Computational analysis and improvement of SIRT

Noise characterization analysis of dynamic dual-energy CT and its advantage in suppressing statistical noise

Objective.Multi-energy CT conducted by photon-counting detector has a wide range of applications, especially in multiple contrast agents imaging. However, static multi-energy (SME) CT imaging suffers from higher statistical noise because of increased energy bins with static energy thresholds. Our team has proposed a dynamic dual-energy (DDE) CT detector model and the corresponding iterative reconstruction algorithm to solve this problem. However, rigorous and detailed analysis of the statistical noise characterization in this DDE CT was lacked.Approach.Starting from the properties of the Poisson random variable, this paper analyzes the noise characterization of the DDE CT and compares it with the SME CT. It is proved that the multi-energy CT projections and reconstruction images calculated from the proposed DDE CT algorithm have less statistical noise than that of the SME CT.Main results.Simulations and experiments verify that the expectations of the multi-energy CT projections calculated from DDE CT are the same as those of the SME projections. Still, the variance of the former is smaller. We further analyze the convergence of the iterative DDE CT algorithm through simulations and prove that the derived noise characterization can be realized under different CT imaging configurations.Significance.The low statistical noise characteristics demonstrate the value of DDE CT imaging technology.

Enabling 3D CT-scanning of cultural heritage objects using only in-house 2D X-ray equipment in museums

Visualizing the internal structure of museum objects is a crucial step in acquiring knowledge about the origin, state, and composition of cultural heritage artifacts. Among the most powerful techniques for exposing the interior of museum objects is computed tomography (CT), a technique that computationally forms a 3D image using hundreds of radiographs acquired in a full circular range. However, the lack of affordable and versatile CT equipment in museums, combined with the challenge of transporting precious collection objects, currently keeps this technique out of reach for most cultural heritage applications. We propose an approach for creating accurate CT reconstructions using only standard 2D radiography equipment already available in most larger museums. Specifically, we demonstrate that a combination of basic X-ray imaging equipment, a tailored marker-based image acquisition protocol, and sophisticated data-processing algorithms, can achieve 3D imaging of collection objects without the need for a costly CT imaging system. We implemented this approach in the British Museum (London), the J. Paul Getty Museum (Los Angeles), and the Rijksmuseum (Amsterdam). Our work paves the way for broad facilitation and adoption of CT technology across museums worldwide.

Modular and Cost-Effective Computed Tomography Design

We present a modular and cost-effective gamma ray computed tomography system for multiphase flow investigations in industrial apparatuses. It mainly comprises a 137Cs isotopic source and an in-house-assembled detector arc, with a total of 16 scintillation detectors, offering a quantum efficiency of approximately 75% and an active area of 10 × 10 mm2 each. The detectors are operated in pulse mode to exclude scattered gamma photons from counting by using a dual-energy discrimination stage. Flexible application of the computed tomography system, i.e., for various object sizes and densities, is provided by an elaborated detector arc design, in combination with a scanning procedure that allows for simultaneous parallel beam projection acquisition. This allows the scan time to be scaled down with the number of individual detectors. Eventually, the developed scanner successfully upgrades the existing tomography setup in the industry. Here, single pencil beam gamma ray computed tomography is already used to study hydraulics in gas-liquid contactors, with inner diameters of up to 440 mm. We demonstrate the functionality of the new system for radiographic and computed tomographic scans of DN110 and DN440 columns that are operated at varying iso-hexane/nitrogen liquid-gas flow rates.

Two-and-a-half order score-based model for solving 3D ill-posed inverse problems

Computed Tomography (CT) and Magnetic Resonance Imaging (MRI) are crucial technologies in the field of medical imaging. Score-based models demonstrated effectiveness in addressing different inverse problems encountered in the field of CT and MRI, such as sparse-view CT and fast MRI reconstruction. However, these models face challenges in achieving accurate three dimensional (3D) volumetric reconstruction. The existing score-based models predominantly concentrate on reconstructing two-dimensional (2D) data distributions, resulting in inconsistencies between adjacent slices in the reconstructed 3D volumetric images. To overcome this limitation, we propose a novel two-and-a-half order score-based model (TOSM). During the training phase, our TOSM learns data distributions in 2D space, simplifying the training process compared to working directly on 3D volumes. However, during the reconstruction phase, the TOSM utilizes complementary scores along three directions (sagittal, coronal, and transaxial) to achieve a more precise reconstruction. The development of TOSM is built on robust theoretical principles, ensuring its reliability and efficacy. Through extensive experimentation on large-scale sparse-view CT and fast MRI datasets, our method achieved state-of-the-art (SOTA) results in solving 3D ill-posed inverse problems, averaging a 1.56 dB peak signal-to-noise ratio (PSNR) improvement over existing sparse-view CT reconstruction methods across 29 views and 0.87 dB PSNR improvement over existing fast MRI reconstruction methods with × 2 acceleration. In summary, TOSM significantly addresses the issue of inconsistency in 3D ill-posed problems by modeling the distribution of 3D data rather than 2D distribution which has achieved remarkable results in both CT and MRI reconstruction tasks.

Joint denoising and interpolating network for low-dose cone-beam CT reconstruction under hybrid dose-reduction strategy

Cone-beam computed tomography (CBCT) is generally reconstructed with hundreds of two-dimensional X-Ray projections through the FDK algorithm, and its excessive ionizing radiation of X-Ray may impair patients' health. Two common dose-reduction strategies are to either lower the intensity of X-Ray, i.e., low-intensity CBCT, or reduce the number of projections, i.e., sparse-view CBCT. Existing efforts improve the low-dose CBCT images only under a single dose-reduction strategy. In this paper, we argue that applying the two strategies simultaneously can reduce dose in a gentle manner and avoid the extreme degradation of the projection data in a single dose-reduction strategy, especially under ultra-low-dose situations. Therefore, we develop a Joint Denoising and Interpolating Network (JDINet) in projection domain to improve the CBCT quality with the hybrid low-intensity and sparse-view projections. Specifically, JDINet mainly includes two important components, i.e., denoising module and interpolating module, to respectively suppress the noise caused by the low-intensity strategy and interpolate the missing projections caused by the sparse-view strategy. Because FDK actually utilizes the projection information after ramp-filtering, we develop a filtered structural similarity constraint to help JDINet focus on the reconstruction-required information. Afterward, we employ a Postprocessing Network (PostNet) in the reconstruction domain to refine the CBCT images that are reconstructed with denoised and interpolated projections. In general, a complete CBCT reconstruction framework is built with JDINet, FDK, and PostNet. Experiments demonstrate that our framework decreases RMSE by approximately 8 %, 15 %, and 17 %, respectively, on the 1/8, 1/16, and 1/32 dose data, compared to the latest methods. In conclusion, our learning-based framework can be deeply imbedded into the CBCT systems to promote the development of CBCT. Source code is available at https://github.com/LianyingChao/FusionLowDoseCBCT.

WRAP: A wavelet-regularised reconstruction algorithm for magnetic vector electron tomography

Magnetic vector electron tomography (VET) is a promising technique that enables better understanding of micro- and nano-magnetic phenomena through the reconstruction of 3D magnetic fields at high spatial resolution. Here we introduce WRAP (Wavelet Regularised A Program), a reconstruction algorithm for magnetic VET that directly reconstructs the magnetic vector potential A using a compressed sensing framework which regularises for sparsity in the wavelet domain. We demonstrate that using WRAP leads to a significant increase in the fidelity of the 3D reconstruction and is especially robust when dealing with very limited data; using datasets simulated with realistic noise, we compare WRAP to a conventional reconstruction algorithm and find an improvement of ca. 60% when averaged over several performance metrics. Moreover, we further validate WRAP's performance on experimental electron holography data, revealing the detailed magnetism of vortex states in a CuCo nanowire. We believe WRAP represents a major step forward in the development of magnetic VET as a tool for probing magnetism at the nanoscale.

Automatic Differentiation for Inverse Problems in X-ray Imaging and Microscopy

Computational techniques allow breaking the limits of traditional imaging methods, such as time restrictions, resolution, and optics flaws. While simple computational methods can be enough for highly controlled microscope setups or just for previews, an increased level of complexity is instead required for advanced setups, acquisition modalities or where uncertainty is high; the need for complex computational methods clashes with rapid design and execution. In all these cases, Automatic Differentiation, one of the subtopics of Artificial Intelligence, may offer a functional solution, but only if a GPU implementation is available. In this paper, we show how a framework built to solve just one optimisation problem can be employed for many different X-ray imaging inverse problems.

TomocuPy - efficient GPU-based tomographic reconstruction with asynchronous data processing

Fast 3D data analysis and steering of a tomographic experiment by changing environmental conditions or acquisition parameters require fast, close to real-time, 3D reconstruction of large data volumes. Here a performance-optimized TomocuPy package is presented as a GPU alternative to the commonly used central processing unit (CPU) based TomoPy package for tomographic reconstruction. TomocuPy utilizes modern hardware capabilities to organize a 3D asynchronous reconstruction involving parallel read/write operations with storage drives, CPU-GPU data transfers, and GPU computations. In the asynchronous reconstruction, all the operations are timely overlapped to almost fully hide all data management time. Since most cameras work with less than 16-bit digital output, the memory usage and processing speed are furthermore optimized by using 16-bit floating-point arithmetic. As a result, 3D reconstruction with TomocuPy became 20-30 times faster than its multi-threaded CPU equivalent. Full reconstruction (including read/write operations and methods initialization) of a 20483 tomographic volume takes less than 7 s on a single Nvidia Tesla A100 and PCIe 4.0 NVMe SSD, and scales almost linearly increasing the data size. To simplify operation at synchrotron beamlines, TomocuPy provides an easy-to-use command-line interface. Efficacy of the package was demonstrated during a tomographic experiment on gas-hydrate formation in porous samples, where a steering option was implemented as a lens-changing mechanism for zooming to regions of interest.

Three-dimensional phase and intensity reconstruction from coherent modulation imaging measurements

Coherent modulation imaging is a lensless imaging technique, where a complex-valued image can be recovered from a single diffraction pattern using the iterative algorithm. Although mostly applied in two dimensions, it can be tomographically combined to produce three-dimensional (3D) images. Here we present a 3D reconstruction procedure for the sample's phase and intensity from coherent modulation imaging measurements. Pre-processing methods to remove illumination probe, inherent ambiguities in phase reconstruction results, and intensity fluctuation are given. With the projections extracted by our method, standard tomographic reconstruction frameworks can be used to recover accurate quantitative 3D phase and intensity images. Numerical simulations and optical experiments validate our method.

High-performance reconstruction of CT medical images by using out-of-core methods in GPU

BACKGROUND AND OBJECTIVE

Since Computed Tomography (CT) is one of the most widely used medical imaging tests, it is essential to work on methods that reduce the radiation the patient is exposed to. Although there are several possible approaches to achieve this, we focus on reducing the exposure time through sparse sampling. With this approach, efficient algebraic methods are needed to be able to generate the images in real time, and since their computational cost is high, using high-performance computing is essential.

METHODS

In this paper we present a GPU (Graphics Processing Unit) software for solving the CT image reconstruction problem using the QR factorization performed with out-of-core (OOC) techniques. This implementation is optimized to reduce the data transfer times between disk, CPU, and GPU, as well as to overlap input/output operations and computations.

RESULTS

The experimental study shows that a block cache stored on main page-locked memory is more efficient than using a cache on GPU memory or mirroring it in both GPU and CPU memory. Compared to a CPU version, this implementation is up to 6.5 times faster, providing an improved image quality when compared to other reconstruction methods.

CONCLUSIONS

The software developed is an optimized version of the QR factorization for GPU that allows the algebraic reconstruction of CT images with high quality and resolution, with a performance that can be compared with state-of-the-art methods used in clinical practice. This approach allows reducing the exposure time of the patient and thus the radiation dose.

Significance of the spectral correction of photon counting detector response in material classification from spectral x-ray CT

Purpose: Photon counting imaging detectors (PCD) has paved the way for spectral x-ray computed tomography (spectral CT), which simultaneously measures a sample's linear attenuation coefficient (LAC) at multiple energies. However, cadmium telluride (CdTe)-based PCDs working under high flux suffer from detector effects, such as charge sharing and photon pileup. These effects result in the severe spectral distortions of the measured spectra and significant deviation of the extracted LACs from the reference attenuation curve. We analyze the influence of the spectral distortion correction on material classification performance. Approach: We employ a spectral correction algorithm to reduce the primary spectral distortions. We use a method for material classification that measures system-independent material properties, such as electron density, ρ e , and effective atomic number, Z eff . These parameters are extracted from the LACs using attenuation decomposition and are independent of the scanner specification. The classification performance with the raw and corrected data is tested on different numbers of energy bins and projections and different radiation dose levels. We use experimental data with a broad range of materials in the range of 6 ≤ Z eff ≤ 15 , acquired with a custom laboratory instrument for spectral CT. Results: We show that using the spectral correction leads to an accuracy increase of 1.6 and 3.8 times in estimating ρ e and Z eff , respectively, when the image reconstruction is performed from only 12 projections and the 15 energy bins approach is used. Conclusions: The correction algorithm accurately reconstructs the measured attenuation curve and thus gives better classification performance.

Multi source translation based projection completion for interior region of interest tomography with CBCT

Interior tomography by rotary computed tomography (RCT) is an effective method to improve the detection efficiency and achieve high-resolution imaging for the region of interest (ROI) within a large-scale object. However, because only the X-rays through the ROI can be received by detector, the projection data is inevitably truncated, resulting in truncation artifacts in the reconstructed image. When the ROI is totally within the object, the solution of the problem is not unique, which is named interior problem. Fortunately, projection completion (PC) is an effective technique to solve the interior problem. In this study, we proposed a multi source translation CT based PC method (mSTCT-PC) to cope with the interior problem. Firstly, mSTCT-PC employs multi-source translation to sparsely obtain the global projection which covered the whole object. Secondly, the sparse global projection is utilized to fill up the truncated projection of ROI. The global projection and truncated projection are obtained under the same geometric parameters. Therefore, it omits the registration of projection. To verify the feasibility of this method, simulation and practical experiments were implemented. Compared with the results of ROI reconstructed by filtered back-projection (FBP), simultaneous iterative reconstruction technique-total variation (SIRT-TV) and the multi-resolution based method (mR-PC), the proposed mSTCT-PC is good at mitigating truncation artifacts, preserving details and improving the accuracy of ROI images.

Differentiable Direct Volume Rendering

We present a differentiable volume rendering solution that provides differentiability of all continuous parameters of the volume rendering process. This differentiable renderer is used to steer the parameters towards a setting with an optimal solution of a problem-specific objective function. We have tailored the approach to volume rendering by enforcing a constant memory footprint via analytic inversion of the blending functions. This makes it independent of the number of sampling steps through the volume and facilitates the consideration of small-scale changes. The approach forms the basis for automatic optimizations regarding external parameters of the rendering process and the volumetric density field itself. We demonstrate its use for automatic viewpoint selection using differentiable entropy as objective, and for optimizing a transfer function from rendered images of a given volume. Optimization of per-voxel densities is addressed in two different ways: First, we mimic inverse tomography and optimize a 3D density field from images using an absorption model. This simplification enables comparisons with algebraic reconstruction techniques and state-of-the-art differentiable path tracers. Second, we introduce a novel approach for tomographic reconstruction from images using an emission-absorption model with post-shading via an arbitrary transfer function.

Iterative dynamic dual-energy CT algorithm in reducing statistical noise in multi-energy CT imaging

Multi-energy spectral CT has a broader range of applications with the recent development of photon-counting detectors. However, the photons counted in each energy bin decrease when the number of energy bins increases, which causes a higher statistical noise level of the CT image. In this work, we propose a novel iterative dynamic dual-energy CT algorithm to reduce the statistical noise. In the proposed algorithm, the multi-energy projections are estimated from the dynamic dual-energy CT data during the iterative process. The proposed algorithm is verified on sufficient numerical simulations and a laboratory two-energy-threshold PCD system. By applying the same reconstruction algorithm, the dynamic dual-energy CT's final reconstruction results have a much lower statistical noise level than the conventional multi-energy CT. Moreover, based on the analysis of the simulation results, we explain why the dynamic dual-energy CT has a lower statistical noise level than the conventional multi-energy CT. The reason is that: the statistical noise level of multi-energy projection estimated with the proposed algorithm is much lower than that of the conventional multi-energy CT, which leads to less statistical noise of the dynamic dual-energy CT imaging.

Deep learning based classification of dynamic processes in time-resolved X-ray tomographic microscopy

Time-resolved X-ray tomographic microscopy is an invaluable technique to investigate dynamic processes in 3D for extended time periods. Because of the limited signal-to-noise ratio caused by the short exposure times and sparse angular sampling frequency, obtaining quantitative information through post-processing remains challenging and requires intensive manual labor. This severely limits the accessible experimental parameter space and so, prevents fully exploiting the capabilities of the dedicated time-resolved X-ray tomographic stations. Though automatic approaches, often exploiting iterative reconstruction methods, are currently being developed, the required computational costs typically remain high. Here, we propose a highly efficient reconstruction and classification pipeline (SIRT-FBP-MS-D-DIFF) that combines an algebraic filter approximation and machine learning to significantly reduce the computational time. The dynamic features are reconstructed by standard filtered back-projection with an algebraic filter to approximate iterative reconstruction quality in a computationally efficient manner. The raw reconstructions are post-processed with a trained convolutional neural network to extract the dynamic features from the low signal-to-noise ratio reconstructions in a fully automatic manner. The capabilities of the proposed pipeline are demonstrated on three different dynamic fuel cell datasets, one exploited for training and two for testing without network retraining. The proposed approach enables automatic processing of several hundreds of datasets in a single day on a single GPU node readily available at most institutions, so extending the possibilities in future dynamic X-ray tomographic investigations.

Tomosipo: fast, flexible, and convenient 3D tomography for complex scanning geometries in Python

Tomography is a powerful tool for reconstructing the interior of an object from a series of projection images. Typically, the source and detector traverse a standard path (e.g., circular, helical). Recently, various techniques have emerged that use more complex acquisition geometries. Current software packages require significant handwork, or lack the flexibility to handle such geometries. Therefore, software is needed that can concisely represent, visualize, and compute reconstructions of complex acquisition geometries. We present tomosipo, a Python package that provides these capabilities in a concise and intuitive way. Case studies demonstrate the power and flexibility of tomosipo.

Improving a Rapid Alignment Method of Tomography Projections by a Parallel Approach

The high resolution of synchrotron cryo-nano tomography can be easily undermined by setup instabilities and sample stage deficiencies such as runout or backlash. At the cost of limiting the sample visibility, especially in the case of bio-specimens, high contrast nano-beads are often added to the solution to provide a set of landmarks for a manual alignment. However, the spatial distribution of these reference points within the sample is difficult to control, resulting in many datasets without a sufficient amount of such critical features for tracking. Fast automatic methods based on tomography consistency are thus desirable, especially for biological samples, where regular, high contrast features can be scarce. Current off-the-shelf implementations of such classes of algorithms are slow if used on a real-world high-resolution dataset. In this paper, we present a fast implementation of a consistency-based alignment algorithm especially tailored to a multi-GPU system. Our implementation is released as open-source.

Suppression of Cone-Beam Artefacts with Direct Iterative Reconstruction Computed Tomography Trajectories (DIRECTT)

The reconstruction of cone-beam computed tomography data using filtered back-projection algorithms unavoidably results in severe artefacts. We describe how the Direct Iterative Reconstruction of Computed Tomography Trajectories (DIRECTT) algorithm can be combined with a model of the artefacts for the reconstruction of such data. The implementation of DIRECTT results in reconstructed volumes of superior quality compared to the conventional algorithms.

Extended imaging volume in cone-beam x-ray tomography using the weighted simultaneous iterative reconstruction technique

An issue in computerized x-ray tomography is the limited size of available detectors relative to objects of interest. A solution was provided in the past two decades by positioning the detector in a lateral offset position, increasing the effective field of view (FOV) and thus the diameter of the reconstructed volume. However, this introduced artifacts in the obtained reconstructions, caused by projection truncation and data redundancy. These issues can be addressed by incorporating an additional data weighting step in the reconstruction algorithms, known as redundancy weighting. In this work, we present an implementation of redundancy weighting in the widely-used simultaneous iterative reconstruction technique (SIRT), yielding the weighted SIRT (W-SIRT) method. The new technique is validated using geometric phantoms and a rabbit specimen, by performing both simulation studies as well as physical experiments. The experiments are carried out in a highly flexible stereoscopic x-ray system equipped with x-ray image intensifiers (XRIIs). The simulations showed that higher values of contrast-to-noise ratio could be obtained using the W-SIRT approach as compared to a weighted implementation of the simultaneous algebraic reconstruction technique (SART). The convergence rate of the W-SIRT was accelerated by including a relaxation parameter in the W-SIRT algorithm, creating the aW-SIRT algorithm. This allowed to obtain the same results as the W-SIRT algorithm, but at half the number of iterations, yielding a much shorter computation time. The aW-SIRT algorithm has proven to perform well for both large as well as small regions of overlap, outperforming the pre-convolutional Feldkamp-David-Kress algorithm for small overlap regions (or large detector offsets). The experiments confirmed the results of the simulations. Using the aW-SIRT algorithm, the effective FOV was increased by >75%, only limited by experimental constraints. Although an XRII is used in this work, the method readily applies to flat-panel detectors as well.

Improved dynamic imaging of multiphase flow by constrained tomographic reconstruction

Dynamic tomography has become an important technique to study fluid flow processes in porous media. The use of laboratory X-ray tomography instruments is, however, limited by their low X-ray brilliance. The prolonged exposure times, in turn, greatly limit temporal resolution. We have developed a tomographic reconstruction algorithm that maintains high image quality, despite reducing the exposure time and the number of projections significantly. Our approach, based on the Simultaneous Iterative Reconstruction Technique, mitigates the problem of few and noisy exposures by utilising a high-quality scan of the system before the dynamic process is started. We use the high-quality scan to initialise the first time step of the dynamic reconstruction. We further constrain regions of the dynamic reconstruction with a segmentation of the static system. We test the performance of the algorithm by reconstructing the dynamics of fluid separation in a multiphase system. The algorithm is compared quantitatively and qualitatively with several other reconstruction algorithms and we show that it can maintain high image quality using only a fraction of the normally required number of projections and with a substantially larger noise level. By robustly allowing fewer projections and shorter exposure, our algorithm enables the study of faster flow processes using laboratory tomography instrumentation but it can also be used to improve the reconstruction quality of dynamic synchrotron experiments.

Deep denoising for multi-dimensional synchrotron X-ray tomography without high-quality reference data

Synchrotron X-ray tomography enables the examination of the internal structure of materials at submicron spatial resolution and subsecond temporal resolution. Unavoidable experimental constraints can impose dose and time limits on the measurements, introducing noise in the reconstructed images. Convolutional neural networks (CNNs) have emerged as a powerful tool to remove noise from reconstructed images. However, their training typically requires collecting a dataset of paired noisy and high-quality measurements, which is a major obstacle to their use in practice. To circumvent this problem, methods for CNN-based denoising have recently been proposed that require no separate training data beyond the already available noisy reconstructions. Among these, the Noise2Inverse method is specifically designed for tomography and related inverse problems. To date, applications of Noise2Inverse have only taken into account 2D spatial information. In this paper, we expand the application of Noise2Inverse in space, time, and spectrum-like domains. This development enhances applications to static and dynamic micro-tomography as well as X-ray diffraction tomography. Results on real-world datasets establish that Noise2Inverse is capable of accurate denoising and enables a substantial reduction in acquisition time while maintaining image quality.

A novel method for dendrochronology of large historical wooden objects using line trajectory X-ray tomography

Dendrochronology is an essential tool to determine the date and provenance of wood from historical art objects. As standard methods to access the tree rings are invasive, X-ray computed tomography (CT) has been proposed for non-invasive dendrochronological investigation. While traditional CT can provide clear images of the inner structure of wooden objects, it requires their full rotation, imposing strong limitations on the size of the object. These limitations have previously encouraged investigations into alternative acquisition trajectories, including trajectories with only linear movement. In this paper, we use such a line-trajectory (LT) X-ray tomography technique to retrieve tree-ring patterns from large wooden objects. We demonstrate that by moving a wooden artifact sideways between the static X-ray source and the detector during acquisition, sharp reconstruction images of the tree rings can be produced. We validate this technique using computer simulations and two wooden test planks, and demonstrate it on a large iconic chest from the Rijksmuseum collection (Amsterdam, The Netherlands). The LT scanning method can be easily implemented in standard X-ray imaging units available at museum research facilities. Therefore, this scanning technique represents a major step towards the standard implementation of non-invasive dendrochronology on large wooden cultural heritage objects.

Structural and chemical characterization of MoO2/MoS2 triple-hybrid materials using electron microscopy in up to three dimensions

This work presents the synthesis of MoO₂/MoS₂ core/shell nanoparticles within a carbon nanotube network and their detailed electron microscopy investigation in up to three dimensions. The triple-hybrid core/shell material was prepared by atomic layer deposition of molybdenum oxide onto carbon nanotube networks, followed by annealing in a sulfur-containing gas atmosphere. High-resolution transmission electron microscopy together with electron diffraction, supported by chemical analysis via energy dispersive X-ray and electron energy loss spectroscopy, gave proof of a MoO₂ core covered by few layers of a MoS₂ shell within an entangled network of carbon nanotubes. To gain further insights into this complex material, the analysis was completed with 3D electron tomography. By using Z-contrast imaging, distinct reconstruction of core and shell material was possible, enabling the analysis of the 3D structure of the material. These investigations showed imperfections in the nanoparticles which can impact material performance, i.e. for faradaic charge storage or electrocatalysis.

Accelerated strategy for the MLEM algorithm

BACKGROUND

A statistical method called maximum likelihood expectation maximization (MLEM) is quite attractive, especially in PET/SPECT. However, the convergence rate of the iterative scheme of MLEM is quite slow.

OBJECTIVE

This study aims to develop and test a new method to speed up the convergence rate of the MLEM algorithm.

METHODS

We introduce a relaxation parameter in the conventional MLEM iterative formula and propose the relaxation strategy on the condition that the spectral radius of the derived iterative matrix from the iterative scheme with the accelerated parameter reaches a minimum value.

RESULTS

Experiments with Shepp-Logan phantom and an annual tree image demonstrate that the new computational strategy effectively accelerates computation time while maintains reasonable image quality.

CONCLUSIONS

The proposed new computational method involving the relaxation strategy has a faster convergence speed than the original method.

Extraction of 3D quantitative maps using EDS-STEM tomography and HAADF-EDS bimodal tomography

Electron tomography has been widely applied to three-dimensional (3D) morphology characterization and chemical analysis at the nanoscale. A HAADF-EDS bimodal tomographic (HEBT) reconstruction technique has been developed to extract high resolution element-specific information. However, the reconstructed elemental maps cannot be directly converted to quantitative compositional information. In this work, we propose a quantification approach for obtaining elemental weight fraction maps from the HEBT reconstruction technique using the physical parameters extracted from a Monte Carlo code, MC X-ray. A similar quantification approach is proposed for the EDS-STEM tomographic reconstruction. The performance of the two quantitative reconstruction methods, using the simultaneous iterative reconstruction technique, are evaluated and compared for a simulated dataset of a two-dimensional phantom sample. The effects of the reconstruction parameters including the number of iterations and the weight of the HAADF signal are discussed. Finally, the two approaches are applied to an experimental dataset to show the 3D structure and quantitative elemental maps of a particle of flux melted metal-organic framework glass.

Laser wakefield accelerated electron beams and betatron radiation from multijet gas targets

Laser Plasma Wakefield Accelerated (LWFA) electron beams and efficiency of betatron X-ray sources is studied using laser micromachined supersonic gas jet nozzle arrays. Separate sections of the target are used for the injection, acceleration and enhancement of electron oscillation. In this report, we present the results of LWFA and X-ray generation using dynamic gas density grid built by shock-waves of colliding jets. The experiment was done with the 40 TW, 35 fs laser at the Lund Laser Centre. Electron energies of 30–150 MeV and 1.0 × 10⁸–5.5 × 10⁸ photons per shot of betatron radiation have been measured. The implementation of the betatron source with separate regions of LWFA and plasma density grid raised the efficiency of X-ray generation and increased the number of photons per shot by a factor of 2–3 relative to a single-jet gas target source.

Unveiling water dynamics in fuel cells from time-resolved tomographic microscopy data

X-ray dynamic tomographic microscopy offers new opportunities in the volumetric investigation of dynamic processes. Due to data complexity and their sheer amount, extraction of comprehensive quantitative information remains challenging due to the intensive manual interaction required. Particularly for dynamic investigations, these intensive manual requirements significantly extend the total data post-processing time, limiting possible dynamic analysis realistically to a few samples and time steps, hindering full exploitation of the new capabilities offered at dedicated time-resolved X-ray tomographic stations. In this paper, a fully automatized iterative tomographic reconstruction pipeline (rSIRT-PWC-DIFF) designed to reconstruct and segment dynamic processes within a static matrix is presented. The proposed algorithm includes automatic dynamic feature separation through difference sinograms, a virtual sinogram step for interior tomography datasets, time-regularization extended to small sub-regions for increased robustness and an automatic stopping criterion. We demonstrate the advantages of our approach on dynamic fuel cell data, for which the current data post-processing pipeline heavily relies on manual labor. The proposed approach reduces the post-processing time by at least a factor of 4 on limited computational resources. Full independence from manual interaction additionally allows straightforward up-scaling to efficiently process larger data, extensively boosting the possibilities in future dynamic X-ray tomographic investigations.

Direct Iterative Reconstruction of Computed Tomography Trajectories Reconstruction from limited number of projections with DIRECTT

X-ray computed tomography has many applications in materials science and non-destructive testing. While the standard filtered back-projection reconstruction of the radiographic datasets is fast and simple, it typically fails in returning accurate results from missing or inconsistent projections. Among the alternative techniques that have been proposed to handle such data is the Direct Iterative REconstruction of Computed Tomography Trajectories (DIRECTT) algorithm. We describe a new approach to the algorithm, which significantly decreases the computational time while achieving a better reconstruction quality than that of other established algorithms.

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.

A Consensus Framework of Distributed Multiple-Tilt Reconstruction in Electron Tomography

The "missing wedge" of a single tilt in electron tomography introduces severe artifacts into the reconstructed results. To reduce the "missing wedge" effect, a widely used method is "multiple-tilt reconstruction," which collects projections using multiple axes. However, as the number of tilt series increases, the computing and memory costs also rise. The degree of parallelism is limited by the sample thickness, and a large memory requirement cannot be met by most multicore computers. In our study, we present a new fully distributed multiple-tilt simultaneous iterative reconstruction technique (DM-SIRT). To improve the parallelism of the reconstruction process and reduce the memory requirements of each process, we formulate the multiple-tilt reconstruction as a consensus optimization problem and design a DM-SIRT algorithm. Experiments show that in addition to slightly better resolution, DM-SIRT can obtain a 13.9 × accelerated ratio compared with the full multiple-tilt reconstruction version. It also has a 97% decrease in memory overhead and is 16 times more scalable than the full reconstruction version.

The Influence of X-Ray Computed Tomography Acquisition Parameters on Image Quality and Probability of Detection of Additive Manufacturing Defects

X-ray computed tomography (XCT) is a promising nondestructive evaluation technique for additive manufacturing (AM) parts with complex shapes. Industrial XCT scanning is a relatively new development, and XCT has several acquisition parameters that a user can change for a scan whose effects are not fully understood. An artifact incorporating simulated defects of different sizes was produced using laser powder bed fusion (LPBF) AM. The influence of six XCT acquisition parameters was investigated experimentally based on a fractional factorial designed experiment. Twenty experimental runs were performed. The noise level of the XCT images was affected by the acquisition parameters, and the importance of the acquisition parameters was ranked. The measurement results were further analyzed to understand the probability of detection (POD) of the simulated defects. The POD determination process is detailed, including estimation of the POD confidence limit curve using a bootstrap method. The results are interpreted in the context of the AM process and XCT acquisition parameters.

Dynamic Volume Lines: Visual Comparison of 3D Volumes through Space-filling Curves

The comparison of many members of an ensemble is difficult, tedious, and error-prone, which is aggravated by often just subtle differences. In this paper, we introduce Dynamic Volume Lines for the interactive visual analysis and comparison of sets of 3D volumes. Each volume is linearized along a Hilbert space-filling curve into a 1D Hilbert line plot, which depicts the intensities over the Hilbert indices. We present a nonlinear scaling of these 1D Hilbert line plots based on the intensity variations in the ensemble of 3D volumes, which enables a more effective use of the available screen space. The nonlinear scaling builds the basis for our interactive visualization techniques. An interactive histogram heatmap of the intensity frequencies serves as overview visualization. When zooming in, the frequencies are replaced by detailed 1D Hilbert line plots and optional functional boxplots. To focus on important regions of the volume ensemble, nonlinear scaling is incorporated into the plots. An interactive scaling widget depicts the local ensemble variations. Our brushing and linking interface reveals, for example, regions with a high ensemble variation by showing the affected voxels in a 3D spatial view. We show the applicability of our concepts using two case studies on ensembles of 3D volumes resulting from tomographic reconstruction. In the first case study, we evaluate an artificial specimen from simulated industrial 3D X-ray computed tomography (XCT). In the second case study, a real-world XCT foam specimen is investigated. Our results show that Dynamic Volume Lines can identify regions with high local intensity variations, allowing the user to draw conclusions, for example, about the choice of reconstruction parameters. Furthermore, it is possible to detect ring artifacts in reconstructions volumes.

Can portable tomosynthesis improve the diagnostic value of bedside chest X-ray in the intensive care unit? A proof of concept study

Portable bedside chest X-ray (CXR) is an important and frequently used tool in the intensive care unit (ICU). Unfortunately, the diagnostic value of portable CXR is often low due to technical limitations and suboptimal patient positioning. Additionally, abnormalities in the chest may be hidden on the projection image by overlapping anatomy and devices such as endotracheal tubes, lines and catheters. Digital tomosynthesis (DTS) can solve the problem of anatomical overlap. In DTS, several low-dose X-ray images from different angles are acquired and subsequently used by a reconstruction algorithm to compute section images along planes parallel to the detector. However, a portable device to be used for portable bedside chest DTS is not on the market yet. In this work, we discuss modifications to a portable X-ray device to enable portable DTS and illustrate the potential of portable DTS to improve the diagnostic value of bedside CXR in the ICU. A simulation, based on computed tomography scans, is presented. Our experiments comparing portable DTS with conventional bedside CXR showed a substantially improved detection of pneumothorax and other abnormalities.

Optimization of Three-Dimensional (3D) Chemical Imaging by Soft X-Ray Spectro-Tomography Using a Compressed Sensing Algorithm

Soft X-ray spectro-tomography provides three-dimensional (3D) chemical mapping based on natural X-ray absorption properties. Since radiation damage is intrinsic to X-ray absorption, it is important to find ways to maximize signal within a given dose. For tomography, using the smallest number of tilt series images that gives a faithful reconstruction is one such method. Compressed sensing (CS) methods have relatively recently been applied to tomographic reconstruction algorithms, providing faithful 3D reconstructions with a much smaller number of projection images than when conventional reconstruction methods are used. Here, CS is applied in the context of scanning transmission X-ray microscopy tomography. Reconstructions by weighted back-projection, the simultaneous iterative reconstruction technique, and CS are compared. The effects of varying tilt angle increment and angular range for the tomographic reconstructions are examined. Optimization of the regularization parameter in the CS reconstruction is explored and discussed. The comparisons show that CS can provide improved reconstruction fidelity relative to weighted back-projection and simultaneous iterative reconstruction techniques, with increasingly pronounced advantages as the angular sampling is reduced. In particular, missing wedge artifacts are significantly reduced and there is enhanced recovery of sharp edges. Examples of using CS for low-dose scanning transmission X-ray microscopy spectroscopic tomography are presented.

MoVIT: a tomographic reconstruction framework for 4D-CT

4D computed tomography (4D-CT) aims to visualise the temporal dynamics of a 3D sample with a sufficiently high temporal and spatial resolution. Successive time frames are typically obtained by sequential scanning, followed by independent reconstruction of each 3D dataset. Such an approach requires a large number of projections for each scan to obtain images with sufficient quality (in terms of artefacts and SNR). Hence, there is a clear trade-off between the rotation speed of the gantry (i.e. time resolution) and the quality of the reconstructed images. In this paper, the MotionVector-based Iterative Technique (MoVIT) is introduced which reconstructs a particular time frame by including the projections of neighbouring time frames as well. It is shown that such a strategy improves the trade-off between the rotation speed and the SNR. The framework is tested on both numerical simulations and on 4D X-ray CT datasets of polyurethane foam under compression. Results show that reconstructions obtained with MoVIT have a significantly higher SNR compared to the SNR of conventional 4D reconstructions.

Local attenuation curve optimization framework for high quality perfusion maps in low-dose cerebral perfusion CT

PURPOSE

Cerebral perfusion x-ray computed tomography (PCT) is a powerful tool for noninvasive imaging of hemodynamic information throughout the brain. Conventional PCT requires the brain to be imaged multiple times during the perfusion process, and hence radiation dose is a major concern. The authors propose a PCT reconstruction algorithm that allows for lowering the dose while maintaining a high quality of the perfusion maps. It relies on an accurate estimation of the arterial input function (AIF), which in turn depends on the quality of the attenuation curves in the arterial region.

METHODS

The authors propose the local attenuation curve optimization (LACO) framework. It accurately models the attenuation curves inside the vessel and arterial regions and optimizes its shape directly based on the acquired x-ray projection data.

RESULTS

The LACO algorithm is extensively validated with simulation and real clinical experiments. Quantitative and qualitative results show that our proposed approach accurately estimates the vessel and arterial attenuation curves from only few x-ray projections. In contrast to conventional approaches, where the AIF is estimated based on the reconstructed images, our method computes an optimal AIF directly based on the projection data, resulting in far more accurate perfusion maps.

CONCLUSIONS

The LACO algorithm allows estimating high quality perfusion maps in low dose scanning protocols.

Data-Driven Affine Deformation Estimation and Correction in Cone Beam Computed Tomography

In computed tomography (CT), motion and deformation during the acquisition lead to streak artefacts and blurring in the reconstructed images. To remedy these artefacts, we introduce an efficient algorithm to estimate and correct for global affine deformations directly on the cone beam projections. The proposed technique is data driven and thus removes the need for markers and/or a tracking system. A relationship between affine transformations and the cone beam transform is proved and used to correct the projections. The deformation parameters that describe deformation perpendicular to the projection direction are estimated for each projection by minimizing a plane-based inconsistency criterion. The criterion compares each projection of the main scan with all projections of a fast reference scan, which is acquired prior or posterior to the main scan. Experiments with simulated and experimental data show that the proposed affine deformation estimation method is able to substantially reduce motion artefacts in cone beam CT images.

Improved tomographic reconstruction of large-scale real-world data by filter optimization

In advanced tomographic experiments, large detector sizes and large numbers of acquired datasets can make it difficult to process the data in a reasonable time. At the same time, the acquired projections are often limited in some way, for example having a low number of projections or a low signal-to-noise ratio. Direct analytical reconstruction methods are able to produce reconstructions in very little time, even for large-scale data, but the quality of these reconstructions can be insufficient for further analysis in cases with limited data. Iterative reconstruction methods typically produce more accurate reconstructions, but take significantly more time to compute, which limits their usefulness in practice. In this paper, we present the application of the SIRT-FBP method to large-scale real-world tomographic data. The SIRT-FBP method is able to accurately approximate the simultaneous iterative reconstruction technique (SIRT) method by the computationally efficient filtered backprojection (FBP) method, using precomputed experiment-specific filters. We specifically focus on the many implementation details that are important for application on large-scale real-world data, and give solutions to common problems that occur with experimental data. We show that SIRT-FBP filters can be computed in reasonable time, even for large problem sizes, and that precomputed filters can be reused for future experiments. Reconstruction results are given for three different experiments, and are compared with results of popular existing methods. The results show that the SIRT-FBP method is able to accurately approximate iterative reconstructions of experimental data. Furthermore, they show that, in practice, the SIRT-FBP method can produce more accurate reconstructions than standard direct analytical reconstructions with popular filters, without increasing the required computation time.

A distributed ASTRA toolbox

While iterative reconstruction algorithms for tomography have several advantages compared to standard backprojection methods, the adoption of such algorithms in large-scale imaging facilities is still limited, one of the key obstacles being their high computational load. Although GPU-enabled computing clusters are, in principle, powerful enough to carry out iterative reconstructions on large datasets in reasonable time, creating efficient distributed algorithms has so far remained a complex task, requiring low-level programming to deal with memory management and network communication. The ASTRA toolbox is a software toolbox that enables rapid development of GPU accelerated tomography algorithms. It contains GPU implementations of forward and backprojection operations for many scanning geometries, as well as a set of algorithms for iterative reconstruction. These algorithms are currently limited to using GPUs in a single workstation. In this paper, we present an extension of the ASTRA toolbox and its Python interface with implementations of forward projection, backprojection and the SIRT algorithm that can be distributed over multiple GPUs and multiple workstations, as well as the tools to write distributed versions of custom reconstruction algorithms, to make processing larger datasets with ASTRA feasible. As a result, algorithms that are implemented in a high-level conceptual script can run seamlessly on GPU-enabled computing clusters, up to 32 GPUs or more. Our approach is not limited to slice-based reconstruction, facilitating a direct portability of algorithms coded for parallel-beam synchrotron tomography to cone-beam laboratory tomography setups without making changes to the reconstruction algorithm.

Fast and flexible X-ray tomography using the ASTRA toolbox

Object reconstruction from a series of projection images, such as in computed tomography (CT), is a popular tool in many different application fields. Existing commercial software typically provides sufficiently accurate and convenient-to-use reconstruction tools to the end-user. However, in applications where a non-standard acquisition protocol is used, or where advanced reconstruction methods are required, the standard software tools often are incapable of computing accurate reconstruction images. This article introduces the ASTRA Toolbox. Aimed at researchers across multiple tomographic application fields, the ASTRA Toolbox provides a highly efficient and highly flexible open source set of tools for tomographic projection and reconstruction. The main features of the ASTRA Toolbox are discussed and several use cases are presented.

Recent Advances in X-ray Cone-beam Computed Laminography

X-ray computed tomography is an established volume imaging technique used routinely in medical diagnosis, industrial non-destructive testing, and a wide range of scientific fields. Traditionally, computed tomography uses scanning geometries with a single axis of rotation together with reconstruction algorithms specifically designed for this setup. Recently there has however been increasing interest in more complex scanning geometries. These include so called X-ray computed laminography systems capable of imaging specimens with large lateral dimensions or large aspect ratios, neither of which are well suited to conventional CT scanning procedures. Developments throughout this field have thus been rapid, including the introduction of novel system trajectories, the application and refinement of various reconstruction methods, and the use of recently developed computational hardware and software techniques to accelerate reconstruction times. Here we examine the advances made in the last several years and consider their impact on the state of the art.

Three-dimensional full-field X-ray orientation microscopy

A previously introduced mathematical framework for full-field X-ray orientation microscopy is for the first time applied to experimental near-field diffraction data acquired from a polycrystalline sample. Grain by grain tomographic reconstructions using convex optimization and prior knowledge are carried out in a six-dimensional representation of position-orientation space, used for modelling the inverse problem of X-ray orientation imaging. From the 6D reconstruction output we derive 3D orientation maps, which are then assembled into a common sample volume. The obtained 3D orientation map is compared to an EBSD surface map and local misorientations, as well as remaining discrepancies in grain boundary positions are quantified. The new approach replaces the single orientation reconstruction scheme behind X-ray diffraction contrast tomography and extends the applicability of this diffraction imaging technique to material micro-structures exhibiting sub-grains and/or intra-granular orientation spreads of up to a few degrees. As demonstrated on textured sub-regions of the sample, the new framework can be extended to operate on experimental raw data, thereby bypassing the concept of orientation indexation based on diffraction spot peak positions. This new method enables fast, three-dimensional characterization with isotropic spatial resolution, suitable for time-lapse observations of grain microstructures evolving as a function of applied strain or temperature.

An Iterative CT Reconstruction Algorithm for Fast Fluid Flow Imaging

The study of fluid flow through solid matter by computed tomography (CT) imaging has many applications, ranging from petroleum and aquifer engineering to biomedical, manufacturing, and environmental research. To avoid motion artifacts, current experiments are often limited to slow fluid flow dynamics. This severely limits the applicability of the technique. In this paper, a new iterative CT reconstruction algorithm for improved a temporal/spatial resolution in the imaging of fluid flow through solid matter is introduced. The proposed algorithm exploits prior knowledge in two ways. First, the time-varying object is assumed to consist of stationary (the solid matter) and dynamic regions (the fluid flow). Second, the attenuation curve of a particular voxel in the dynamic region is modeled by a piecewise constant function over time, which is in accordance with the actual advancing fluid/air boundary. Quantitative and qualitative results on different simulation experiments and a real neutron tomography data set show that, in comparison with the state-of-the-art algorithms, the proposed algorithm allows reconstruction from substantially fewer projections per rotation without image quality loss. Therefore, the temporal resolution can be substantially increased, and thus fluid flow experiments with faster dynamics can be performed.