X-ray phase-attenuation duality and phase retrieval

A closer look at high-energy X-ray-induced bubble formation during soft tissue imaging

Improving the scalability of tissue imaging throughput with bright, coherent X-rays requires identifying and mitigating artifacts resulting from the interactions between X-rays and matter. At synchrotron sources, long-term imaging of soft tissues in solution can result in gas bubble formation or cavitation, which dramatically compromises image quality and integrity of the samples. By combining in-line phase-contrast imaging with gas chromatography in real time, we were able to track the onset and evolution of high-energy X-ray-induced gas bubbles in ethanol-embedded soft tissue samples for tens of minutes (two to three times the typical scan times). We demonstrate quantitatively that vacuum degassing of the sample during preparation can significantly delay bubble formation, offering up to a twofold improvement in dose tolerance, depending on the tissue type. However, once nucleated, bubble growth is faster in degassed than undegassed samples, indicating their distinct metastable states at bubble onset. Gas chromatography analysis shows increased solvent vaporization concurrent with bubble formation, yet the quantities of dissolved gasses remain unchanged. By coupling features extracted from the radiographs with computational analysis of bubble characteristics, we uncover dose-controlled kinetics and nucleation site-specific growth. These hallmark signatures provide quantitative constraints on the driving mechanisms of bubble formation and growth. Overall, the observations highlight bubble formation as a critical yet often overlooked hurdle in upscaling X-ray imaging for biological tissues and soft materials and we offer an empirical foundation for their understanding and imaging protocol optimization. More importantly, our approaches establish a top-down scheme to decipher the complex, multiscale radiation-matter interactions in these applications.

ICF-PR-Net: a deep phase retrieval neural network for X-ray phase contrast imaging of inertial confinement fusion capsules

X-ray phase contrast imaging (XPCI) has demonstrated capability to characterize inertial confinement fusion (ICF) capsules, and phase retrieval can reconstruct phase information from intensity images. This study introduces ICF-PR-Net, a novel deep learning-based phase retrieval method for ICF-XPCI. We numerically constructed datasets based on ICF capsule shape features, and proposed an object-image loss function to add image formation physics to network training. ICF-PR-Net outperformed traditional methods as it exhibited satisfactory robustness against strong noise and nonuniform background and was well-suited for ICF-XPCI's constrained experimental conditions and single exposure limit. Numerical and experimental results showed that ICF-PR-Net accurately retrieved the phase and absorption while maintaining retrieval quality in different situations. Overall, the ICF-PR-Net enables the diagnosis of the inner interface and electron density of capsules to address ignition-preventing problems, such as hydrodynamic instability growth.

Quantitative phase contrast X-ray tomography of aluminium metal matrix composite

The quantitative assessment of micro-structure and load-induced damages in Al-SiC metal matrix composites (MMC) is important for its design optimization, performance evaluation and structure-property correlation. X-ray Phase contrast micro-tomography is potentially used for evaluation of its 3 dimensional micro-structure manifested in the form of voids, cracks, embedded particles, and load-induced damages. However, the contrast between Al matrix and SiC particles is insufficient for their clear morphological identification and quantitative assessment. In the present study, we have proposed and applied single image-based phase retrieval as a pre-processing step to micro-tomography reconstruction for improved assessment of micro-structure and cohesion-induced damages in Al-SiC MMC. The advantages of applying different phase retrieval techniques in the enhancement of image quality and morphological quantification of SiC particles, pores and cohesion damages are discussed. It is observed that the Paganin method offers the best improvement in contrast to noise ratio for the measurement of SiC particles embedded in the Al matrix.

Morphological variations to a ptychographic algorithm

Ptychography is a technique widely used in microscopy for achieving high-resolution imaging. This method relies on computational processing of images gathered from diffraction patterns produced by several partial illuminations of a sample. We numerically studied the effect of using different shapes for illuminating the aforementioned sample: convex shapes, such as circles and regular polygons, and unconnected shapes that resemble a QR code. Our results suggest that the use of unconnected shapes seems to outperform convex shapes in terms of convergence and, in some cases, accuracy.

PhaseX: an X-ray phase-contrast imaging simulation code for matter under extreme conditions

We present PhaseX, a simulation code for X-ray phase-contrast imaging (XPCI), specially dedicated to the study of matter under extreme conditions (of pressure and density). Indeed, XPCI can greatly benefit the diagnosis of such states of matter. This is due to the noticeable contrast enhancement obtained thanks to the exploitation of both attenuation and phase-shift of the electromagnetic waves crossing the sample to be diagnosed. PhaseX generates synthetic images with and without phase contrast. Thanks to its modular design PhaseX can adapt to any imaging set-up and accept as inputs objects generated by hydrodynamic or particle-in-cell codes. We illustrate Phase-X capabilities by showing a few examples concerning laser-driven implosions and laser-driven shock waves.

Evaluation and comparison of a CdTe based photon counting detector with an energy integrating detector for X-ray phase sensitive imaging of breast cancer

PURPOSE

To compare imaging performance of a cadmium telluride (CdTe) based photon counting detector (PCD) with a CMOS based energy integrating detector (EID) for potential phase sensitive imaging of breast cancer.

METHODS

A high energy inline phase sensitive imaging prototype consisting of a microfocus X-ray source with geometric magnification of 2 was employed. The pixel pitch of the PCD was 55μm, while 50μm for EID. The spatial resolution was quantitatively and qualitatively assessed through modulation transfer function (MTF) and bar pattern images. The edge enhancement visibility was assessed by measuring edge enhancement index (EEI) using the acrylic edge acquired images. A contrast detail (CD) phantom was utilized to compare detectability of simulated tumors, while an American College of Radiology (ACR) accredited phantom for mammography was used to compare detection of simulated calcification clusters. A custom-built phantom was employed to compare detection of fibrous structures. The PCD images were acquired at equal, and 30% less mean glandular dose (MGD) levels as of EID images. Observer studies along with contrast to noise ratio (CNR) and signal to noise ratio (SNR) analyses were performed for comparison of two detection systems.

RESULTS

MTF curves and bar pattern images revealed an improvement of about 40% in the cutoff resolution with the PCD. The excellent spatial resolution offered by PCD system complemented superior detection of the diffraction fringes at boundaries of the acrylic edge and resulted in an EEI value of 3.64 as compared to 1.44 produced with EID image. At equal MGD levels (standard dose), observer studies along with CNR and SNR analyses revealed a substantial improvement of PCD acquired images in detection of simulated tumors, calcification clusters, and fibrous structures. At 30% less MGD, PCD images preserved image quality to yield equivalent (slightly better) detection as compared to the standard dose EID images.

CONCLUSION

CdTe-based PCDs are technically feasible to image breast abnormalities (low/high contrast structures) at low radiation dose levels using the high energy inline phase sensitive imaging technique.

A phase sensitive x-ray breast tomosynthesis system: Preliminary patient images with cancer lesions

Phase-sensitive x-ray imaging continues to attract research for its ability to visualize weakly absorbing details like those often encountered in biology and medicine. We have developed and assembled the first inline-based high-energy phase sensitive breast tomosynthesis (PBT) system, which is currently undergoing patient imaging testing at a clinical site. The PBT system consists of a microfocus polychromatic x-ray source and a direct conversion-based flat panel detector coated with a 1 mm thick amorphous selenium layer allowing a high detective quantum efficiency at high energies. The PBT system scans a compressed breast over 15° with 9 angular projection views. The high-energy scan parameters are carefully selected to ensure similar or lower mean glandular dose levels to the clinical standard of care systems. Phase retrieval and data binning are applied to the phase contrast angular projection views and a filtered back-projection algorithm is used to reconstruct the final images. This article reports the distributions of radiation dose versus thickness of the compressed breasts at 59 and 89 kV and sample PBT images acquired from 3 patients. Preliminary PBT images demonstrate the feasibility of this new imaging modality to acquire breast images at lower radiation dose as compared to the clinical digital breast tomosynthesis system with enhanced lesion characteristics (i.e. lesion spiculation and margins).

Dual-energy phase retrieval algorithm for inline phase sensitive x-ray imaging system

Phase retrieval is vital for quantitative x-ray phase contrast imaging. This work presents an iterative method to simultaneously retrieve the x-ray absorption and phase images from a single x-ray exposure. The proposed approach uses the photon-counting detectors' energy-resolving capability in providing multiple spectrally resolved phase contrast images from a single x-ray exposure. The retrieval method is derived, presented, and experimentally tested with a multi-material phantom in an inline phase contrast imaging setup. By separating the contributions of photoelectric absorption and Compton scattering to the attenuation, the authors divide the phase contrast image into two portions, the attenuation map arises from photoelectric absorption and a pseudo phase contrast image generated by electron density. This way one can apply the Phase Attenuation Dualiby (PAD) algorithm and Fresnel propagation for the iteration. The retrieval results from the experimental images show that this iterative method is fast, accurate, robust against noise, and thus yields noticeable enhancement in contrast to noise ratios.

Phase retrieval-based phase-contrast CT for vascular imaging with microbubble contrast agent

PURPOSE

The introduction of microbubble contrast agent into tissues can create significant phase shifts. Phase retrieval (PR)-based phase-contrast computed tomography (PCCT) is an imaging method for retrieving and reconstructing the phase shifts within an object. This study aimed to evaluate the feasibility of PR-based PCCT with microbubble contrast agent for vascular imaging.

METHODS

Projection phase-contrast images of individual microbubbles and a cluster of microbubbles were captured and compared. Contrast enhancement from microbubbles was evaluated by comparing to the gold standard iodine-based contrast agent in vitro. The arterial systems of 14 Sprague-Dawley rats were perfused with microbubbles or saline. The rat hearts and the arterial systems were excised and imaged ex vivo. CT imaging was performed at the energy of 22 keV. PR was performed using the phase-attenuation duality (PAD) method with different δ/β values (PAD property). The contrast-to-noise ratio (CNR) was used for quantitatively assessing the contrast enhancement.

RESULTS

Individual microbubbles functioned as a lens to focus the x rays, whereas, a cluster of microbubbles scattered the x rays. In the in vitro experiment, the contrast enhancement from iodine was significantly greater than that from microbubbles (P < 0.05). In the heart samples, the CNRs for microbubbles on PR-based PCCT were significantly greater than those on absorption-contrast CT (ACCT) and PR-free PCCT (both P < 0.001). The CNRs for microbubbles were also significantly greater than those for saline on PR-based PCCT in the samples (P < 0.001). Although they provided weaker contrast enhancement than that from iodine, microbubbles could still provide sufficient contrast enhancement to clearly show the 3D architecture of rat aortas and their main branches.

CONCLUSION

The imaging modality can currently be used as a complement or alternative to absorption-based microCT for imaging vessels in biological samples.

Iterative reconstruction algorithm based on discriminant adaptive-weighted TV regularization for fibrous biological tissues using in-line X-ray phase-contrast imaging

In-line X-ray phase-contrast computed tomography (IL-PCCT) can produce high-contrast and high-resolution images of biological samples, and it has a great advantage with regard to imaging the microstructures and morphologies of fibrous biological tissues (FBTs). Filtered back projection (FBP) is widely used in ILPCCT. However, it requires long scanning times and high radiation doses to produce high-quality CT images, and this restricts its applicability in biomedical and preclinical studies on FBTs. To solve this problem, a novel IL-PCCT reconstruction algorithm is proposed to decrease the radiation dose by reducing the number of projections and reconstruct high-quality CT images of FBTs. The proposed algorithm incorporates the FBP method into the iterative reconstruction framework. Considering the area types and anisotropic edge properties of FBTs, a discriminant adaptive-weighted total variation model is introduced to optimize the intermediate reconstructed images. A fibrous phantom simulation and real experiment were performed to assess the performance of the proposed algorithm. Simulation and experimental results demonstrated that the proposed algorithm is an effective IL-PCCT reconstruction method for FBTs with incomplete projection data, and it has a great ability to suppress artifacts and preserve the edges of fibrous structures.

Development and preclinical evaluation of a patient-specific high energy x-ray phase sensitive breast tomosynthesis system

BACKGROUND

This article reports the first x-ray phase sensitive breast tomosynthesis (PBT) system that is aimed for direct translation to clinical practice for the diagnosis of breast cancer.

PURPOSE

To report the preclinical evaluation and comparison of the newly built PBT system with a conventional digital breast tomosynthesis (DBT) system.

METHODS AND MATERIALS

The PBT system is developed based on a comprehensive inline phase contrast theoretical model. The system consists of a polyenergetic microfocus x-ray source and a flat panel detector mounted on an arm that is attached to a rotating gantry. It acquires nine projections over a 15° angular span in a stop-and-shoot manner. A dedicated phase retrieval algorithm is integrated with a filtered back-projection method that reconstructs tomographic slices. The American College of Radiology (ACR) accreditation phantom, a contrast detail (CD) phantom and mastectomy tissue samples were imaged at the same glandular dose levels by both the PBT and a standard of care DBT system for image quality characterizations and comparisons.

RESULTS

The PBT imaging scores with the ACR phantom are in good to excellent range and meet the quality assurance criteria set by the Mammography Quality Standard Act. The CD phantom image comparison and associated statistical analyses from two-alternative forced-choice reader studies confirm the improvement offered by the PBT system in terms of contrast resolution, spatial resolution, and conspicuity. The artifact spread function (ASF) analyses revealed a sizable lateral spread of metal artifacts in PBT slices as compared to DBT slices. Signal-to-noise ratio values for various inserts of the ACR and CD phantoms further validated the superiority of the PBT system. Mastectomy sample images acquired by the PBT system showed a superior depiction of microcalcifications vs the DBT system.

CONCLUSION

The PBT imaging technology can be clinically employed for improving the accuracy of breast cancer screening and diagnosis.

Quantitative phase retrieval with low photon counts using an energy resolving quantum detector

X-ray phase contrast imaging (PCI) combined with phase retrieval has the potential to improve soft-material visibility and discrimination. This work examined the accuracy, image quality gains, and robustness of a spectral phase retrieval method proposed by our group. Spectroscopic PCI measurements of a physical phantom were obtained using state-of-the-art photon-counting detectors in combination with a polychromatic x-ray source. The phantom consisted of four poorly attenuating materials. Excellent accuracy was demonstrated in simultaneously retrieving the complete refractive properties (photoelectric absorption, attenuation, and phase) of these materials. Approximately 10 times higher SNR was achieved in retrieved images compared to the original PCI intensity image. These gains are also shown to be robust against increasing quantum noise, even for acquisition times as low as 1 s with a low-flux microfocus x-ray tube (average counts of 250 photons/pixels). We expect that this spectral phase retrieval method, adaptable to several PCI geometries, will allow significant dose reduction and improved material discrimination in clinical and industrial x-ray imaging applications.

The Potential of Utilizing Mid-Energy X-Rays for In-Line Phase Sensitive Breast Cancer Imaging

OBJECTIVE

The objective of this study is to demonstrate the potential of utilizing mid-energy x-rays for in-line phase-sensitive breast cancer imaging by phantom studies.

METHODS

The midenergy (50-80kV) in-line phase sensitive imaging prototype was used to acquire images of the contrast-detail mammography (CDMAM) phantom, an ACR accreditation phantom, and an acrylic edge phantom. The low-dose mid-energy phase-sensitive images were acquired at 60 kV with a radiation dose of 0.9 mGy, while the high-energy phase-sensitive images were acquired at 90 kV with a radiation dose of 1.2 mGy. The Phase-Attenuation Duality (PAD) principle for soft tissue was used for the phase retrieval. A blind observer study was conducted and paired-sample T-test were performed to compare the mean differences in the two imaging systems.

RESULTS

The correct detection ratio for the CDMAM phantom for phase-contrast images acquired by the low-dose mid-energy system was 56.91%, whereas images acquired by the high-energy system correctly revealed only 40.97% of discs. The correct detection ratios were 57.88% and 43.41% for phase-retrieved images acquired by the low-dose mid-energy and high-energy imaging systems, respectively. The reading scores for all three groups of objects in the ACR phantom were higher for the mid energy imaging system as compared to the high-energy system for both phase-contrast and phase- retrieved images. The calculated edge enhancement index (EEI) from the acrylic edge phantom image for the mid-energy system was higher than that calculated for the high-energy imaging system. The quantitative analyses showed a higher Contrast to Noise Ratio (CNR) as well as a higher Figure of Merit (FOM) in images acquired by the low-dose mid-energy imaging system.

CONCLUSION

The PAD based retrieval method can be applied in mid-energy system without remarkably affecting the image quality, and in fact, it improves the lesion detectability with a patient dose saving of 25%.

Material Decomposition Using Spectral Propagation-Based Phase-Contrast X-Ray Imaging

Material decomposition in X-ray imaging uses the energy-dependence of attenuation to digitally decompose an object into specific constituent materials, generally at the cost of enhanced image noise. Propagation-based X-ray phase-contrast imaging is a developing technique that can be used to reduce image noise, in particular from weakly attenuating objects. In this paper, we combine spectral phase-contrast imaging with material decomposition to both better visualize weakly attenuating features and separate them from overlying objects in radiography. We derive an algorithm that performs both tasks simultaneously and verify it against numerical simulations and experimental measurements of ideal two-component samples composed of pure aluminum and poly(methyl methacrylate). Additionally, we showcase first imaging results of a rabbit kitten's lung. The attenuation signal of a thorax, in particular, is dominated by the strongly attenuating bones of the ribcage. Combined with the weak soft tissue signal, this makes it difficult to visualize the fine anatomical structures across the whole lung. In all cases, clean material decomposition was achieved, without residual phase-contrast effects, from which we generate an un-obstructed image of the lung, free of bones. Spectral propagation-based phase-contrast imaging has the potential to be a valuable tool, not only in future lung research, but also in other systems for which phase-contrast imaging in combination with material decomposition proves to be advantageous.

Dark-field signal extraction in propagation-based phase-contrast imaging

A method for extracting the dark-field signal in propagation-based phase-contrast imaging is proposed. In the case of objects consisting predominantly of a single material, or several different materials with similar ratios of the real decrement to the imaginary part of the complex refractive index, the proposed method requires a single image for extraction of the dark-field signal in two-dimensional projection imaging. In the case of three-dimensional tomographic imaging, the method needs only one image to be collected at each projection angle. Initial examples using simulated and experimental data indicate that this method can improve visualization of small sharp features inside a larger object, e.g. the visualization of microcalcifications in propagation-based x-ray breast cancer imaging. It is suggested that the proposed approach may be useful in other forms of biomedical imaging, where it can help one to obtain additional small-angle scattering information without increasing the radiation dose to the sample.

Spectral x-ray imaging: Conditions under which propagation-based phase-contrast is beneficial

Energy-resolved attenuation data in spectral x-ray imaging enables material decomposition, in which the different materials inside an object can be identified and separated virtually. Material decomposition has the drawback of increased noise in the resulting material images relative to the measured images. Recently, spectral x-ray imaging was combined with propagation-based x-ray phase-contrast imaging, an x-ray technique that has the potential to greatly reduce image noise by utilizing wave-optical effects. The net combined effects on image noise of performing spectral material decomposition with phase-contrast are not yet well understood, and we provide a detailed theoretical investigation of this topic here. In particular, we investigate how the addition of phase-contrast in spectral imaging affects material decomposition compared to using conventional spectral attenuation data. We show how the underlying equations can be rearranged into parts that resemble low- and high-pass filters on the input images, from which we are able to identify different energy-dependent cases where phase-contrast is or is not advantageous. Our results suggest that the benefits of phase-contrast in the context of material decomposition are primarily restricted to x-ray energies under a certain threshold, where that threshold depends on the given material combination, and sits in a region where photoelectric absorption dominates x-ray attenuation. Additionally, we show that decomposition of the electron density using an image basis spanned by functions of the Alvarez-Macovski model benefits from phase-contrast, regardless of the x-ray energies. All our findings are based purely on theoretical considerations, and can, therefore, be used to determine the feasibility and utility of propagation-based phase-contrast in spectral x-ray imaging ahead of any data collection.

High resolution 3D visualization of the spinal cord in a post-mortem murine model

A crucial issue in the development of therapies to treat pathologies of the central nervous system is represented by the availability of non-invasive methods to study the three-dimensional morphology of spinal cord, with a resolution able to characterize its complex vascular and neuronal organization. X-ray phase contrast micro-tomography enables a high-quality, 3D visualization of both the vascular and neuronal network simultaneously without the need of contrast agents, destructive sample preparations or sectioning. Until now, high resolution investigations of the post-mortem spinal cord in murine models have mostly been performed in spinal cords removed from the spinal canal. We present here post-mortem phase contrast micro-tomography images reconstructed using advanced computational tools to obtain high-resolution and high-contrast 3D images of the fixed spinal cord without removing the bones and preserving the richness of micro-details available when measuring exposed spinal cords. We believe that it represents a significant step toward the in-vivo application.

Impact of a single distance phase retrieval algorithm on spatial resolution in X-ray inline phase sensitive imaging

A single-projection based phase retrieval method based on the phase attenuation duality principle (PAD) was used to compare the spatial resolution of the acquired phase sensitive and PAD processed phase retrieved images. An inline phase sensitive prototype was used to acquire the phase sensitive images. The prototype incorporates a micro-focus x-ray source and a flat panel detector with a 50 μm pixel pitch. A phantom composed of a 2 cm thick 50-50 adipose-glandular mimicking slab sandwiched with a 0.82 cm thick slanted PMMA sharp edge was used. Phase sensitive image of the phantom was acquired at 120 kV, 3.35 mAs with a 16 μm tube focal spot size under a geometric magnification (M) of 2.5. The PAD based method was applied to the acquired phase sensitive image for the retrieval of phase values. With necessary data processing, modulation transfer function (MTF) curves were determined for the estimation and comparison of the spatial resolution. The PAD processed phase retrieved values of the phantom were in good agreement with the theoretically calculated values. Phase sensitive images showed higher spatial resolution at all spatial frequencies compared to the phase retrieved images. It was noted that the high-frequency signal components in the retrieved image were suppressed that resulted in lower MTF values. When compared to the phase sensitive image, the cutoff resolution (10% MTF) for phase retrieved image dropped 32% from 15.6 lp/mm (32μm) to 10.6 lp/mm (47μm). The resolution offered by this phase sensitive prototype is radiographically enough to detect breast cancer.

Improved phase-attenuation duality method with space-frequency joint domain iterative regularization

PURPOSE

A common problem of in-line phase contrast imaging systems based on laboratory source and detector is the negative effects of finite source size, limited spatial resolution, and system noise. These negative effects swamp the fine phase contrast fringes and impede the precise retrieval of phase maps. This study aims to develop a novel phase retrieval method to restore phase information that is lost due to an imperfect system.

METHODS

An improved phase-attenuation duality (PAD) method based on space-frequency joint domain iterative regularization (JDIR) is proposed to overcome the problems of the analytical PAD method and the spatial-domain iterative regularization (SDIR) based PAD method. These problems include noise robustness and optical transfer function compensation. The proposed method was compared with the two former PAD methods through computer simulations and experiments for validation.

RESULTS

Results reveal that JDIR method outperforms the other two methods in terms of improving the visibility of structures in the retrieved phase maps. Among all the phase retrieval algorithms, the TV-norm-based JDIR method performed the best in considering the contrast and noise performance.

CONCLUSIONS

This paper provides a new method to investigate quantitative phase-contrast imaging when considering the negative effects of an imperfect system.

X-ray based virtual histology allows guided sectioning of heavy ion stained murine lungs for histological analysis

Examination of histological or immunohistochemically stained 2D sections of embedded tissue is one of the most frequently used tools in biomedical research and clinical routine. Since to date, targeted sectioning of specific regions of interest (ROI) in the sample is not possible, we aimed at developing a guided sectioning approach based on x-ray 3D virtual histology for heavy ion stained murine lung samples. For this purpose, we increased the contrast to noise ratio of a standard benchtop microCT by 5–10-fold using free-propagation phase contrast imaging and thus substantially improved image quality. We then show that microCT 3D datasets deliver more precise anatomical information and quantification of the sample than traditional histological sections, which display deformations of the tissue. To quantify these deformations caused by sectioning we developed the “Displacement Index (DI)”, which combines block-matching with the calculation of the local mutual information. We show that the DI substantially decreases when a femtosecond laser microtome is used for sections as opposed to a traditional microtome. In conclusion, our microCT based virtual histology approach can be used as a supplement and a guidance tool for traditional histology, providing 3D measurement capabilities and offering the ability to perform sectioning directly at an ROI.

Detectability comparison of simulated tumors in digital breast tomosynthesis using high-energy X-ray inline phase sensitive and commercial imaging systems

This study compared the detectability of simulated tumors using a high-energy X-ray inline phase sensitive digital breast tomosynthesis (DBT) prototype and a commercial attenuation-based DBT system. Each system imaged a 5-cm thick modular breast phantom with 50-50 adipose-glandular percentage density containing contrast-detail (CD) test objects to simulate different tumor sizes. A commercial DBT system acquired 15 projection views over 15 degrees (15d-15p) was used to acquire the attenuation-based projection views and to reconstruct the conventional DBT slices. Attenuation-based projection views were acquired at 32 kV, 46 mAs with a mean glandular dose (D_g) of 1.6 mGy. For acquiring phase sensitive projection views, the prototype utilized two acquisition geometries: 11 projection views were acquired over 15 degrees (15d-11p), and 17 projection views were acquired over 16 degrees (16d-17p) at 120 kV, 5.27 mAs with 1.51 mGy under the magnification (M) of 2. A phase retrieval algorithm based on the phase-attenuation duality (PAD) was applied to each projection view, and a modified Feldkamp-Davis-Kress (FDK) algorithm was used to reconstruct the phase sensitive DBT slices. Simulated tumor margins were rated as more conspicuous and better visualized for both phase sensitive acquisition geometries versus conventional DBT imaging. The CD curves confirmed the improvement in both contrast and spatial resolutions with the phase sensitive DBT imaging. The superiority of the phase sensitive DBT imaging was further endorsed by higher contrast to noise ratio (CNR) and figure-of-merit (FOM) values. The CNR improvements provided by the phase sensitive DBT prototype were sufficient to offset the noise reduction provided by the attenuation-based DBT imaging.

Robust phase-retrieval-based X-ray tomography for morphological assessment of early hepatic echinococcosis infection in rats

Propagation-based phase-contrast computed micro-tomography (PPCT) dominates the non-destructive, three-dimensional inner-structure measurement in synchrotron-based biomedical research due to its simple experimental setup. To quantitatively visualize tiny density variations in soft tissues and organs closely related to early pathological morphology, an experimental study of synchrotron-based X-ray PPCT combined with generalized phase and attenuation duality (PAD) phase retrieval was implemented with the hepatic echinococcosis (HE) infection rat model at different stages. We quantitatively analyzed and evaluated the different pathological characterizations of hepatic echinococcosis during the development of this disease via our PAD-based PPCT and especially provided evidence that hepatic alveolar echinococcosis invades the liver tissue and spreads through blood flow systems with abundant blood supply in the early stage. Additionally, the infiltration of tiny vesicles in HE lesions can be clearly observed by our PAD-PPCT technique due to the striking contrast-to-noise ratio (CNR) and mass density resolution, which cannot be found by the medical imaging techniques, such as magnetic resonance imaging (MRI), computed tomography (CT), and ultrasound, in hospitals. The results demonstrated that our PAD-PPCT technique has a great potential for indicating the subtle structural information of pathological changes in soft biomedical specimens, especially helpful for the research of early micro-morphology of diseases.

Detectability comparison between a high energy x-ray phase sensitive and mammography systems in imaging phantoms with varying glandular-adipose ratios

The objective of this study was to demonstrate the potential benefits of using high energy x-rays in comparison with the conventional mammography imaging systems for phase sensitive imaging of breast tissues with varying glandular-adipose ratios. This study employed two modular phantoms simulating the glandular (G) and adipose (A) breast tissue composition in 50 G-50 A and 70 G-30 A percentage densities. Each phantom had a thickness of 5 cm with a contrast detail test pattern embedded in the middle. For both phantoms, the phase contrast images were acquired using a micro-focus x-ray source operated at 120 kVp and 4.5 mAs, with a magnification factor (M) of 2.5 and a detector with a 50 µm pixel pitch. The mean glandular dose delivered to the 50 G-50 A and 70 G-30 A phantom sets were 1.33 and 1.3 mGy, respectively. A phase retrieval algorithm based on the phase attenuation duality that required only a single phase contrast image was applied. Conventional low energy mammography images were acquired using GE Senographe DS and Hologic Selenia systems utilizing their automatic exposure control (AEC) settings. In addition, the automatic contrast mode (CNT) was also used for the acquisition with the GE system. The AEC mode applied higher dose settings for the 70 G-30 A phantom set. As compared to the phase contrast images, the dose levels for the AEC mode acquired images were similar while the dose levels for the CNT mode were almost double. The observer study, contrast-to-noise ratio and figure of merit comparisons indicated a large improvement with the phase retrieved images in comparison to the AEC mode images acquired with the clinical systems for both density levels. As the glandular composition increased, the detectability of smaller discs decreased with the clinical systems, particularly with the GE system, even at higher dose settings. As compared to the CNT mode (double dose) images, the observer study also indicated that the phase retrieved images provided similar or improved detection for all disc sizes except for the disk diameters of 2 mm and 1 mm for the 50 G-50 A phantom and 3 mm and 0.5 mm for the 70 G-30 A phantom. This study demonstrated the potential of utilizing a high energy phase sensitive x-ray imaging system to improve lesion detection and reduce radiation dose when imaging breast tissues with varying glandular compositions.

Visualization and Pathological Characteristics of Hepatic Alveolar Echinococcosis with Synchrotron-based X-ray Phase Sensitive Micro-tomography

Propagation-based phase-contrast computed tomography (PPCT) utilizes highly sensitive phase-contrast technology applied to X-ray micro-tomography, especially with the extensive use of synchrotron radiation (SR). Performing phase retrieval (PR) on the acquired angular projections can enhance image contrast and enable quantitative imaging. We employed the combination of SR-PPCT and PR for the histopathological evaluation of hepatic alveolar echinococcosis (HAE) disease and demonstrated the validity and superiority of PR-based SR-PPCT. A high-resolution angular projection data set of a human postoperative specimen of HAE disease was acquired, which was processed by graded ethanol concentration fixation (GECF). The reconstructed images from both approaches, with the projection data directly used and preprocessed by PR for tomographic reconstruction, were compared in terms of the tissue contrast-to-noise ratio and density spatial resolution. The PR-based SR-PPCT was selected for microscale measurement and the 3D visualization of HAE disease. Our experimental results demonstrated that the PR-based SR-PPCT technique is greatly suitable for the discrimination of pathological tissues and the characterization of HAE. In addition, this new technique is superior to conventional hospital CT and microscopy for the three-dimensional, non-destructive microscale measurement of HAE. This PR-based SR-PPCT technique has great potential for in situmicroscale histopathological analysis and diagnosis, especially for applications involving soft tissues and organs.

Hard X-ray index of refraction tomography of a whole rabbit knee joint: A feasibility study

We report results of the computed tomography reconstruction of the index of refraction in a whole rabbit knee joint examined at the photon energy of 51keV. Refraction based images make it possible to delineate the bone, cartilage, and soft tissues without adjusting the contrast window width and level. Density variations, which are related to tissue composition and are not visible in absorption X-ray images, are detected in the obtained refraction based images. We discuss why refraction-based images provide better detectability of low contrast features than absorption images.

Technical Note: Synchrotron-based high-energy x-ray phase sensitive microtomography for biomedical research

PURPOSE

Propagation-based phase-contrast CT (PPCT) utilizes highly sensitive phase-contrast technology applied to x-ray microtomography. Performing phase retrieval on the acquired angular projections can enhance image contrast and enable quantitative imaging. In this work, the authors demonstrate the validity and advantages of a novel technique for high-resolution PPCT by using the generalized phase-attenuation duality (PAD) method of phase retrieval.

METHODS

A high-resolution angular projection data set of a fish head specimen was acquired with a monochromatic 60-keV x-ray beam. In one approach, the projection data were directly used for tomographic reconstruction. In two other approaches, the projection data were preprocessed by phase retrieval based on either the linearized PAD method or the generalized PAD method. The reconstructed images from all three approaches were then compared in terms of tissue contrast-to-noise ratio and spatial resolution.

RESULTS

The authors' experimental results demonstrated the validity of the PPCT technique based on the generalized PAD-based method. In addition, the results show that the authors' technique is superior to the direct PPCT technique as well as the linearized PAD-based PPCT technique in terms of their relative capabilities for tissue discrimination and characterization.

CONCLUSIONS

This novel PPCT technique demonstrates great potential for biomedical imaging, especially for applications that require high spatial resolution and limited radiation exposure.

Phase Imaging Using Focused Polycapillary Optics

Conventional radiographic techniques depend on attenuation, which provides low contrast between soft tissues. However, X rays can accumulate large differential phase delays even in weakly absorbing materials. This can produce significantly higher contrast. One technique for taking advantage of phase effects, propagation-based phase imaging, can yield marked edge enhancement but requires spatially coherent intense sources. Microfocus sources have sizes on the order of tens of microns but necessarily are low power and hence require long exposures. In this project, X-ray optical and computational techniques were explored to develop both edge-enhancement and phase imaging using a large spot conventional source. A polycapillary optic was employed to create a small secondary source from a large spot rotating anode X-ray generator. The secondary spot created by the focusing polycapillary optic was 114 µm ± 50 µm. Images of a 1.6 mm polyethylene rod were taken at varying distances from the optic. Edge enhancement was observed with a maximum edge-enhancement-to-noise ratio of 6.5. Insect images were also acquired and analyzed. Phase reconstructions were computed using two different approaches, weak attenuation and phase attenuation duality. Pure phase images were successfully reconstructed from the phase contrast images by employing the weak attenuation model.

Amyloid-β plaque deposition measured using propagation-based X-ray phase contrast CT imaging

Amyloid beta accumulation into insoluble plaques (Aβp) is known to play a significant role in the pathological process in Alzheimer's disease (AD). The presence of Aβp is also one of the neuropathological hallmarks for the disease. AD final diagnosis is generally acknowledged after the evaluation of Aβp deposition in the brain. Insoluble Aβp accumulation may also concur to cause AD as postulated in the so-called amyloid hypothesis. Therefore, the visualization, evaluation and quantification of Aβp are nowadays the keys for a better understanding of the disease, which may point to a possible cure for AD in the near future. Synchrotron-based X-ray phase contrast (XPC) has been demonstrated as the only imaging method that can retrieve the Aβp signal with high spatial resolution (up to 10 µm), high sensitivity and three-dimensional information at the same time. Although at the moment XPC is suitable for ex vivo samples only, it may develop into an alternative to positron emission tomography and magnetic resonance imaging in Aβp imaging. In this contribution the possibility of using synchrotron-based X-ray phase propagation computed tomography to visualize and measure Aβp on mouse brains is presented. A careful setup optimization for this application leads to a significant improvement of spatial resolution (∼1 µm), data acquisition speed (five times faster), X-ray dose (five times lower) and setup complexity, without a substantial loss in sensitivity when compared with the classic implementation of grating-based X-ray interferometry.

Gauging low-dose X-ray phase-contrast imaging at a single and large propagation distance

The interactions of a beam of hard and spatio-temporally coherent X-rays with a soft-matter sample primarily induce a transverse distribution of exit phase variations δϕ (retardations or advancements in pieces of the wave front exiting the object compared to the incoming wave front) whose free-space propagation over a distance z gives rise to intensity contrast gz. For single-distance image detection and |δϕ| ≪ 1 all-order-in-z phase-intensity contrast transfer is linear in δϕ. Here we show that ideal coherence implies a decay of the (shot-)noise-to-signal ratio in gz and of the associated phase noise as z(-1/2) and z(-1), respectively. Limits on X-ray dose thus favor large values of z. We discuss how a phase-scaling symmetry, exact in the limit δϕ → 0 and dynamically unbroken up to |δϕ| ∼ 1, suggests a filtering of gz in Fourier space, preserving non-iterative quasi-linear phase retrieval for phase variations up to order unity if induced by multi-scale objects inducing phase variations δϕ of a broad spatial frequency spectrum. Such an approach continues to be applicable under an assumed phase-attenuation duality. Using synchrotron radiation, ex and in vivo microtomography on frog embryos exemplifies improved resolution compared to a conventional single-distance phase-retrieval algorithm.

Three-dimensional propagation in near-field tomographic X-ray phase retrieval

An extension of phase retrieval algorithms for near-field X-ray (propagation) imaging to three dimensions is presented, enhancing the quality of the reconstruction by exploiting previously unused three-dimensional consistency constraints.

This paper presents an extension of phase retrieval algorithms for near-field X-ray (propagation) imaging to three dimensions, enhancing the quality of the reconstruction by exploiting previously unused three-dimensional consistency constraints. The approach is based on a novel three-dimensional propagator and is derived for the case of optically weak objects. It can be easily implemented in current phase retrieval architectures, is computationally efficient and reduces the need for restrictive prior assumptions, resulting in superior reconstruction quality.

Optimization of reconstructed quality of hard x-ray phase microtomography

For applications of hard x-ray propagation-based phase-contrast computed microtomography (PPCT) in high-resolution biological research, high spatial resolution and high contrast-to-noise ratio are simultaneously required for tiny structural discrimination and characterization. Most existing micro-CT techniques to improve image quality are limited by high cost, physical limitations, and complexity of the experimental hardware and setup. In this work, a novel PPCT technique, which combines a wavelet-transform-based modulation transform function compensation algorithm and a generalized phase-retrieval algorithm, is proposed to optimize the reconstruction quality of tomographic slices. Our experimental results, which compared the spatial resolutions and contrast-to-noise ratios of reconstructed images, demonstrated the validity of the proposed generalized PPCT technique. The experimental results showed that the proposed generalized PPCT technique is superior to the direct PPCT and the linearized phase-retrieval PPCT techniques. This novel PPCT technique demonstrates great potential for biological imaging, especially for applications that require high spatial resolution and limit radiation exposure.

Characterization of a high-energy in-line phase contrast tomosynthesis prototype

PURPOSE

In this research, a high-energy in-line phase contrast tomosynthesis prototype was developed and characterized through quantitative investigations and phantom studies.

METHODS

The prototype system consists of an x-ray source, a motorized rotation stage, and a CMOS detector with a pixel pitch of 0.05 mm. The x-ray source was operated at 120 kVp for this study, and the objects were mounted on the rotation stage 76.2 cm (R1) from the source and 114.3 cm (R2) from the detector. The large air gap between the object and detector guarantees sufficient phase-shift effects. The quantitative evaluation of this prototype included modulation transfer function and noise power spectrum measurements conducted under both projection mode and tomosynthesis mode. Phantom studies were performed including three custom designed phantoms with complex structures: a five-layer bubble wrap phantom, a fishbone phantom, and a chicken breast phantom with embedded fibrils and mass structures extracted from an ACR phantom. In-plane images of the phantoms were acquired to investigate their image qualities through observation, intensity profile plots, edge enhancement evaluations, and/or contrast-to-noise ratio calculations. In addition, the robust phase-attenuation duality (PAD)-based phase retrieval method was applied to tomosynthesis for the first time in this research. It was utilized as a preprocessing method to fully exhibit phase contrast on the angular projection before reconstruction.

RESULTS

The resolution and noise characteristics of this high-energy in-line phase contrast tomosynthesis prototype were successfully investigated and demonstrated. The phantom studies demonstrated that this imaging prototype can successfully remove the structure overlapping in phantom projections, obtain delineate interfaces, and achieve better contrast-to-noise ratio after applying phase retrieval to the angular projections.

CONCLUSIONS

This research successfully demonstrated a high-energy in-line phase contrast tomosynthesis prototype. In addition, the PAD-based method of phase retrieval was combined with tomosynthesis imaging for the first time, which demonstrated its capability in significantly improving the contrast-to-noise ratios in the images.

Phase retrieval method for in-line phase contrast x-ray imaging and denoising by regularization

Phase contrast X-ray imaging is increasingly popular in the past decade. In order to acquire phase contrast X-ray images, different types of imaging mechanisms have been proposed. Among them, in-line phase contrast X-ray imaging shows the highest potential because of its simplicity. In the study of in-line phase contrast imaging, based on different physical assumptions, many non-iterative phase retrieval methods, such as Bronnikov method, modified Bronnikov method, phase-attenuation duality (PAD) method, single-material method, and two-material method have been proposed. The main step of the non-iterative methods is a filtering process, thus different methods involve different filter design. In this paper we showed that every filter applied in the methods listed above is indeed the minimizer of a L(2)-norm regularization problem. In addition, two methods were proposed to overcome the over smoothing problem owing to the nature of L(2)-norm regularization.

Complex dark-field contrast and its retrieval in x-ray phase contrast imaging implemented with Talbot interferometry

PURPOSE

Under the existing theoretical framework of x-ray phase contrast imaging methods implemented with Talbot interferometry, the dark-field contrast refers to the reduction in interference fringe visibility due to small-angle x-ray scattering of the subpixel microstructures of an object to be imaged. This study investigates how an object's subpixel microstructures can also affect the phase of the intensity oscillations.

METHODS

Instead of assuming that the object's subpixel microstructures distribute in space randomly, the authors' theoretical derivation starts by assuming that an object's attenuation projection and phase shift vary at a characteristic size that is not smaller than the period of analyzer grating G₂ and a characteristic length dc. Based on the paraxial Fresnel-Kirchhoff theory, the analytic formulae to characterize the zeroth- and first-order Fourier coefficients of the x-ray irradiance recorded at each detector cell are derived. Then the concept of complex dark-field contrast is introduced to quantify the influence of the object's microstructures on both the interference fringe visibility and the phase of intensity oscillations. A method based on the phase-attenuation duality that holds for soft tissues and high x-ray energies is proposed to retrieve the imaginary part of the complex dark-field contrast for imaging. Through computer simulation study with a specially designed numerical phantom, they evaluate and validate the derived analytic formulae and the proposed retrieval method.

RESULTS

Both theoretical analysis and computer simulation study show that the effect of an object's subpixel microstructures on x-ray phase contrast imaging method implemented with Talbot interferometry can be fully characterized by a complex dark-field contrast. The imaginary part of complex dark-field contrast quantifies the influence of the object's subpixel microstructures on the phase of intensity oscillations. Furthermore, at relatively high energies, for soft tissues it can be retrieved for imaging with a method based on the phase-attenuation duality.

CONCLUSIONS

The analytic formulae derived in this work to characterize the complex dark-field contrast in x-ray phase contrast imaging method implemented with Talbot interferometry are of significance, which may initiate more activities in the research and development of x-ray differential phase contrast imaging for extensive biomedical applications.

Approximated transport-of-intensity equation for coded-aperture x-ray phase-contrast imaging

Transport-of-intensity equations (TIEs) allow better understanding of image formation and assist in simplifying the "phase problem" associated with phase-sensitive x-ray measurements. In this Letter, we present for the first time to our knowledge a simplified form of TIE that models x-ray differential phase-contrast (DPC) imaging with coded-aperture (CA) geometry. The validity of our approximation is demonstrated through comparison with an exact TIE in numerical simulations. The relative contributions of absorption, phase, and differential phase to the acquired phase-sensitive intensity images are made readily apparent with the approximate TIE, which may prove useful for solving the inverse phase-retrieval problem associated with these CA geometry based DPC.

Contrast enhancement in X-ray phase contrast tomography

We demonstrate phase contrast enhancement of X-ray computed tomography derived from propagation based imaging. In this method, the absorption and phase components are assumed to be correlated, allowing for phase retrieval from a single image. Experimental results are shown for liquid samples. Signal-to-noise ratio is greatly enhanced relative to pure attenuation based imaging.

Quantitative evaluation of a single-distance phase-retrieval method applied on in-line phase-contrast images of a mouse lung

Propagation-based X-ray phase-contrast computed tomography (PBI) has already proven its potential in a great variety of soft-tissue-related applications including lung imaging. However, the strong edge enhancement, caused by the phase effects, often hampers image segmentation and therefore the quantitative analysis of data sets. Here, the benefits of applying single-distance phase retrieval prior to the three-dimensional reconstruction (PhR) are discussed and quantified compared with three-dimensional reconstructions of conventional PBI data sets in terms of contrast-to-noise ratio (CNR) and preservation of image features. The PhR data sets show more than a tenfold higher CNR and only minor blurring of the edges when compared with PBI in a predominately absorption-based set-up. Accordingly, phase retrieval increases the sensitivity and provides more functionality in computed tomography imaging.

Dose and detectability improvements with high energy phase sensitive x-ray imaging in comparison to low energy conventional imaging

The objective of this study was to demonstrate the potential benefits of using high energy x-rays for phase sensitive breast imaging through a comparison with conventional mammography imaging. We compared images of a contrast-detail phantom acquired on a prototype phase sensitive x-ray imaging system with images acquired on a commercial flat panel digital mammography unit. The phase contrast images were acquired using a micro-focus x-ray source with a 50 µm focal spot at 120 kVp and 4.5 mAs, with a magnification factor of 2.46 and a 50 µm pixel pitch. A phase attenuation duality-based phase retrieval algorithm that requires only a single phase contrast image was applied. Conventional digital mammography images were acquired at 27 kVp, 131 mAs and 28 kVp, 54 mAs. For the same radiation dose, both the observer study and signal-to-noise ratio (SNR)/figure of merit comparisons indicated a large improvement by the phase retrieved image as compared to the clinical system for the larger disc sizes, but the improvement was not enough to detect the smallest discs. Compared to the double dose image acquired with the clinical system, the observer study also indicated that the phase retrieved image provided improved detection capabilities for all disc sizes except the smallest discs. Thus the SNR improvement provided by phase contrast imaging is not yet enough to offset the noise reduction provided by the clinical system at the doubled dose level. However, the potential demonstrated by this study for high energy phase sensitive x-ray imaging to improve lesion detection and reduce radiation dose in mammography warrants further investigation of this technique.

Priors for X-ray in-line phase tomography of heterogeneous objects

We present a new prior for phase retrieval from X-ray Fresnel diffraction patterns. Fresnel diffraction patterns are achieved by letting a highly coherent X-ray beam propagate in free space after interaction with an object. Previously, either homogeneous or multi-material object assumptions have been used. The advantage of the homogeneous object assumption is that the prior can be introduced in the Radon domain. Heterogeneous object priors, on the other hand, have to be applied in the object domain. Here, we let the relationship between attenuation and refractive index vary as a function of the measured attenuation index. The method is evaluated using images acquired at beamline ID19 (ESRF, Grenoble, France) of a phantom where the prior is calculated by linear interpolation and of a healing bone obtained from a rat osteotomy model. It is shown that the ratio between attenuation and refractive index in bone for different levels of mineralization follows a power law. Reconstruction was performed using the mixed approach but is compatible with other, more advanced models. We achieve more precise reconstructions than previously reported in literature. We believe that the proposed method will find application in biomedical imaging problems where the object is strongly heterogeneous, such as bone healing and biomaterials engineering.

Grating-based phase contrast tomosynthesis imaging: proof-of-concept experimental studies

PURPOSE

This paper concerns the feasibility of x-ray differential phase contrast (DPC) tomosynthesis imaging using a grating-based DPC benchtop experimental system, which is equipped with a commercial digital flat-panel detector and a medical-grade rotating-anode x-ray tube. An extensive system characterization was performed to quantify its imaging performance.

METHODS

The major components of the benchtop system include a diagnostic x-ray tube with a 1.0 mm nominal focal spot size, a flat-panel detector with 96 μm pixel pitch, a sample stage that rotates within a limited angular span of ± 30°, and a Talbot-Lau interferometer with three x-ray gratings. A total of 21 projection views acquired with 3° increments were used to reconstruct three sets of tomosynthetic image volumes, including the conventional absorption contrast tomosynthesis image volume (AC-tomo) reconstructed using the filtered-backprojection (FBP) algorithm with the ramp kernel, the phase contrast tomosynthesis image volume (PC-tomo) reconstructed using FBP with a Hilbert kernel, and the differential phase contrast tomosynthesis image volume (DPC-tomo) reconstructed using the shift-and-add algorithm. Three inhouse physical phantoms containing tissue-surrogate materials were used to characterize the signal linearity, the signal difference-to-noise ratio (SDNR), the three-dimensional noise power spectrum (3D NPS), and the through-plane artifact spread function (ASF).

RESULTS

While DPC-tomo highlights edges and interfaces in the image object, PC-tomo removes the differential nature of the DPC projection data and its pixel values are linearly related to the decrement of the real part of the x-ray refractive index. The SDNR values of polyoxymethylene in water and polystyrene in oil are 1.5 and 1.0, respectively, in AC-tomo, and the values were improved to 3.0 and 2.0, respectively, in PC-tomo. PC-tomo and AC-tomo demonstrate equivalent ASF, but their noise characteristics quantified by the 3D NPS were found to be different due to the difference in the tomosynthesis image reconstruction algorithms.

CONCLUSIONS

It is feasible to simultaneously generate x-ray differential phase contrast, phase contrast, and absorption contrast tomosynthesis images using a grating-based data acquisition setup. The method shows promise in improving the visibility of several low-density materials and therefore merits further investigation.

A robust general phase retrieval method for medical applications

From medical imaging perspective the robustness of a phase retrieval method is of critical importance. In this presentation we compare the robustness of two general phase retrieval methods, namely the transport of intensity equation inversion (TIE-inversion) method and the attenuation partition based (AP-based) method. We showed that the TIE-inversion method, regardless if being assisted with the Tikhonov regularization, failed to retrieve the phase maps in two experimental studies. The failure exposes this method's weakness as being unstable against the noise. In contrast, the sample phase maps are retrieved successfully by using the AP-based method. The stark performance differences of the two methods are rooted in their different techniques dealing with the singularity problem. This comparison shows that the robust AP-based phase retrieval method will be superior to the TIE-inversion method for medical imaging applications where radiation doses are stringently limited.

Single-step absorption and phase retrieval with polychromatic x rays using a spectral detector

In this Letter, we present a single-step method to simultaneously retrieve x-ray absorption and phase images valid for a broad range of imaging energies and material properties. Our method relies on the availability of spectrally resolved intensity measurements, which is now possible using semiconductor x-ray photon counting detectors. The retrieval method is derived and presented, with results showing good agreement.