and impacts the precision of the measurement. A thorough theoretical analysis was performed in this work to demonstrate the quantitative impacts of phase wrapping on both signal bias and noise variance and thus on the actual system SNR. The joint effect of phase wrapping in both the signal bias and noise variance yields an optimal system sensitivity to achieve the highest SNR. Both extensive numerical simulation studies and experimental studies were performed to validate the theoretical analysis.

RESULTS

Both theoretical analysis and experimental studies show that the SNR of the DPC signal is not always proportional to the sensitivity due to the cyclic nature of the signal and the phase wrapping effect. For a given refraction angle and exposure level, there exists an optimal sensitivity factor that maximizes the SNR, beyond which, increasing the sensitivity will decrease the SNR.

CONCLUSIONS

Increase of system sensitivity does not always improve x-ray DPC imaging performance provided that the standard phase-stepping acquisition and phase retrieval methods are used.

Impact of the sensitivity factor on the signal-to-noise ratio in grating-based phase contrast imaging

The sensitivity factor of a grating-based x-ray differential phase contrast (DPC) imaging system determines how much fringe shift can be observed for a given refraction angle. It is commonly believed that increasing the sensitivity factor will improve the signal-to-noise ratio (SNR) of the phase signal. However, this may not always be the case if the intrinsic phase wrapping effect is taken into consideration. In this work, a theoretical derivation is provided to quantify relationship between the sensitivity and SNR for a given refraction angle, exposure level, and grating based x-ray DPC system. The theoretical derivation shows that the expected phase signal is not always proportional to the sensitivity factor and may even decrease when the sensitivity factor becomes too large. The noise variance of the signal is not always solely dependent on the exposure level and fringe visibility but may become signal-dependent under certain circumstances. As a result, SNR of the phase signal does not always increase with higher sensitivity. Numerical simulation studies were performed to validate the theoretical models. Results show that when the fringe visibility and exposure level are fixed, there exists an optimal sensitivity factor which maximizes the SNR for a given refraction angle; further increase of the sensitivity factor may decrease the SNR.

Single-shot Talbot-Lau x-ray dark-field imaging of a porcine lung applying the moiré imaging approach

Talbot-Lau x-ray imaging provides additionally to the conventional attenuation image, two further images: the differential phase-contrast image which is especially sensitive to differences in refractive properties and the dark-field image which is showing the x-ray scattering properties of the object. Thus, in the dark-field image sub-pixeled object information can be observed. As it has been shown in recent studies, this is of special interest for lung imaging. Changes in the alveoli structure, which are in the size of one detector pixel, can be seen in the dark-field images. A fast acquisition process is crucial to avoid motion artifacts due to heartbeat and breathing of the patient. Using moiré imaging the images can be acquired with a single-shot exposure. Nevertheless, the spatial resolution is reduced compared to the phase-stepping acquisition. We evaluate the results of both imaging techniques towards their feasibility in clinical routine. Furthermore, we analyse the influence of artificial linear object movement on the image quality, in order to simulate the heartbeat of a patient.

Implementation of a Talbot-Lau interferometer in a clinical-like c-arm setup: A feasibility study

X-ray grating-based phase-contrast imaging has raised interest regarding a variety of potential clinical applications, whereas the method is feasible using a medical x-ray tube. Yet, the transition towards a clinical setup remains challenging due to the requirement of mechanical robustness of the interferometer and high demands applying to medical equipment in clinical use. We demonstrate the successful implementation of a Talbot-Lau interferometer in an interventional c-arm setup. The consequence of vibrations induced by the rotating anode of the tube is discussed and the prototype is shown to provide a visibility of 21.4% at a tube voltage of 60 kV despite the vibrations. Regarding clinical application, the prototype is mainly set back due to the limited size of the field of view covering an area of 17 mm × 46 mm. A c-arm offers the possibility to change the optical axis according to the requirements of the medical examination. We provide a method to correct for artifacts that result from the angulation of the c-arm. Finally, the images of a series of measurements with the c-arm in different angulated positions are shown. Thereby, it is sufficient to perform a single reference measurement in parking position that is valid for the complete series despite angulation.

Revising the lower statistical limit of x-ray grating-based phase-contrast computed tomography

Phase-contrast x-ray computed tomography (PCCT) is currently investigated as an interesting extension of conventional CT, providing high soft-tissue contrast even if examining weakly absorbing specimen. Until now, the potential for dose reduction was thought to be limited compared to attenuation CT, since meaningful phase retrieval fails for scans with very low photon counts when using the conventional phase retrieval method via phase stepping. In this work, we examine the statistical behaviour of the reverse projection method, an alternative phase retrieval approach and compare the results to the conventional phase retrieval technique. We investigate the noise levels in the projections as well as the image quality and quantitative accuracy of the reconstructed tomographic volumes. The results of our study show that this method performs better in a low-dose scenario than the conventional phase retrieval approach, resulting in lower noise levels, enhanced image quality and more accurate quantitative values. Overall, we demonstrate that the lower statistical limit of the phase stepping procedure as proposed by recent literature does not apply to this alternative phase retrieval technique. However, further development is necessary to overcome experimental challenges posed by this method which would enable mainstream or even clinical application of PCCT.

Improved reconstruction of phase-stepping data for Talbot-Lau x-ray imaging

Grating-based Talbot-Lau x-ray interferometry is a popular method for measuring absorption, phase shift, and small-angle scattering. The standard acquisition method for this modality is phase stepping, where the Talbot pattern is reconstructed from multiple images acquired at different grating positions. We review the implicit assumptions in phase-stepping reconstruction, and find that the assumptions of perfectly known grating positions and homoscedastic noise variance are violated in some scenarios. Additionally, we investigate a recently reported estimation bias in the visibility and dark-field signal. To adapt the phase-stepping reconstruction to these findings, we propose three improvements to the reconstruction. These improvements are (a) to use prior knowledge to compute more accurate grating positions to reduce moiré artifacts, (b) to utilize noise variance information to reduce dark-field and phase noise in high-visibility acquisitions, and (c) to perform correction of an estimation bias in the interferometer visibility, leading to more quantitative dark-field imaging in acquisitions with a low signal-to-noise ratio. We demonstrate the benefit of our methods on simulated data, as well as on images acquired with a Talbot-Lau interferometer.

Studies of signal estimation bias in grating-based x-ray multicontrast imaging

PURPOSE

In grating-based x-ray multi-contrast imaging, signals of three contrast mechanisms-absorption contrast, differential phase contrast (DPC), and dark-field contrast-can be estimated from the same set of acquired data. The estimated signals, N₀ (related to absorption), N₁ (related to dark-field), and φ (related to DPC) may be intrinsically biased. However, it is yet unclear how large these biases are and how the data acquisition parameters affect the biases in the extracted signals. The purpose of this paper was to address these questions.

METHODS

The biases of the extracted signals (i.e., N₀ , N₁ and φ) were theoretically studied for a well-known signal estimation method. Experimental data acquired from a grating-based x-ray multi-contrast benchtop imaging system with a photon counting detector were used to validate the theoretical results for the signal biases of the three contrast mechanisms.

RESULTS

Both theoretical and experimental studies showed the following results: (1) The bias of signal estimation for the absorption contrast signal is zero; (2) The bias of signal estimation for N₁ is inversely proportional to the number of phase steps and to the average fringe visibility of the grating interferometer, but the ratio between the bias and the signal level (i.e., the relative bias) is independent of the number of phase steps; (3) The bias of signal estimation for φ depends on the mean DPC signal level, the total exposure level of the multi-contrast data acquisition, and the mean fringe visibility of the interferometer.

CONCLUSIONS

In grating-based x-ray multi-contrast imaging, the estimated absorption contrast signal is unbiased; the estimated dark-field contrast signal is biased, but the relative bias is only dependent on the mean fringe visibility of the interferometer and the exposure level. The estimated DPC signal may be biased, and the bias level depends on the mean signal level, the exposure level, and the interferometer performance.

On the relative performance of edge illumination x-ray phase-contrast CT and conventional, attenuation-based CT

PURPOSE

This article is aimed at comparing edge illumination (EI) x-ray phase contrast computed tomography (PCT) and conventional (attenuation-based) computed tomography (CT), based on their respective contrast and noise transfer.

METHODS

The noise in raw projections obtained with EI PCT is propagated through every step of the data processing, including phase retrieval and tomographic reconstruction, leading to a description of the noise in the reconstructed phase tomograms. This is compared to the noise in corresponding attenuation tomograms obtained with CT. Specifically, a formula is derived that allows evaluating the relative performance of both modalities on the basis of their contrast-to-noise ratio (CNR), for a variety of experimental parameters.

RESULTS

The noise power spectra of phase tomograms are shifted towards lower spatial frequencies, leading to a fundamentally different noise texture. The relative performance of EI PCT and CT, in terms of their CNR, is linked to spatial resolution: the CNR in phase tomograms is generally superior to that in attenuation tomograms for higher spatial resolutions (tens to hundreds of μm), but inferior for lower spatial resolutions (hundreds of μm to mm).

CONCLUSION

These results imply that EI PCT could outperform CT in applications for which high spatial resolutions are key, e.g., small animal or specimen imaging.

Visibility simulation of realistic grating interferometers including grating geometries and energy spectra

The performance of X-ray and neutron grating interferometers is characterised by their visibility, which is a measure for the maximum achievable contrast. In this study we show how the real grating geometry in a grating interferometer with three gratings impacts the interference and self projection that leads to visibility in the first place. We quantify the individual contributions of wavelength distributions and grating shapes in terms of visibility reduction by determining the absolute as well as relative effect of each contribution. The understanding of the impact of changed geometry and wavelength distributions on the interference of neutrons/X-rays allows us to present the first fully quantitative model of a grating interferometer setup. We demonstrate the capability of the simulation framework by building a model of the neutron grating interferometer at the ICON beamline and directly comparing simulated and measured visibility values. The general nature of the model makes it possible to extend it to any given grating interferometer for both X-rays and neutrons.

Two-shot X-ray dark-field imaging

In this article, we report on a novel acquisition scheme for time- and dose-saving retrieval of dark-field data in grating-based phase-contrast imaging. In comparison to currently available techniques, the proposed approach only requires two phase steps. More importantly, our method is capable of accurately retrieving the dark-field signal where conventional approaches fail, for instance in the case of very low photon statistics. Finally, we successfully extend two-shot dark-field imaging to tomographic investigations, by implementing an iterative reconstruction with appropriate weights. Our results indicate an important progression towards the clinical feasibility of dark-field tomography.

Penalized maximum likelihood reconstruction for x-ray differential phase-contrast tomography

PURPOSE

The purpose of this work is to propose a cost function with regularization to iteratively reconstruct attenuation, phase, and scatter images simultaneously from differential phase contrast (DPC) acquisitions, without the need of phase retrieval, and examine its properties. Furthermore this reconstruction method is applied to an acquisition pattern that is suitable for a DPC tomographic system with continuously rotating gantry (sliding window acquisition), overcoming the severe smearing in noniterative reconstruction.

METHODS

We derive a penalized maximum likelihood reconstruction algorithm to directly reconstruct attenuation, phase, and scatter image from the measured detector values of a DPC acquisition. The proposed penalty comprises, for each of the three images, an independent smoothing prior. Image quality of the proposed reconstruction is compared to images generated with FBP and iterative reconstruction after phase retrieval. Furthermore, the influence between the priors is analyzed. Finally, the proposed reconstruction algorithm is applied to experimental sliding window data acquired at a synchrotron and results are compared to reconstructions based on phase retrieval.

RESULTS

The results show that the proposed algorithm significantly increases image quality in comparison to reconstructions based on phase retrieval. No significant mutual influence between the proposed independent priors could be observed. Further it could be illustrated that the iterative reconstruction of a sliding window acquisition results in images with substantially reduced smearing artifacts.

CONCLUSIONS

Although the proposed cost function is inherently nonconvex, it can be used to reconstruct images with less aliasing artifacts and less streak artifacts than reconstruction methods based on phase retrieval. Furthermore, the proposed method can be used to reconstruct images of sliding window acquisitions with negligible smearing artifacts.

Improving radiation dose efficiency of X-ray differential phase contrast imaging using an energy-resolving grating interferometer and a novel rank constraint

In this paper, a novel method was developed to improve the radiation dose efficiency, viz., contrast to noise ratio normalized by dose (CNRD), of the grating-based X-ray differential phase contrast (DPC) imaging system that is integrated with an energy-resolving photon counting detector. The method exploits the low-dimensionality of the spatial-spectral DPC image matrix acquired from different energy windows. A low rank approximation of the spatial-spectral image matrix was developed to reduce image noise while retaining the DPC signal accuracy for every energy window. Numerical simulations and experimental phantom studies have been performed to validate the proposed method by showing noise reduction and CNRD improvement for each energy window.

Designing the phase grating for Talbot-Lau phase-contrast imaging systems: a simulation and experiment study

The performance of a Talbot-Lau interferometer depends to a great extent on its visibility. This means, to obtain high quality phase-contrast and dark-field images a high visibility is mandatory. Several parameters influence the visibility of such a system, like for example the x-ray spectrum, the inter-grating distances or the parameters of the three gratings. In this multidimensional space, wave field simulations help to find the optimal combination of the grating specifications to construct a setup with a high visibility while retaining a fixed angular sensitivity. In this work we specifically analyzed the influence of the G1 grating duty cycle in simulations and experiments. We show that there is a lot of room for improvement by varying the duty cycle of the phase-shifting grating G1. As a result, by employing a third-integer duty cycle we can increase the visibility to up to 53 % in a laboratory setup with a polychromatic spectrum. The achieved visibility is more than two times higher compared to the result with a standard-type setup. This visibility gain allows a dose reduction by a factor of 5 preserving the same image quality.

Bilateral filtering using the full noise covariance matrix applied to x-ray phase-contrast computed tomography

The purpose of this work is to develop an image-based de-noising algorithm that exploits complementary information and noise statistics from multi-modal images, as they emerge in x-ray tomography techniques, for instance grating-based phase-contrast CT and spectral CT. Among the noise reduction methods, image-based de-noising is one popular approach and the so-called bilateral filter is a well known algorithm for edge-preserving filtering. We developed a generalization of the bilateral filter for the case where the imaging system provides two or more perfectly aligned images. The proposed generalization is statistically motivated and takes the full second order noise statistics of these images into account. In particular, it includes a noise correlation between the images and spatial noise correlation within the same image. The novel generalized three-dimensional bilateral filter is applied to the attenuation and phase images created with filtered backprojection reconstructions from grating-based phase-contrast tomography. In comparison to established bilateral filters, we obtain improved noise reduction and at the same time a better preservation of edges in the images on the examples of a simulated soft-tissue phantom, a human cerebellum and a human artery sample. The applied full noise covariance is determined via cross-correlation of the image noise. The filter results yield an improved feature recovery based on enhanced noise suppression and edge preservation as shown here on the example of attenuation and phase images captured with grating-based phase-contrast computed tomography. This is supported by quantitative image analysis. Without being bound to phase-contrast imaging, this generalized filter is applicable to any kind of noise-afflicted image data with or without noise correlation. Therefore, it can be utilized in various imaging applications and fields.

An x-ray backlit Talbot-Lau deflectometer for high-energy-density electron density diagnostics

X-ray phase-contrast techniques can measure electron density gradients in high-energy-density plasmas through refraction induced phase shifts. An 8 keV Talbot-Lau interferometer consisting of free standing ultrathin gratings was deployed at an ultra-short, high-intensity laser system using K-shell emission from a 1-30 J, 8 ps laser pulse focused on thin Cu foil targets. Grating survival was demonstrated for 30 J, 8 ps laser pulses. The first x-ray deflectometry images obtained under laser backlighting showed up to 25% image contrast and thus enabled detection of electron areal density gradients with a maximum value of 8.1 ± 0.5 × 10(23) cm(-3) in a low-Z millimeter sized sample. An electron density profile was obtained from refraction measurements with an error of <8%. The 50 ± 15 μm spatial resolution achieved across the full field of view was found to be limited by the x-ray source-size, similar to conventional radiography.

A novel crystal-analyzer phase retrieval algorithm and its noise property

A description of the rocking curve in diffraction enhanced imaging (DEI) is presented in terms of the angular signal response function and a simple multi-information retrieval algorithm based on the cosine function fitting. A comprehensive analysis of noise properties of DEI is also given considering the noise transfer characteristic of the X-ray source. The validation has been performed with synchrotron radiation experimental data and Monte Carlo simulations based on the Geant4 toolkit combined with the refractive process of X-rays, which show good agreement with each other. Moreover, results indicate that the signal-to-noise ratios of the refraction and scattering images are about one order of magnitude better than that of the absorption image at the edges of low-Z samples. The noise penalty is drastically reduced with the increasing photon flux and visibility. Finally, this work demonstrates that the analytical method can build an interesting connection between DEI and GDPCI (grating-based differential phase contrast imaging) and is widely suitable for a variety of measurement noise in the angular signal response imaging prototype. The analysis significantly contributes to the understanding of noise characteristics of DEI images and may allow improvements to the signal-to-noise ratio in biomedical and material science imaging.

Phase unwrapping in spectral X-ray differential phase-contrast imaging with an energy-resolving photon-counting pixel detector

Grating-based differential phase-contrast imaging has proven to be feasible with conventional X-ray sources. The polychromatic spectrum generally limits the performance of the interferometer but benefit can be gained with an energy-sensitive detector. In the presented work, we employ the energy-discrimination capability to correct for phase-wrapping artefacts. We propose to use the phase shifts, which are measured in distinct energy bins, to estimate the optimal phase shift in the sense of maximum likelihood. We demonstrate that our method is able to correct for phase-wrapping artefacts, to improve the contrast-to-noise ratio and to reduce beam hardening due to the modelled energy dependency. The method is evaluated on experimental data which are measured with a laboratory Talbot-Lau interferometer equipped with a conventional polychromatic X-ray source and an energy-sensitive photon-counting pixel detector. Our work shows, that spectral imaging is an important step to move differential phase-contrast imaging closer to pre-clinical and clinical applications, where phase wrapping is particularly problematic.

High sensitivity phase retrieval method in grating-based x-ray phase contrast imaging

PURPOSE

Grating-based x-ray phase contrast imaging is considered as one of the most promising techniques for future medical imaging. Many different methods have been developed to retrieve phase signal, among which the phase stepping (PS) method is widely used. However, further practical implementations are hindered, due to its complex scanning mode and high radiation dose. In contrast, the reverse projection (RP) method is a novel fast and low dose extraction approach. In this contribution, the authors present a quantitative analysis of the noise properties of the refraction signals retrieved by the two methods and compare their sensitivities.

METHODS

Using the error propagation formula, the authors analyze theoretically the signal-to-noise ratios (SNRs) of the refraction images retrieved by the two methods. Then, the sensitivities of the two extraction methods are compared under an identical exposure dose. Numerical experiments are performed to validate the theoretical results and provide some quantitative insight.

RESULTS

The SNRs of the two methods are both dependent on the system parameters, but in different ways. Comparison between their sensitivities reveals that for the refraction signal, the RP method possesses a higher sensitivity, especially in the case of high visibility and/or at the edge of the object.

CONCLUSIONS

Compared with the PS method, the RP method has a superior sensitivity and provides refraction images with a higher SNR. Therefore, one can obtain highly sensitive refraction images in grating-based phase contrast imaging. This is very important for future preclinical and clinical implementations.

Energy weighted x-ray dark-field imaging

The dark-field image obtained in grating-based x-ray phase-contrast imaging can provide information about the objects' microstructures on a scale smaller than the pixel size even with low geometric magnification. In this publication we demonstrate that the dark-field image quality can be enhanced with an energy-resolving pixel detector. Energy-resolved x-ray dark-field images were acquired with a 16-energy-channel photon-counting pixel detector with a 1 mm thick CdTe sensor in a Talbot-Lau x-ray interferometer. A method for contrast-noise-ratio (CNR) enhancement is proposed and validated experimentally. In measurements, a CNR improvement by a factor of 1.14 was obtained. This is equivalent to a possible radiation dose reduction of 23%.

Performance and optimization of X-ray grating interferometry

The monochromatic and polychromatic performance of a grating interferometer is theoretically analysed. The smallest detectable refraction angle is used as a metric for the efficiency in acquiring a differential phase-contrast image. Analytical formulae for the visibility and the smallest detectable refraction angle are derived for Talbot-type and Talbot-Lau-type interferometers, respectively, providing a framework for the optimization of the geometry. The polychromatic performance of a grating interferometer is investigated analytically by calculating the energy-dependent interference fringe visibility, the spectral acceptance and the polychromatic interference fringe visibility. The optimization of grating interferometry is a crucial step for the design of application-specific systems with maximum performance.

Comparison of two x-ray phase-contrast imaging methods with a microfocus source

We present a comparison for high-resolution imaging with a laboratory source between grating-based (GBI) and propagation-based (PBI) x-ray phase-contrast imaging. The comparison is done through simulations and experiments using a liquid-metal-jet x-ray microfocus source. Radiation doses required for detection in projection images are simulated as a function of the diameter of a cylindrical sample. Using monochromatic radiation, simulations show a lower dose requirement for PBI for small object features and a lower dose for GBI for larger object features. Using polychromatic radiation, such as that from a laboratory microfocus source, experiments and simulations show a lower dose requirement for PBI for a large range of feature sizes. Tested on a biological sample, GBI shows higher noise levels than PBI, but its advantage of quantitative refractive index reconstruction for multi-material samples becomes apparent.

Grating-based x-ray phase-contrast imaging with a multi energy-channel photon-counting pixel detector

We have carried out grating-based x-ray differential phase-contrast measurements with a hybrid pixel detector in 16 energy channels simultaneously. A method for combining the energy resolved phase-contrast images based on energy weighting is presented. An improvement in contrast-to-noise ratio by 58.2% with respect to an emulated integrating detector could be observed in the final image. The same image quality could thus be achieved with this detector and with energy weighting at 60.0% reduced dose compared to an integrating detector. The benefit of the method depends on the object, spectrum, interferometer design and the detector efficiency.

Increasing the darkfield contrast-to-noise ratio using a deconvolution-based information retrieval algorithm in X-ray grating-based phase-contrast imaging

A novel information retrieval algorithm for X-ray grating-based phase-contrast imaging based on the deconvolution of the object and the reference phase stepping curve (PSC) as proposed by Modregger et al. was investigated in this paper. We applied the method for the first time on data obtained with a polychromatic spectrum and compared the results to those, received by applying the commonly used method, based on a Fourier analysis. We confirmed the expectation, that both methods deliver the same results for the absorption and the differential phase image. For the darkfield image, a mean contrast-to-noise ratio (CNR) increase by a factor of 1.17 using the new method was found. Furthermore, the dose saving potential was estimated for the deconvolution method experimentally. It is found, that for the conventional method a dose which is higher by a factor of 1.66 is needed to obtain a similar CNR value compared to the novel method. A further analysis of the data revealed, that the improvement in CNR and dose efficiency is due to the superior background noise properties of the deconvolution method, but at the cost of comparability between measurements at different applied dose values, as the mean value becomes dependent on the photon statistics used.

X-ray phase-contrast imaging: from pre-clinical applications towards clinics

Phase-contrast x-ray imaging (PCI) is an innovative method that is sensitive to the refraction of the x-rays in matter. PCI is particularly adapted to visualize weakly absorbing details like those often encountered in biology and medicine. In past years, PCI has become one of the most used imaging methods in laboratory and preclinical studies: its unique characteristics allow high contrast 3D visualization of thick and complex samples even at high spatial resolution. Applications have covered a wide range of pathologies and organs, and are more and more often performed in vivo. Several techniques are now available to exploit and visualize the phase-contrast: propagation- and analyzer-based, crystal and grating interferometry and non-interferometric methods like the coded aperture. In this review, covering the last five years, we will give an overview of the main theoretical and experimental developments and of the important steps performed towards the clinical implementation of PCI.

Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue

PURPOSE

An experimental comparison of the contrast-to-noise ratio (CNR) between transmission and dark-field signals in grating-based X-ray imaging for ex-vivo murine lung tissue.

MATERIALS AND METHODS

Lungs from three healthy mice were imaged ex vivo using a laser-driven compact synchrotron X-ray source. Background noise of transmission and dark-field signal was quantified by measuring the standard deviation in a region of interest (ROI) placed in a homogeneous area outside the specimen. Image contrast was quantified by measuring the signal range in rectangular ROIs placed in central and peripheral lung parenchyma. The relative contrast gain (RCG) of dark-field over transmission images was calculated as CNRDF / CNRT.

RESULTS

In all images, there was a trend for contrast-to-noise ratios of dark-field images (CNRDF) to be higher than for transmission images (CNRT) for all ROIs (median 61 vs. 38, p=0.10), but the difference was statistically significant only for peripheral ROIs (61 vs. 32, p=0.03). Median RCG was >1 for all ROIs (1.84). RCG values were significantly smaller for central ROIs than for peripheral ROIs (1.34 vs. 2.43, p=0.03).

CONCLUSION

The contrast-to-noise ratio of dark-field images compares more favorably to the contrast-to-noise ratio of transmission images for peripheral lung regions as compared to central regions. For any specific specimen, a calculation of the RCG allows comparing which X-ray modality (dark-field or transmission imaging) produces better contrast-to-noise characteristics in a well-defined ROI.