A simplified approach to quantitative coded aperture X-ray phase imaging

Virtual differential phase-contrast and dark-field imaging of x-ray absorption images via deep learning

Weak absorption contrast in biological tissues has hindered x-ray computed tomography from accessing biological structures. Recently, grating-based imaging has emerged as a promising solution to biological low-contrast imaging, providing complementary and previously unavailable structural information of the specimen. Although it has been successfully applied to work with conventional x-ray sources, grating-based imaging is time-consuming and requires a sophisticated experimental setup. In this work, we demonstrate that a deep convolutional neural network trained with a generative adversarial network can directly convert x-ray absorption images into differential phase-contrast and dark-field images that are comparable to those obtained at both a synchrotron beamline and a laboratory facility. By smearing back all of the virtual projections, high-quality tomographic images of biological test specimens deliver the differential phase-contrast- and dark-field-like contrast and quantitative information, broadening the horizon of x-ray image contrast generation.

The effect of a variable focal spot size on the contrast channels retrieved in edge-illumination X-ray phase contrast imaging

Multi-modal X-ray imaging allows the extraction of phase and dark-field (or “Ultra-small Angle Scatter”) images alongside conventional attenuation ones. Recently, scan-based systems using conventional sources that can simultaneously output the above three images on relatively large-size objects have been developed by various groups. One limitation is the need for some degree of spatial coherence, achieved either through the use of microfocal sources, or by placing an absorption grating in front of an extended source. Both these solutions limit the amount of flux available for imaging, with the latter also leading to a more complex setup with additional alignment requirements. Edge-illumination partly overcomes this as it was proven to work with focal spots of up to 100 micron. While high-flux, 100 micron focal spot sources do exist, their comparatively large footprint and high cost can be obstacles to widespread translation. A simple solution consists in placing a single slit in front of a large focal spot source. We used a tunable slit to study the system performance at various effective focal spot sizes, by extracting transmission, phase and dark-field images of the same specimens for a range of slit widths. We show that consistent, repeatable results are obtained for varying X-ray statistics and effective focal spot sizes. As the slit width is increased, the expected reduction in the raw differential phase peaks is observed, compensated for in the retrieval process by a broadened sensitivity function. This leads to the same values being correctly retrieved, but with a slightly larger error bar i.e. a reduction in phase sensitivity. Concurrently, a slight increase in the dark-field signal is also observed.

Optimization of multipoint phase retrieval in edge illumination X-ray imaging: A theoretical and experimental analysis

PURPOSE

In this work, an analytical model describing the noise in the retrieved three contrast channels, transmission, refraction, and ultra small-angle scattering, obtained with edge illumination X-ray phase-based imaging system is presented and compared to experimental data.

METHODS

In EI, images acquired at different displacements of the presample mask (i.e., different illumination levels referred to as points on the "illumination curve"), followed by pixel-wise curve fitting, are exploited to quantitatively retrieve the three contrast channels. Therefore, the noise in the final image will depend on the error associated with the fitting process. We use a model based on the derivation of the standard error on fitted parameters, which relies on the calculation of the covariance matrix, to estimate the noise and the cross-channel correlation as a function of the position of the sampling points. In particular, we investigated the most common cases of 3 and 5 sampling points. In addition, simulations have been used to better understand the role of the integration time for each sampling point. Finally, the model is validated by comparison with the experimental data acquired with an edge illumination setup based on a tungsten rotating anode X-ray source and a photon counting detector.

RESULTS

We found a good match between the predictions of the model and the experimental data. In particular, for the investigated cases, an arrangement of the sampling points leading to minimum noise and cross-channel correlation can be found. Simulations revealed that, given a fixed overall scanning time, its distribution into the smallest possible number of sampling points needed for phase retrieval leads to minimum noise thanks to higher statistics per point.

CONCLUSIONS

This work presents an analytical model describing the noise in the various contrast channels retrieved in edge illumination as a function of the illumination curve sampling. In particular, an optimal sampling scheme leading to minimum noise has been determined for the case where 3 or 5 sampling points are used, which represent two of the most common acquisition schemes. In addition, the correlation between noise in the different channels and the role of the number of points and exposure time have been also investigated. In general, our results suggest a series of procedures that should be followed in order to optimize the experimental acquisitions.

Edge-illumination x-ray phase-contrast imaging

Although early demonstration dates back to the mid-sixties, x-ray phase-contrast imaging (XPCI) became hugely popular in the mid-90s, thanks to the advent of 3rd generation synchrotron facilities. Its ability to reveal object features that had so far been considered invisible to x-rays immediately suggested great potential for applications across the life and the physical sciences, and an increasing number of groups worldwide started experimenting with it. At that time, it looked like a synchrotron facility was strictly necessary to perform XPCI with some degree of efficiency-the only alternative being micro-focal sources, the limited flux of which imposed excessively long exposure times. However, new approaches emerged in the mid-00s that overcame this limitation, and allowed XPCI implementations with conventional, non-micro-focal x-ray sources. One of these approaches showing particular promise for 'real-world' applications is edge-illumination XPCI: this article describes the key steps in its evolution in the context of contemporary developments in XPCI research, and presents its current state-of-the-art, especially in terms of transition towards practical applications.

A partial-dithering strategy for edge-illumination x-ray phase-contrast tomography enabled by a joint reconstruction method

Edge-illumination x-ray phase-contrast tomography (EIXPCT) is a promising imaging technology where partially opaque masks are utilized with laboratory-based x-ray sources to estimate the distribution of the complex-valued refractive index. EIXPCT resolution is mainly determined by the period of a sample mask, but can be significantly improved by a dithering technique. Here, dithering means that multiple images per tomographic view angle are acquired as the object is moved over sub-pixel distances. Drawbacks of dithering include increased data-acquisition times and radiation doses. Motivated by the flexibility in data-acquisition designs enabled by a recently developed joint reconstruction method, a novel partial-dithering strategy for EIXPCT data-acquisition is proposed. In this strategy, dithering is implemented at only a subset of the tomographic view angles. The strategy can result in spatial resolution comparable to that of the conventional full-dithering strategy, where dithering is performed at every view angle, but the acquisition time is substantially decreased. Here, the effect of dithering parameters on image resolution is explored.

Comparison of data-acquisition designs for single-shot edge-illumination X-ray phase-contrast tomography

Edge-illumination X-ray phase-contrast tomography (EIXPCT) is an emerging technique that enables practical phase-contrast imaging with laboratory-based X-ray sources. A joint reconstruction method was proposed for reconstructing EIXPCT images, enabling novel flexible data-acquisition designs. However, only limited efforts have been devoted to optimizing data-acquisition designs for use with the joint reconstruction method. In this study, several promising designs are introduced, such as the constant aperture position (CAP) strategy and the alternating aperture position (AAP) strategy covering different angular ranges. In computer-simulation studies, these designs are analyzed and compared. Experimental data are employed to test the designs in real-world applications. All candidate designs are also compared for their implementation complexity. The tradeoff between data-acquisition time and image quality is discussed.

Retrieval of weak x-ray scattering using edge illumination

X-ray phase contrast imaging provides additional modes of image contrast compared to conventional attenuation-based x-ray imaging, thus providing additional structural and functional information about the sample. The edge-illumination (EI) technique has been used to provide attenuation, refraction, and scattering contrast in both biological and non-biological samples. However, the retrieval of low scattering signals by fitting a single Gaussian remains problematic, principally due to the inability of the EI system to achieve perfect dark-field illumination. We present a new retrieval method that fits three Gaussians, which successfully overcomes this limitation, and provide examples of the retrieval of such signals in highly absorbing, weakly scattering samples.

Subspace-based resolution-enhancing image reconstruction method for few-view differential phase-contrast tomography

It is well known that properly designed image reconstruction methods can facilitate reductions in imaging doses and data-acquisition times in tomographic imaging. The ability to do so is particularly important for emerging modalities, such as differential x-ray phase-contrast tomography (D-XPCT), which are currently limited by these factors. An important application of D-XPCT is high-resolution imaging of biomedical samples. However, reconstructing high-resolution images from few-view tomographic measurements remains a challenging task due to the high-frequency information loss caused by data incompleteness. In this work, a subspace-based reconstruction strategy is proposed and investigated for use in few-view D-XPCT image reconstruction. By adopting a two-step approach, the proposed method can simultaneously recover high-frequency details within a certain region of interest while suppressing noise and/or artifacts globally. The proposed method is investigated by the use of few-view experimental data acquired by an edge-illumination D-XPCT scanner.

Properties of a Joint Reconstruction Method for Edge-Illumination X-Ray Phase-Contrast Tomography

Edge illumination X-ray phase-contrast tomography (EIXPCT) is an emerging technique for estimating the complex-valued refractive index distribution of an imaged object. A conventional EIXPCT system requires measurement of multiple images at each tomographic view angle, leading to prolonged data acquisition times. Recently, a joint reconstruction (JR) method has been developed to enable single-shot EIXPCT imaging without restrictive assumptions related to the object, imaging geometry or hardware. In the JR method, estimates of the refractive index distribution are recast as the solution to a nonlinear optimization problem. While a preliminary study has demonstrated the potential usefulness of the JR method, its numerical properties remain largely unexplored. In this project, the convexity, cross-talk properties and noise properties of the JR method are investigated.

Recent advances in edge illumination x-ray phase-contrast tomography

Edge illumination (EI) is an x-ray phase-contrast imaging technique, exploiting sensitivity to x-ray refraction to visualize features, which are often not detected by conventional absorption-based radiography. The method does not require a high degree of spatial coherence and is achromatic and, therefore, can be implemented with both synchrotron radiation and commercial x-ray tubes. Using different retrieval algorithms, information about an object's attenuation, refraction, and scattering properties can be obtained. In recent years, a theoretical framework has been developed that enables EI computed tomography (CT) and, hence, three-dimensional imaging. This review provides a summary of these advances, covering the development of different image acquisition schemes, retrieval approaches, and applications. These developments constitute an integral part in the transformation of EI CT into a widely spread imaging tool for use in a range of fields.

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.

Single-shot edge illumination x-ray phase-contrast tomography enabled by joint image reconstruction

Edge illumination x-ray phase-contrast tomography (EIXPCT) is an emerging x-ray phase-contrast tomography technique for reconstructing the complex-valued x-ray refractive index distribution of an object. Conventional image reconstruction approaches for EIXPCT require multiple images to be acquired at each tomographic view angle. This contributes to prolonged data-acquisition times and elevated radiation doses, which can hinder in vivo applications. In this work, a new "single-shot" method is proposed for joint reconstruction (JR) of the real and imaginary-valued components of the refractive index distribution from a tomographic data set that contains only a single image acquired at each view angle. The proposed method is predicated on a nonlinear formulation of the inverse problem that is solved by using a gradient-based optimization method. The method is validated and investigated using computer-simulated and experimental EIXPCT data sets.

Concept of contrast transfer function for edge illumination x-ray phase-contrast imaging and its comparison with the free-space propagation technique

Previous studies on edge illumination (EI) X-ray phase-contrast imaging (XPCi) have investigated the nature and amplitude of the signal provided by this technique. However, the response of the imaging system to different object spatial frequencies was never explicitly considered and studied. This is required in order to predict the performance of a given EI setup for different classes of objects. To this scope, in the present work we derive analytical expressions for the contrast transfer function of an EI imaging system, using the approximation of near-field regime, and study its dependence upon the main experimental parameters. We then exploit these results to compare the frequency response of an EI system with respect of that of a free-space propagation XPCi one. The results achieved in this work can be useful for predicting the signals obtainable for different types of objects and also as a basis for new retrieval methods.

High contrast microstructural visualization of natural acellular matrices by means of phase-based x-ray tomography

Acellular scaffolds obtained via decellularization are a key instrument in regenerative medicine both per se and to drive the development of future-generation synthetic scaffolds that could become available off-the-shelf. In this framework, imaging is key to the understanding of the scaffolds’ internal structure as well as their interaction with cells and other organs, including ideally post-implantation. Scaffolds of a wide range of intricate organs (esophagus, lung, liver and small intestine) were imaged with x-ray phase contrast computed tomography (PC-CT). Image quality was sufficiently high to visualize scaffold microarchitecture and to detect major anatomical features, such as the esophageal mucosal-submucosal separation, pulmonary alveoli and intestinal villi. These results are a long-sought step for the field of regenerative medicine; until now, histology and scanning electron microscopy have been the gold standard to study the scaffold structure. However, they are both destructive: hence, they are not suitable for imaging scaffolds prior to transplantation, and have no prospect for post-transplantation use. PC-CT, on the other hand, is non-destructive, 3D and fully quantitative. Importantly, not only do we demonstrate achievement of high image quality at two different synchrotron facilities, but also with commercial x-ray equipment, which makes the method available to any research laboratory.

Evaluation of microbubble contrast agents for dynamic imaging with x-ray phase contrast

X-rays are commonly used as a means to image the inside of objects opaque to visible light, as their short wavelength allows penetration through matter and the formation of high spatial resolution images. This physical effect has found particular importance in medicine where x-ray based imaging is routinely used as a diagnostic tool. Increasingly, however, imaging modalities that provide functional as well as morphological information are required. In this study the potential to use x-ray phase based imaging as a functional modality through the use of microbubbles that can be targeted to specific biological processes is explored. We show that the concentration of a microbubble suspension can be monitored quantitatively whilst in flow using x-ray phase contrast imaging. This could provide the basis for a dynamic imaging technique that combines the tissue penetration, spatial resolution, and high contrast of x-ray phase based imaging with the functional information offered by targeted imaging modalities.

Single-image phase retrieval using an edge illumination X-ray phase-contrast imaging setup

A method is proposed which enables the retrieval of the thickness or of the projected electron density of a sample from a single input image acquired with an edge illumination phase-contrast imaging setup. The method assumes the case of a quasi-homogeneous sample, i.e. a sample with a constant ratio between the real and imaginary parts of its complex refractive index. Compared with current methods based on combining two edge illumination images acquired in different configurations of the setup, this new approach presents advantages in terms of simplicity of acquisition procedure and shorter data collection time, which are very important especially for applications such as computed tomography and dynamical imaging. Furthermore, the fact that phase information is directly extracted, instead of its derivative, can enable a simpler image interpretation and be beneficial for subsequent processing such as segmentation. The method is first theoretically derived and its conditions of applicability defined. Quantitative accuracy in the case of homogeneous objects as well as enhanced image quality for the imaging of complex biological samples are demonstrated through experiments at two synchrotron radiation facilities. The large range of applicability, the robustness against noise and the need for only one input image suggest a high potential for investigations in various research subjects.

A simplified edge illumination set-up for quantitative phase contrast mammography with synchrotron radiation at clinical doses

This work presents the first study of x-ray phase contrast imaging based on a simple implementation of the edge illumination method (EIXPCi) in the field of mammography with synchrotron radiation. A simplified EIXPCi set-up was utilized to study a possible application in mammography at clinical doses. Moreover, through a novel algorithm capable of separating and quantifying absorption and phase perturbations of images acquired in EIXPCi modality, it is possible to extract quantitative information on breast images, allowing an accurate tissue identification. The study was carried out at the SYRMEP beamline of Elettra synchrotron radiation facility (Trieste, Italy), where a mastectomy specimen was investigated with the EIXPCi technique. The sample was exposed at three different energies suitable for mammography with synchrotron radiation in order to test the validity of the novel algorithm in extracting values of linear attenuation coefficients integrated over the sample thickness. It is demonstrated that the quantitative data are in good agreement with the theoretical values of linear attenuation coefficients calculated on the hypothesis of the breast with a given composition. The results are promising and encourage the current efforts to apply the method in mammography with synchrotron radiation.

On the origin of contrast in edge illumination X-ray phase-contrast imaging

Edge illumination (EI) has emerged as an X-ray phase-contrast imaging (XPCi) modality which could present significant advantages in terms of translation to clinical and laboratory applications. In this paper, we model its signal through the use of the "transport of intensity" equation. The validity conditions for this approach and its relationship with previous theoretical models for EI XPCi are discussed. The proposed model enables a simple estimation of the different contributions to the signal, which is shown to complement previously obtained results. In particular, it allows taking into account the effect of both slowly and rapidly varying refraction angles, corresponding to large and small object features. The derived framework is then used to investigate the effect on the signal of the smoothness of the mask edges, of the blurring from the source size and of the width of the object edge.

Phase-contrast microscopy at high x-ray energy with a laboratory setup

We report on the design and realization of an x-ray imaging system for quantitative phase-contrast microscopy at high x-ray energy with laboratory-scale instrumentation. Phase and amplitude were separated quantitatively at x-ray energies up to 80 keV with micrometric spatial resolution. The accuracy of the results was tested against numerical simulations, and the spatial resolution was experimentally quantified by measuring a Siemens star phase object. This simple setup should find broad application in those areas of x-ray imaging where high energy and spatial resolution are simultaneously required and in those difficult cases where the sample contains materials with similar x-ray absorption.

Theory and preliminary experimental verification of quantitative edge illumination x-ray phase contrast tomography

X-ray phase contrast imaging (XPCi) methods are sensitive to phase in addition to attenuation effects and, therefore, can achieve improved image contrast for weakly attenuating materials, such as often encountered in biomedical applications. Several XPCi methods exist, most of which have already been implemented in computed tomographic (CT) modality, thus allowing volumetric imaging. The Edge Illumination (EI) XPCi method had, until now, not been implemented as a CT modality. This article provides indications that quantitative 3D maps of an object's phase and attenuation can be reconstructed from EI XPCi measurements. Moreover, a theory for the reconstruction of combined phase and attenuation maps is presented. Both reconstruction strategies find applications in tissue characterisation and the identification of faint, weakly attenuating details. Experimental results for wires of known materials and for a biological object validate the theory and confirm the superiority of the phase over conventional, attenuation-based image contrast.

Synchrotron- and laboratory-based X-ray phase-contrast imaging for imaging mouse articular cartilage in the absence of radiopaque contrast agents

The mouse model of osteoarthritis (OA) has been recognized as the most promising research tool for the identification of new OA therapeutic targets. However, this model is currently limited by poor throughput, dependent on the extremely time-consuming histopathology assessment of the articular cartilage (AC). We have recently shown that AC in the rat tibia can be imaged both in air and in saline solution using a laboratory system based on coded-aperture X-ray phase-contrast imaging (CAXPCi). Here, we explore ways to extend the methodology for imaging the much thinner AC of the mouse, by means of gold-standard synchrotron-based phase-contrast methods. Specifically, we have used analyser-based phase-contrast micro-computed tomography (micro-CT) for its high sensitivity to faint phase changes, coupled with a high-resolution (4.5 μm pixel) detector. Healthy, diseased (four weeks post induction of OA) and artificially damaged mouse AC was imaged at the Elettra synchrotron in Trieste, Italy, using the above method. For validation, we used conventional micro-CT combined with radiopaque soft-tissue staining and standard histomorphometry. We show that mouse cartilage can be visualized correctly by means of the synchrotron method. This suggests that: (i) further developments of the laboratory-based CAXPCi system, especially in terms of pushing the resolution limits, might have the potential to resolve mouse AC ex vivo and (ii) additional improvements may lead to a new generation of CAXPCi micro-CT scanners which could be used for in vivo longitudinal pre-clinical imaging of soft tissue at resolutions impossible to achieve by current MRI technology.