Fast three-dimensional phase retrieval in propagation-based X-ray tomography

Three-dimensional contrast-transfer-function approach in phase-contrast tomography

A new method is developed for 3D reconstruction of multimaterial objects using propagation-based x-ray phase-contrast tomography (PB-CT) with phase retrieval via contrast-transfer-function (CTF) formalism. The approach differs from conventional PB-CT algorithms, which apply phase retrieval to individual 2D projections. Instead, this method involves performing phase retrieval to the CT-reconstructed volume in 3D. The CTF formalism is further extended to the cases of partially coherent illumination and strongly absorbing samples. Simulated results demonstrate that the proposed post-reconstruction CTF method provides fast and stable phase retrieval, producing results equivalent to conventional pre-reconstruction 2D CTF phase retrieval. Moreover, it is shown that application can be highly localized to isolated objects of interest, without a significant loss of quality, thus leading to increased computational efficiency. Combined with the extended validity of the CTF to greater propagation distances, this method provides additional advantages over approaches based on the transport-of-intensity equation.

Unified fast reconstruction algorithm for conventional, phase-contrast, and diffraction tomography

A unified method for three-dimensional reconstruction of objects from transmission images collected at multiple illumination directions is described. The method may be applicable to experimental conditions relevant to absorption-based, phase-contrast, or diffraction imaging using x rays, electrons, and other forms of penetrating radiation or matter waves. Both the phase retrieval (also known as contrast transfer function correction) and the effect of Ewald sphere curvature (in the cases with a shallow depth of field and significant in-object diffraction) are incorporated in the proposed algorithm and can be taken into account. Multiple scattering is not treated explicitly but can be mitigated as a result of angular averaging that constitutes an essential feature of the method. The corresponding numerical algorithm is based on three-dimensional gridding which allows for fast computational implementation, including a straightforward parallelization. The algorithm can be used with any scanning geometry involving plane-wave illumination. A software code implementing the proposed algorithm has been developed, tested on simulated and experimental image data, and made publicly available.

Optimization of a customized simultaneous algebraic reconstruction technique algorithm for phase-contrast breast computed tomography

Objective. To introduce the optimization of a customized GPU-based simultaneous algebraic reconstruction technique (cSART) in the field of phase-contrast breast computed tomography (bCT). The presented algorithm features a 3D bilateral regularization filter that can be tuned to yield optimal performance for clinical image visualization and tissues segmentation. Approach. Acquisitions of a dedicated test object and a breast specimen were performed at Elettra, the Italian synchrotron radiation (SR) facility (Trieste, Italy) using a large area CdTe single-photon counting detector. Tomographic images were obtained at 5 mGy of mean glandular dose, with a 32 keV monochromatic x-ray beam in the free-space propagation mode. Three independent algorithms parameters were optimized by using contrast-to-noise ratio (CNR), spatial resolution, and noise texture metrics. The results obtained with the cSART algorithm were compared with conventional SART and filtered back projection (FBP) reconstructions. Image segmentation was performed both with gray scale-based and supervised machine-learning approaches. Main results. Compared to conventional FBP reconstructions, results indicate that the proposed algorithm can yield images with a higher CNR (by 35% or more), retaining a high spatial resolution while preserving their textural properties. Alternatively, at the cost of an increased image ‘patchiness’, the cSART can be tuned to achieve a high-quality tissue segmentation, suggesting the possibility of performing an accurate glandularity estimation potentially of use in the realization of realistic 3D breast models starting from low radiation dose images. Significance. The study indicates that dedicated iterative reconstruction techniques could provide significant advantages in phase-contrast bCT imaging. The proposed algorithm offers great flexibility in terms of image reconstruction optimization, either toward diagnostic evaluation or image segmentation.

Tomographic phase and attenuation extraction for a sample composed of unknown materials using x-ray propagation-based phase-contrast imaging

Propagation-based phase-contrast x-ray imaging (PB-PCXI) generates image contrast by utilizing sample-imposed phase-shifts. This has proven useful when imaging weakly attenuating samples, as conventional attenuation-based imaging does not always provide adequate contrast. We present a PB-PCXI algorithm capable of extracting the x-ray attenuation  β and refraction  δ, components of the complex refractive index of distinct materials within an unknown sample. The method involves curve fitting an error-function-based model to a phase-retrieved interface in a PB-PCXI tomographic reconstruction, which is obtained when Paganin-type phase retrieval is applied with incorrect values of δ and β. The fit parameters can then be used to calculate true δ and β values for composite materials. This approach requires no a priori sample information, making it broadly applicable. Our PB-PCXI reconstruction is single-distance, requiring only one exposure per tomographic angle, which is important for radiosensitive samples. We apply this approach to a breast-tissue sample, recovering the refraction component  δ, with 0.6-2.4% accuracy compared with theoretical values.

Improving spatial resolution with an edge-enhancement model for low-dose propagation-based X-ray phase-contrast computed tomography

Propagation-based X-ray phase-contrast computed tomography (PB-PCCT) has been increasingly popular for distinguishing low contrast tissues. Phase retrieval is an important step to quantitatively obtain the phase information before the tomographic reconstructions, while typical phase retrieval methods in PB-PCCT, such as homogenous transport of intensity equation (TIE-Hom), are essentially low-pass filters and thus improve the signal to noise ratio at the expense of the reduced spatial resolution of the reconstructed image. To improve the reconstructed spatial resolution, measured phase contrast projections with high edge enhancement and the phase projections retrieved by TIE-Hom were weighted summed and fed into an iterative tomographic algorithm within the framework of the adaptive steepest descent projections onto convex sets (ASD-POCS), which was employed for suppressing the image noise in low dose reconstructions because of the sparse-view scanning strategy or low exposure time for single phase contrast projection. The merging strategy decreases the accuracy of the linear model of PB-PCCT and would finally lead to the reconstruction failure in iterative reconstructions. Therefore, the additive median root prior is also introduced in the algorithm to partly increase the model accuracy. The reconstructed spatial resolution and noise performance can be flexibly balanced by a pair of antagonistic hyper-parameters. Validations were performed by the established phase-contrast Feldkamp-Davis-Kress, phase-retrieved Feldkamp-Davis-Kress, conventional ASD-POCS and the proposed enhanced ASD-POCS with a numerical phantom dataset and experimental biomaterial dataset. Simulation results show that the proposed algorithm outperforms the conventional ASD-POCS in spatial evaluation assessments such as root mean square error (a ratio of 9.78%), contrast to noise ratio (CNR) (a ratio of 7.46%), and also frequency evaluation assessments such as modulation transfer function (a ratio of 66.48% of MTF_50% (50% MTF value)), noise power spectrum (a ratio of 35.25% of f_50% (50% value of the Nyquist frequency)) and noise equivalent quanta (1-2 orders of magnitude at high frequencies). Experimental results again confirm the superiority of proposed strategy relative to the conventional one in terms of edge sharpness and CNR (an average increase of 67.35%).

Relative roles of multiple scattering and Fresnel diffraction in the imaging of small molecules using electrons, Part II: Differential Holographic Tomography

It has been argued that in atomic-resolution transmission electron microscopy (TEM) of sparse weakly scattering structures, such as small biological molecules, multiple electron scattering usually has only a small effect, while the in-molecule Fresnel diffraction can be significant due to the intrinsically shallow depth of focus. These facts suggest that the three-dimensional reconstruction of such structures from defocus image series collected at multiple rotational orientations of a molecule can be effectively performed for each atom separately, using the incoherent first Born approximation. The corresponding reconstruction method, termed here Differential Holographic Tomography, is developed theoretically and demonstrated computationally on several numerical models of biological molecules. It is shown that the method is capable of accurate reconstruction of the locations of atoms in a molecule from TEM data collected at a small number of random orientations of the molecule, with one or more defocus images per orientation. Possible applications to cryogenic electron microscopy and other areas are briefly discussed.

X-ray tomography with multiple ultranarrow cone beams

Hollow glass microcapillaries or x-ray waveguides very efficiently confine x-rays to submicron or nanospots, which can be used for point projection imaging. However, x-ray beams exiting from such devices have ultranarrow cones that are limited by the critical angle for the total external reflection to a few milliradians. Narrow cone beams result in small fields of view, and the application of multiple-reflection optics to cone beam tomography is challenging. In this work, we describe a new nonconventional tomographic geometry realized with multiple confocal ultranarrow cone beams. The geometry enables an increase in the effective radiation cone to over 10^° without resolution reduction. The proposed tomographic scans can be performed without truncations of the field of view or limitations of the angular range and do not require sample translations, which are inherent to other multibeam x-ray techniques. Volumetric imaging is possible with a simultaneous iterative reconstruction technique or with a fast approximate noniterative two-step approach. A proof-of-principle experiment was performed in the multipoint projection geometry with polycapillary optics and a multi-pinhole mask inserted upstream of the optics. The geometry is suited for phase-contrast tomography with polychromatic laboratory and synchrotron sources.

Model-Based Iterative Reconstruction for Propagation-Based Phase-Contrast X-Ray CT including Models for the Source and the Detector

Propagation-based phase-contrast X-ray computed tomography is a valuable tool for high-resolution visualization of biological samples, giving distinct improvements in terms of contrast and dose requirements compared to conventional attenuation-based computed tomography. Due to its ease of implementation and advances in laboratory X-ray sources, this imaging technique is increasingly being transferred from synchrotron facilities to laboratory environments. This however poses additional challenges, such as the limited spatial coherence and flux of laboratory sources, resulting in worse resolution and higher noise levels. Here we extend a previously developed iterative reconstruction algorithm for this imaging technique to include models for the reduced spatial coherence and the signal spreading of efficient scintillator-based detectors directly into the physical forward model. Furthermore, we employ a noise model which accounts for the full covariance statistics of the image formation process. In addition, we extend the model describing the interference effects such that it now matches the formalism of the widely-used single-material phase-retrieval algorithm, which is based on the sample-homogeneity assumption. We perform a simulation study as well as an experimental study at a laboratory inverse Compton source and compare our approach to the conventional analytical approaches. We find that the modeling of the source and the detector inside the physical forward model can tremendously improve the resolution at matched noise levels and that the modeling of the covariance statistics reduces overshoots (i.e. incorrect increase / decrease in sample properties) at the sample edges significantly.

Photon-counting, energy-resolving and super-resolution phase contrast X-ray imaging using an integrating detector

This work demonstrates the use of a scientific-CMOS (sCMOS) energy-integrating detector as a photon-counting detector, thereby eliminating dark current and read-out noise issues, that simultaneously provides both energy resolution and sub-pixel spatial resolution for X-ray imaging. These capabilities are obtained by analyzing visible light photon clouds that result when X-ray photons produce fluorescence from a scintillator in front of the visible light sensor. Using low-fluence monochromatic X-ray projections to avoid overlapping photon clouds, the centroid of individual X-ray photon interactions was identified. This enabled a tripling of the spatial resolution of the detector to 6.71 ± 0.04 µm. By calculating the total charge deposited by this interaction, an energy resolution of 61.2 ± 0.1% at 17 keV was obtained. When combined with propagation-based phase contrast imaging and phase retrieval, a signal-to-noise ratio of up to 15 ± 3 was achieved for an X-ray fluence of less than 3 photons/mm².