DART: a practical reconstruction algorithm for discrete tomography

Multiscale drainage dynamics with Haines jumps monitored by stroboscopic 4D X-ray microscopy

Slow multiphase flow in porous media is intriguing because its underlying dynamics is almost deterministic, yet depends on a hierarchy of spatiotemporal processes. There has been great progress in the experimental study of such multiphase flows, but three-dimensional (3D) microscopy methods probing the pore-scale fluid dynamics with millisecond resolution have been lacking. Yet, it is precisely at these length and time scales that the crucial pore-filling events known as Haines jumps take place. Here, we report four-dimensional (4D) (3D + time) observations of multiphase flow in a consolidated porous medium as captured in situ by stroboscopic X-ray micro-tomography. With a total duration of 6.5 s and 2 kHz frame rate, our experiments provide unprecedented access to the multiscale liquid dynamics. Our tomography strategy relies on the fact that Haines jumps, although irregularly spaced in time, are almost deterministic, and therefore repeatable during imbibition-drainage cycling. We studied the time-dependent flow pattern in a porous medium consisting of sintered glass shards. Exploiting the repeatability, we could combine the radiographic projections recorded under different angles during successive cycles into a 3D movie, allowing us to reconstruct pore-scale events, such as Haines jumps, with a spatiotemporal resolution that is two orders of magnitude higher than was hitherto possible. This high resolution allows us to explore the detailed interfacial dynamics during drainage, including fluid-front displacements and velocities. Our experimental approach opens the way to the study of fast, yet deterministic mesoscopic processes also other than flow in porous media.

Evaluation of Electron Tomography Capabilities for Shale Imaging

Despite the advantageous resolution of electron tomography (ET), reconstruction of three-dimensional (3D) images from multiple two-dimensional (2D) projections presents several challenges, including small signal-to-noise ratios, and a limited projection range. This study evaluates the capabilities of ET for thin sections of shale, a complex nanoporous medium. A numerical phantom with 1.24 nm pixel size is constructed based on the tomographic reconstruction of a Barnett shale. A dataset of 2D projection images is numerically generated from the 3D phantom and studied over a range of conditions. First, common reconstruction techniques are used to reconstruct the shale structure. The reconstruction uncertainty is quantified by comparing overall values of storage and transport metrics, as well as the misclassification of pore voxels compared to the phantom. We then select the most robust reconstruction technique and we vary the acquisition conditions to quantify the effect of artifacts. We find a strong agreement for large pores over the different acquisition workflows, while a wider variability exists for nanometer-scale features. The limited projection range and reconstruction are identified as the main experimental bottlenecks, thereby suggesting that sample thinning, advanced holders, and advanced reconstruction algorithms offer opportunities for improvement.

Real-time tilt undersampling optimization during electron tomography of beam sensitive samples using golden ratio scanning and RECAST3D

Electron tomography is a widely used technique for 3D structural analysis of nanomaterials, but it can cause damage to samples due to high electron doses and long exposure times. To minimize such damage, researchers often reduce beam exposure by acquiring fewer projections through tilt undersampling. However, this approach can also introduce reconstruction artifacts due to insufficient sampling. Therefore, it is important to determine the optimal number of projections that minimizes both beam exposure and undersampling artifacts for accurate reconstructions of beam-sensitive samples. Current methods for determining this optimal number of projections involve acquiring and post-processing multiple reconstructions with different numbers of projections, which can be time-consuming and requires multiple samples due to sample damage. To improve this process, we propose a protocol that combines golden ratio scanning and quasi-3D reconstruction to estimate the optimal number of projections in real-time during a single acquisition. This protocol was validated using simulated and realistic nanoparticles, and was successfully applied to reconstruct two beam-sensitive metal-organic framework complexes.

Disclosing the leaching behaviour of Pd@CMK3 catalysts in formic acid decomposition by electron tomography

Supported nanocatalysts exhibit different performances in batch and fixed bed reactors for a wide range of liquid phase catalytic reactions due to differences in metal leaching. To investigate this leaching process and its influence on the catalytic performance, a quantitative 3D characterization of the particle size and the particle distribution is important to follow the structural evolution of the active metal catalysts supported on porous materials during the reaction. In this work, electron tomography has been applied to uncover leaching and redeposition of a Pd@CMK3 catalyst during formic acid decomposition in batch and fixed bed reactors. The 3D distribution of Pd NPs on the mesoporous carbon CMK3 has been determined by a quantitative tomographic analysis and the determined structural changes are correlated with the observed differences in activity and stability of formic acid decomposition using batch and fixed bed reactors.

Dual spectral limited-angle CT imaging regularized by edge-preserving diffusion and smoothing

Limited-angle CT scan is an effective way for nondestructive inspection of planar objects, and various methods have been proposed accordingly. When the scanned object contains high-absorption material, such as metal, existing methods may fail due to the beam hardening of X-rays. In order to overcome this problem, we adopt a dual spectral limited-angle CT scan and propose a corresponding image reconstruction algorithm, which takes the polychromatic property of the X-ray into consideration, makes basis material images free of beam hardening artifacts and metal artifacts, and then helps depress the limited-angle artifacts. Experimental results on both simulated PCB data and real data demonstrate the effectiveness of the proposed algorithm.

Precisely Picking Nanoparticles by a "Nano-Scalpel" for 360° Electron Tomography

Electron tomography (ET) has gained increasing attention for the 3D characterization of nanoparticles. However, the missing wedge problem due to a limited tilt angle range is still the main challenge for accurate reconstruction in most experimental TEM setups. Advanced algorithms could in-paint or compensate to some extent the missing wedge artifacts, but cannot recover the missing structural information completely. 360° ET provides an option to solve this problem by tilting a needle-shaped specimen over the full tilt range and thus filling the missing information. However, sample preparation especially for fine powders to perform full-range ET is still challenging, thus limiting its application. In this work, we propose a new universal sample preparation method that enables the transfer of selected individual nanoparticle or a few separated nanoparticles by cutting a piece of carbon film supporting the specimen particles and mounting them onto the full-range tomography holder tip with the help of an easily prepared sharp tungsten tip. This method is demonstrated by 360° ET of Pt@TiO2 hollow cage catalyst showing high quality reconstruction without missing wedge.

Deep-learning-based projection-domain breast thickness estimation for shape-prior iterative image reconstruction in digital breast tomosynthesis

BACKGROUND

Digital breast tomosynthesis (DBT) is a technique that can overcome the shortcomings of conventional X-ray mammography and can be effective for the early screening of breast cancer. The compression of the breast is essential during the DBT imaging. However, since the periphery of the breast cannot be compressed to a constant value, nonuniformity of thickness and in-plane shape variation happen. These cause inconvenience in diagnosis, scatter correction, and breast density estimation.

PURPOSE

In this study, we propose a deep-learning-based methodology for projection-domain breast thickness estimation and demonstrate a shape-prior iterative DBT image reconstruction.

METHODS

We prepared the Euclidean distance map, the thickness map, and the thickness corrected image of the simulated breast projections for thickness and shape estimation. Each pixel of the Euclidean distance map denotes a distance to the closest skin-line. The thickness map is defined as a conceptual projection of ideal breast support that differentiates the inner and outer regions of the breast phantom. The thickness projection map thus represents the x-ray path lengths of a homogeneous breast phantom. We generated the thickness corrected image by dividing the projection image by the thickness map in a pixel-wise manner. We developed a convolutional neural network for thickness estimation and correction. The network utilizes a projection image and a Euclidean distance image together as a dual input. An estimated breast thickness map is then used for constructing the breast shape mask by use of the discrete algebraic reconstruction technique (DART).

RESULTS

The proposed network effectively corrected the breast thickness in various simulation situations. Low normalized root-mean-squared error (NRMSE; 1.976%) and high structural similarity (SSIM; 99.997%) indicated a good agreement between the network-generated thickness corrected image and the ground-truth image. Compared to the existing methods and simple single-input network, the proposed method showed outperformance in breast thickness estimation and accordingly in breast shape recovery for various numerical phantoms without provoking any significant artifact. We have demonstrated that the uniformity of voxel value has improved by the inclusion of a shape-prior for the iterative DBT reconstruction.

CONCLUSIONS

We presented a novel deep-learning-based breast thickness correction and a shape reconstruction method. This approach to estimating the true thickness map and the shape of the breast undergoing compression can benefit various fields such as improvement of diagnostic breast images, scatter correction, material decomposition, and breast density estimation. This article is protected by copyright. All rights reserved.

Image reconstruction from data over two orthogonal arcs of limited-angular ranges

PURPOSE

Computed tomography (CT) scanning over limited-angular ranges (LARs) is of practical interest in possible reduction of imaging dose and time and in design of non-standard scans. This work aims to investigate image reconstruction for two non-overlapping arcs of LARs, and to demonstrate that they may allow more accurate image reconstruction than may a single arc of LAR.

METHODS

We consider a configuration with two non-overlapping arcs of LARs α₁ and α₂ , whose centers are separated by 90°, and refer to it as a two-orthogonal-arc configuration. Data are generated from a chest phantom with two-orthogonal-arc configurations over total angular coverage α_τ = α₁ + α₂ ranging from 18° to 180°, and images are reconstructed subsequently by use of the directional-total-variation (DTV) algorithm. For comparison, we also consider image reconstruction for a single-arc configuration of angular range α_τ . Quantitative metrics such as the normalized root-mean-square-error (nRMSE) are used for evaluation of image reconstruction accuracy.

RESULTS

Visual inspection and quantitative analysis of images reconstructed reveal that a two-orthogonal-arc configuration generally yields more accurate image reconstruction than does its single-arc counterpart. As total angular range α_τ increases, the DTV algorithm yields image reconstruction with enhanced accuracy, as expected. Also, if α_τ remains constant, the two-orthogonal-arc configuration with α₁ = α₂ generally leads to image reconstruction more accurate than those of two-orthogonal-arc configurations with α₁ ≠ α₂ , as the nRMSE of the former can be lower than that of the latter for up to more than one order of magnitude.

CONCLUSIONS

Appropriately designed two-orthogonal-arc configurations may be exploited for improving image-reconstruction accuracy in CT imaging with reduced angular coverage. This study may yield insights into the design of innovative CT scans for lowering scan time and radiation dose, and/or for avoiding scan collision in, e.g., C-arm CT.

IDART: An Improved Discrete Tomography Algorithm for Reconstructing Images With Multiple Gray Levels

The discrete algebraic reconstruction technique has many advantages in computed tomography and electron tomography. However, the number of gray levels and the absolute gray values that should be known in advance are typically not available in experiments especially when there are many gray levels in the image. In this paper, we report an automatic discrete tomography reconstruction algorithm to improve its feasibility in practice, without needing to know these two parameters. In our algorithm, the number of gray levels is estimated by labeling the connected components in the tomogram and the absolute values of them are determined by the modal value of each domain. The proposed algorithm was extensively validated on both simulated and experimental datasets. The results show that our algorithm can accurately recover not only the morphology but also the gray levels of the interested objects, even in the images with multiple gray levels. It is demonstrated that the presented algorithm is robust for eliminating missing wedge artifacts and tolerable for noisy data.

Projection-based dynamic tomography

Objective. This paper proposes a 4D dynamic tomography framework that allows a moving sample to be imaged in a tomograph as well as the associated space-time kinematics to be measured with nothing more than a single conventional x-ray scan.Approach. The method exploits the consistency of the projection/reconstruction operations through a multi-scale procedure. The procedure is composed of two main parts solved alternatively: a motion-compensated reconstruction algorithm and a projection-based measurement procedure that estimates the displacement field directly on each projection.Main results. The method is applied to two studies: a numerical simulation of breathing from chest computed tomography (4D-CT) and a clinical cone-beam CT of a breathing patient acquired for image guidance of radiotherapy. The reconstructed volume, initially blurred by the motion, is cleaned from motion artifacts.Significance. Applying the proposed approach results in an improved reconstruction quality showing sharper edges and finer details.

Dual-energy CT imaging with limited-angular-range data

In dual-energy computed tomography (DECT), low- and high-kVp data are collected often over a full-angular range (FAR) of 360^○. While there exists strong interest in DECT with low- and high-kVp data acquired over limited-angular ranges (LARs), there remains little investigation of image reconstruction in DECT with LAR data.Objective: We investigate image reconstruction with minimized LAR artifacts from low- and high-kVp data over LARs of ≤180^○by using a directional-total-variation (DTV) algorithm.Methods: Image reconstruction from LAR data is formulated as a convex optimization problem in which data-l₂is minimized with constraints on image's DTVs along orthogonal axes. We then achieve image reconstruction by applying the DTV algorithm to solve the optimization problem. We conduct numerical studies from data generated over arcs of LARs, ranging from 14^○to 180^○, and perform visual inspection and quantitative analysis of images reconstructed.Results: Monochromatic images of interest obtained with the DTV algorithm from LAR data show substantially reduced artifacts that are observed often in images obtained with existing algorithms. The improved image quality also leads to accurate estimation of physical quantities of interest, such as effective atomic number and iodine-contrast concentration.Conclusion: Our study reveals that from LAR data of low- and high-kVp, monochromatic images can be obtained that are visually, and physical quantities can be estimated that are quantitatively, comparable to those obtained in FAR DECT.Significance: As LAR DECT is of high practical application interest, the results acquired in the work may engender insights into the design of DECT with LAR scanning configurations of practical application significance.

A signal detection model for quantifying overregularization in nonlinear image reconstruction

Many useful image quality metrics for evaluating linear image reconstruction techniques do not apply to or are difficult to interpret for nonlinear image reconstruction. The vast majority of metrics employed for evaluating nonlinear image reconstruction are based on some form of global image fidelity, such as image root mean square error (RMSE). Use of such metrics can lead to overregularization in the sense that they can favor removal of subtle details in the image. To address this shortcoming, we develop an image quality metric based on signal detection that serves as a surrogate to the qualitative loss of fine image details. The metric is demonstrated in the context of a breast CT simulation, where different equal-dose configurations are considered. The configurations differ in the number of projections acquired. Image reconstruction is performed with a nonlinear algorithm based on total variation constrained least-squares (TV-LSQ). The resulting images are studied as a function of three parameters: number of views acquired, total variation constraint value, and number of iterations. The images are evaluated visually, with image RMSE, and with the proposed signal-detection-based metric. The latter uses a small signal, and computes detectability in the sinogram and in the reconstructed image. Loss of signal detectability through the image reconstruction process is taken as a quantitative measure of loss of fine details in the image. Loss of signal detectability is seen to correlate well with the blocky or patchy appearance due to overregularization with TV-LSQ, and this trend runs counter to the image RMSE metric, which tends to favor the over-regularized images. The proposed signal detection-based metric provides an image quality assessment that is complimentary to that of image RMSE. Using the two metrics in concert may yield a useful prescription for determining CT algorithm and configuration parameters when nonlinear image reconstruction is used.

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.

Directional-TV algorithm for image reconstruction from limited-angular-range data

Investigation of image reconstruction from data collected over a limited-angular range in X-ray CT remains a topic of active research because it may yield insight into the development of imaging workflow of practical significance. This reconstruction problem is well-known to be challenging, however, because it is highly ill-conditioned. In the work, we investigate optimization-based image reconstruction from data acquired over a limited-angular range that is considerably smaller than the angular range in short-scan CT. We first formulate the reconstruction problem as a convex optimization program with directional total-variation (TV) constraints applied to the image, and then develop an iterative algorithm, referred to as the directional-TV (DTV) algorithm for image reconstruction through solving the optimization program. We use the DTV algorithm to reconstruct images from data collected over a variety of limited-angular ranges for breast and bar phantoms of clinical- and industrial-application relevance. The study demonstrates that the DTV algorithm accurately recovers the phantoms from data generated over a significantly reduced angular range, and that it considerably diminishes artifacts observed otherwise in reconstructions of existing algorithms. We have also obtained empirical conditions on minimal-angular ranges sufficient for numerically accurate image reconstruction with the DTV algorithm.

Anisotropic structure property based image reconstruction method for limited-angle computed tomography

Limited-angle computed tomography (CT) may appear in restricted CT scans. Since the available projection data is incomplete, the images reconstructed by filtered back-projection (FBP) or algebraic reconstruction technique (ART) often encounter shading artifacts. However, using the anisotropy property of the shading artifacts that coincide with the characteristic of limited-angle CT images can reduce the shading artifacts. Considering this concept, we combine the anisotropy property of the shading artifacts with the anisotropic structure property of an image to develop a new algorithm for image reconstruction. Specifically, we propose an image reconstruction method based on adaptive weighted anisotropic total variation (AwATV). This method, termed as AwATV method for short, is designed to preserve image structures and then remove the shading artifacts. It characterizes both of above properties. The anisotropy property of the shading artifacts accounts for reducing artifacts, and the anisotropic structure property of an image accounts for preserving structures. In order to evaluate the performance of AwATV, we use the simulation projection data of FORBILD head phantom and real CT data for image reconstruction. Experimental results show that AwATV can always reconstruct images with higher SSIM and PSNR, and smaller RMSE, which means that AwATV enables to reconstruct images with higher quality in term of artifact reduction and structure preservation.

A preconditioned landweber iteration scheme for the limited-angle image reconstruction

BACKGROUND

The limited-angle reconstruction problem is of both theoretical and practical importance. Due to the severe ill-posedness of the problem, it is very challenging to get a valid reconstructed result from the known small limited-angle projection data. The theoretical ill-posedness leads the normal equation AT Ax = AT b of the linear system derived by discretizing the Radon transform to be severely ill-posed, which is quantified as the large condition number of AT A.

OBJECTIVE

To develop and test a new valid algorithm for improving the limited-angle image reconstruction with the known appropriately small angle range from [0,π3]∼[0,π2].

METHODS

We propose a reweighted method of improving the condition number of AT Ax = AT b and the corresponding preconditioned Landweber iteration scheme. The weight means multiplying AT Ax = AT b by a matrix related to AT A, and the weighting process is repeated multiple times. In the experiment, the condition number of the coefficient matrix in the reweighted linear system decreases monotonically to 1 as the weighting times approaches infinity.

RESULTS

The numerical experiments showed that the proposed algorithm is significantly superior to other iterative algorithms (Landweber, Cimmino, NWL-a and AEDS) and can reconstruct a valid image from the known appropriately small angle range.

CONCLUSIONS

The proposed algorithm is effective for the limited-angle reconstruction problem with the known appropriately small angle range.

LoTToR: An Algorithm for Missing-Wedge Correction of the Low-Tilt Tomographic 3D Reconstruction of a Single-Molecule Structure

A single-molecule three-dimensional (3D) structure is essential for understanding the thermal vibrations and dynamics as well as the conformational changes during the chemical reaction of macromolecules. Individual-particle electron tomography (IPET) is an approach for obtaining a snap-shot 3D structure of an individual macromolecule particle by aligning the tilt series of electron tomographic (ET) images of a targeted particle through a focused iterative 3D reconstruction method. The method can reduce the influence on the 3D reconstruction from large-scale image distortion and deformation. Due to the mechanical tilt limitation, 3D reconstruction often contains missing-wedge artifacts, presented as elongation and an anisotropic resolution. Here, we report a post-processing method to correct the missing-wedge artifact. This low-tilt tomographic reconstruction (LoTToR) method contains a model-free iteration process under a set of constraints in real and reciprocal spaces. A proof of concept is conducted by using the LoTToR on a phantom, i.e., a simulated 3D reconstruction from a low-tilt series of images, including that within a tilt range of ±15°. The method is validated by using both negative-staining (NS) and cryo-electron tomography (cryo-ET) experimental data. A significantly reduced missing-wedge artifact verifies the capability of LoTToR, suggesting a new tool to support the future study of macromolecular dynamics, fluctuation and chemical activity from the viewpoint of single-molecule 3D structure determination.

Explorative Imaging and Its Implementation at the FleX-ray Laboratory

In tomographic imaging, the traditional process consists of an expert and an operator collecting data, the expert working on the reconstructed slices and drawing conclusions. The quality of reconstructions depends heavily on the quality of the collected data, except that, in the traditional process of imaging, the expert has very little influence over the acquisition parameters, experimental plan or the collected data. It is often the case that the expert has to draw limited conclusions from the reconstructions, or adapt a research question to data available. This method of imaging is static and sequential, and limits the potential of tomography as a research tool. In this paper, we propose a more dynamic process of imaging where experiments are tailored around a sample or the research question; intermediate reconstructions and analysis are available almost instantaneously, and expert has input at any stage of the process (including during acquisition) to improve acquisition or image reconstruction. Through various applications of 2D, 3D and dynamic 3D imaging at the FleX-ray Laboratory, we present the unexpected journey of exploration a research question undergoes, and the surprising benefits it yields.

poly-DART: A discrete algebraic reconstruction technique for polychromatic X-ray CT

The discrete algebraic reconstruction technique (DART) is a tomographic method to reconstruct images from X-ray projections in which prior knowledge on the number of object materials is exploited. In monochromatic X-ray CT (e.g., synchrotron), DART has been shown to lead to high-quality reconstructions, even with a low number of projections or a limited scanning view. However, most X-ray sources are polychromatic, leading to beam hardening effects, which significantly degrade the performance of DART. In this work, we propose a new discrete tomography algorithm, poly-DART, that exploits sparsity in the attenuation values using DART and simultaneously accounts for the polychromatic nature of the X-ray source. The results show that poly-DART leads to a vastly improved segmentation on polychromatic data obtained from Monte Carlo simulations as well as on experimental data, compared to DART.

K-edge spectral computed tomography with a photon counting detector and discrete reconstruction

X-ray K-Edge Subtraction Computed Tomography (KES-CT) is based on the acquisition of two images at different energies, one below and one above the Kedge of a contrast agent. KES-CT is mainly performed at synchrotron facilities where a tunable monochromatic X-ray beam is available. Thanks to innovative Photon Counting Xray Detectors (PCXDs), it would be desirable to collect the two images in a single shot with a conventional polychromatic Xray spectrum. This approach, sometimes called spectral-CT or color-CT eliminates the risk of misregistration due to motion between consecutive acquisitions and it should allow for scans with much lower doses of contrast medium. Spectral CT is considered very promising but its practical application is being hampered by several practical issues, one of these being the charge sharing affecting the energy resolution of PCXDs. However, latest generations of PCXDs implement hardware solutions to cope with the charge sharing effects, thus allowing sharper color sensitivity. This work presents a K-edge spectral CT imaging preliminary protocol based on the Pixirad-I/PixieIII detector where discrete tomography is used to present the reconstructed slices as color images. Results show that when a solution for the charge sharing issue is considered and refined reconstruction methods are applied, accurate K-edge subtraction imaging with conventional sources can be performed.

Nonconvex image reconstruction via expectation propagation

The problem of efficiently reconstructing tomographic images can be mapped into a Bayesian inference problem over the space of pixels densities. Solutions to this problem are given by pixels assignments that are compatible with tomographic measurements and maximize a posterior probability density. This maximization can be performed with standard local optimization tools when the log-posterior is a convex function, but it is generally intractable when introducing realistic nonconcave priors that reflect typical images features such as smoothness or sharpness. We introduce a new method to reconstruct images obtained from Radon projections by using expectation propagation, which allows us to approximate the intractable posterior. We show, by means of extensive simulations, that, compared to state-of-the-art algorithms for this task, expectation propagation paired with very simple but non-log-concave priors is often able to reconstruct images up to a smaller error while using a lower amount of information per pixel. We provide estimates for the critical rate of information per pixel above which recovery is error-free by means of simulations on ensembles of phantom and real images.

A Multichannel Cross-Modal Fusion Framework for Electron Tomography

In this paper, we present a multichannel cross-modal fusion algorithm to combine two complementary modalities in electron tomography: X-ray spectroscopy and scanning transmission electron microscopy (STEM). The former reveals compositions with high elemental specificity but low signal-to-noise ratio (SNR), while the latter characterizes the structure with high SNR but little chemical information. We use a multivariate regression to build a cross-modal fusion framework for these two modalities to simultaneously achieve high elemental specificity and high SNR for a target element chosen from the sample under study. Specifically, we first compute three-dimensional tomograms from tilt-series datasets of X-ray and STEM using different reconstruction algorithms. Then, we generate many feature images from each tomogram. Finally, we adopt partial least squares regression to assess the connection between these feature images and the reconstruction of the target element. Based on the simulated and experimental datasets of semiconductor devices, we demonstrate that our algorithm can not only produce continuous edges, homogeneous foreground, and clean background in its element-specific reconstructions but also can more accurately preserve fine structures than state-of-the-art tomography techniques. Moreover, we show that it can deliver results with high fidelity even for X-ray datasets with limited tilts or low counts. This property is highly desired in the semiconductor industry where acquisition time and sample damage are essential.

Electron Tomography: A Unique Tool Solving Intricate Hollow Nanostructures

Innovations in nanofabrication have expedited advances in hollow-structured nanomaterials with increasing complexity, which, at the same time, set challenges for the precise determination of their intriguing and complicated 3D configurations. Conventional transmission electron microscopy (TEM) analysis typically yields 2D projections of 3D objects, which in some cases is insufficient to reflect the genuine architectures of these 3D nano-objects, providing misleading information. Advanced analytical approaches such as focused ion beam (FIB) and ultramicrotomy enable the real slicing of nanomaterials, realizing the direct observation of inner structures but with limited spatial discrimination. Electron tomography (ET) is a technique that retrieves spatial information from a series of 2D electron projections at different tilt angles. As a unique and powerful tool kit, this technique has experienced great advances in its application in materials science, resolving the intricate 3D nanostructures. Here, the exceptional capability of the ET technique in the structural, chemical, and quantitative analysis of hollow-structured nanomaterials is discussed in detail. The distinct information derived from ET analysis is highlighted and compared with conventional analysis methods. Along with the advances in microscopy technologies, the state-of-the-art ET technique offers great opportunities and promise in the development of hollow nanomaterials.

Optimal binary representation via non-convex optimization on tomographic displays

There have been many recent developments in 3D display technology to provide correct accommodation cues over an extended focus range. To this end, those displays rely on scene decomposition algorithms to reproduce accurate occlusion boundaries as well asretinal defocus blur. Recently, tomographic displays have been proposed with improved trade-offs of focus range, spatial resolution, and exit-pupil. The advantage of the system partly stems from a high-speed backlight modulation system based on a digital micromirror device, which only supports 1-bit images. However, its inherent binary constraint hinders achieving the optimal scene decomposition, thus leaving boundary artifacts. In this work, we present a technique for synthesizing optimal imagery of general 3D scenes with occlusion on tomographic displays. Requiring no prior knowledge of the scene geometry, our technique addresses the blending issue via non-convex optimization, inspired by recent studies in discrete tomography. Also, we present a general framework for this rendering algorithm and demonstrate the utility of the technique for volumetric display systems with binary representation.

On-the-Fly Machine Learning for Improving Image Resolution in Tomography

In tomography, the resolution of the reconstructed 3D volume is inherently limited by the pixel resolution of the detector and optical phenomena. Machine learning has demonstrated powerful capabilities for super-resolution in several imaging applications. Such methods typically rely on the availability of high-quality training data for a series of similar objects. In many applications of tomography, existing machine learning methods cannot be used because scanning such a series of similar objects is either impossible or infeasible. In this paper, we propose a novel technique for improving the resolution of tomographic volumes that is based on the assumption that the local structure is similar throughout the object. Therefore, our approach does not require a training set of similar objects. The technique combines a specially designed scanning procedure with a machine learning method for super-resolution imaging. We demonstrate the effectiveness of our approach using both simulated and experimental data. The results show that the proposed method is able to significantly improve resolution of tomographic reconstructions.

A modified discrete tomography for improving the reconstruction of unknown multi-gray-level material in the `missing wedge' situation

Full angular rotational projections cannot always be acquired in tomographic reconstructions because of the limited space in the experimental setup, leading to the `missing wedge' situation. In this paper, a recovering `missing wedge' discrete algebraic reconstruction technique algorithm (rmwDART) has been proposed to solve the `missing wedge' problem and improve the quality of the three-dimensional reconstruction without prior knowledge of the material component's number or the material's values. By using oversegmentation, boundary extraction and mathematical morphological operations, `missing wedge' artifact areas can be located. Then, in the iteration process, by updating the located areas and regions, high-quality reconstructions can be obtained from the simulations, and the reconstructed images based on the rmwDART algorithm can be obtained from soft X-ray nano-computed tomography experiments. The results showed that there is the potential for discrete tomography.

Iterative and discrete reconstruction in the evaluation of the rabbit model of osteoarthritis

Micro-computed tomography (µCT) is a standard method for bone morphometric evaluation. However, the scan time can be long and the radiation dose during the scan may have adverse effects on test subjects, therefore both of them should be minimized. This could be achieved by applying iterative reconstruction (IR) on sparse projection data, as IR is capable of producing reconstructions of sufficient image quality with less projection data than the traditional algorithm requires. In this work, the performance of three IR algorithms was assessed for quantitative bone imaging from low-resolution data in the evaluation of the rabbit model of osteoarthritis. Subchondral bone images were reconstructed with a conjugate gradient least squares algorithm, a total variation regularization scheme, and a discrete algebraic reconstruction technique to obtain quantitative bone morphometry, and the results obtained in this manner were compared with those obtained from the reference reconstruction. Our approaches were sufficient to identify changes in bone structure in early osteoarthritis, and these changes were preserved even when minimal data were provided for the reconstruction. Thus, our results suggest that IR algorithms give reliable performance with sparse projection data, thereby recommending them for use in µCT studies where time and radiation exposure are preferably minimized.

Dynamic Tomographic Reconstruction of Deforming Volumes

The motion of a sample while being scanned in a tomograph prevents its proper volume reconstruction. In the present study, a procedure is proposed that aims at estimating both the kinematics of the sample and its standard 3D imaging from a standard acquisition protocol (no more projection than for a rigid specimen). The proposed procedure is a staggered two-step algorithm where the volume is first reconstructed using a “Dynamic Reconstruction” technique, a variant of Algebraic Reconstruction Technique (ART) compensating for a “frozen” determination of the motion, followed by a Projection-based Digital Volume Correlation (P-DVC) algorithm that estimates the space/time displacement field, with a “frozen” microstructure and shape of the sample. Additionally, this procedure is combined with a multi-scale approach that is essential for a proper separation between motion and microstructure. A proof-of-concept of the validity and performance of this approach is proposed based on two virtual examples. The studied cases involve a small number of projections, large strains, up to 25%, and noise.

Edge information diffusion based reconstruction (EIDR) for cone beam computed laminography

Computed laminography (CL) is a prospective nondestructive testing technique for flat object inspection in industrial applications. However, CL image reconstruction is a challenging task because incomplete projection data are acquired from the CL scan. When a conventional computed tomography (CT) reconstruction method is applied to cone beam CL data, the vertical edges (singularities in the z-direction) in the reconstructed image would be blurred. On the contrary, the horizontal edges (singularities within slices) can be quite accurately reconstructed. Based on this key observation, an edge information diffusion method is developed, which fixes the horizontal edges and propagates their values within the slices. An effective CL reconstruction method is then proposed for flat object inspection by combining the edge information diffusion procedure, which plays the role of regularization, with conventional CT image reconstruction algorithms. Experiments on both simulated data and real data are performed to verify the effectiveness of the proposed method. The results show that the proposed method can effectively suppress the inter-slice aliasing and blurring caused by incompleteness of the CL scan data, and that it outperforms other state-of-the-art methods.

Progress towards a methodology for high throughput 3D reconstruction of soot nanoparticles via electron tomography

The aim of this work is to make progress towards the development of 3D reconstruction as a legitimate alternative to traditional 2D characterization of soot. Time constraints are the greatest opposition to its implementation, as currently reconstruction of a single soot particle takes around 5-6 h to complete. As such, the accuracy and detail gains are currently insufficient to challenge 2D characterization of a representative sample (e.g. 200 particles). This work is a consideration of the optimization of the steps included within the computational reconstruction and manual segmentation of soot particles. Our optimal process reduced the time required by over 70% in comparison to a typical procedure, whilst producing models with no appreciable decrease in quality.

Discrete tomography in an in vivo small animal bone study

This study aimed at assessing the feasibility of a discrete algebraic reconstruction technique (DART) to be used in in vivo small animal bone studies. The advantage of discrete tomography is the possibility to reduce the amount of X-ray projection images, which makes scans faster and implies also a significant reduction of radiation dose, without compromising the reconstruction results. Bone studies are ideal for being performed with discrete tomography, due to the relatively small number of attenuation coefficients contained in the image [namely three: background (air), soft tissue and bone]. In this paper, a validation is made by comparing trabecular bone morphometric parameters calculated from images obtained by using DART and the commonly used standard filtered back-projection (FBP). Female rats were divided into an ovariectomized (OVX) and a sham-operated group. In vivo micro-CT scanning of the tibia was done at baseline and at 2, 4, 8 and 12 weeks after surgery. The cross-section images were reconstructed using first the full set of projection images and afterwards reducing them in number to a quarter and one-sixth (248, 62, 42 projection images, respectively). For both reconstruction methods, similar changes in morphometric parameters were observed over time: bone loss for OVX and bone growth for sham-operated rats, although for DART the actual values were systematically higher (bone volume fraction) or lower (structure model index) compared to FBP, depending on the morphometric parameter. The DART algorithm was, however, more robust when using fewer projection images, where the standard FBP reconstruction was more prone to noise, showing a significantly bigger deviation from the morphometric parameters obtained using all projection images. This study supports the use of DART as a potential alternative method to FBP in X-ray micro-CT animal studies, in particular, when the number of projections has to be drastically minimized, which directly reduces scanning time and dose.

ICON-MIC: Implementing a CPU/MIC Collaboration Parallel Framework for ICON on Tianhe-2 Supercomputer

Electron tomography (ET) is an important technique for studying the three-dimensional structures of the biological ultrastructure. Recently, ET has reached sub-nanometer resolution for investigating the native and conformational dynamics of macromolecular complexes by combining with the sub-tomogram averaging approach. Due to the limited sampling angles, ET reconstruction typically suffers from the "missing wedge" problem. Using a validation procedure, iterative compressed-sensing optimized nonuniform fast Fourier transform (NUFFT) reconstruction (ICON) demonstrates its power in restoring validated missing information for a low-signal-to-noise ratio biological ET dataset. However, the huge computational demand has become a bottleneck for the application of ICON. In this work, we implemented a parallel acceleration technology ICON-many integrated core (MIC) on Xeon Phi cards to address the huge computational demand of ICON. During this step, we parallelize the element-wise matrix operations and use the efficient summation of a matrix to reduce the cost of matrix computation. We also developed parallel versions of NUFFT on MIC to achieve a high acceleration of ICON by using more efficient fast Fourier transform (FFT) calculation. We then proposed a hybrid task allocation strategy (two-level load balancing) to improve the overall performance of ICON-MIC by making full use of the idle resources on Tianhe-2 supercomputer. Experimental results using two different datasets show that ICON-MIC has high accuracy in biological specimens under different noise levels and a significant acceleration, up to 13.3 × , compared with the CPU version. Further, ICON-MIC has good scalability efficiency and overall performance on Tianhe-2 supercomputer.

A Survey of the Use of Iterative Reconstruction Algorithms in Electron Microscopy

One of the key steps in Electron Microscopy is the tomographic reconstruction of a three-dimensional (3D) map of the specimen being studied from a set of two-dimensional (2D) projections acquired at the microscope. This tomographic reconstruction may be performed with different reconstruction algorithms that can be grouped into several large families: direct Fourier inversion methods, back-projection methods, Radon methods, or iterative algorithms. In this review, we focus on the latter family of algorithms, explaining the mathematical rationale behind the different algorithms in this family as they have been introduced in the field of Electron Microscopy. We cover their use in Single Particle Analysis (SPA) as well as in Electron Tomography (ET).

Accelerating electron tomography reconstruction algorithm ICON with GPU

Electron tomography (ET) plays an important role in studying in situ cell ultrastructure in three-dimensional space. Due to limited tilt angles, ET reconstruction always suffers from the "missing wedge" problem. With a validation procedure, iterative compressed-sensing optimized NUFFT reconstruction (ICON) demonstrates its power in the restoration of validated missing information for low SNR biological ET dataset. However, the huge computational demand has become a major problem for the application of ICON. In this work, we analyzed the framework of ICON and classified the operations of major steps of ICON reconstruction into three types. Accordingly, we designed parallel strategies and implemented them on graphics processing units (GPU) to generate a parallel program ICON-GPU. With high accuracy, ICON-GPU has a great acceleration compared to its CPU version, up to 83.7×, greatly relieving ICON's dependence on computing resource.

Statistical characterization of noise for spatial standardization of CT scans: Enabling comparison with multiple kernels and doses

Computerized tomography (CT) is a widely adopted modality for analyzing directly or indirectly functional, biological and morphological processes by means of the image characteristics. However, the potential utilization of the information obtained from CT images is often limited when considering the analysis of quantitative information involving different devices, acquisition protocols or reconstruction algorithms. Although CT scanners are calibrated as a part of the imaging workflow, the calibration is circumscribed to global reference values and does not circumvent problems that are inherent to the imaging modality. One of them is the lack of noise stationarity, which makes quantitative biomarkers extracted from the images less robust and stable. Some methodologies have been proposed for the assessment of non-stationary noise in reconstructed CT scans. However, those methods focused on the non-stationarity only due to the reconstruction geometry and are mainly based on the propagation of the variance of noise throughout the whole reconstruction process. Additionally, the philosophy followed in the state-of-the-art methods is based on the reduction of noise, but not in the standardization of it. This means that, even if the noise is reduced, the statistics of the signal remain non-stationary, which is insufficient to enable comparisons between different acquisitions with different statistical characteristics. In this work, we propose a statistical characterization of noise in reconstructed CT scans that leads to a versatile statistical model that effectively characterizes different doses, reconstruction kernels, and devices. The statistical model is generalized to deal with the partial volume effect via a localized mixture model that also describes the non-stationarity of noise. Finally, we propose a stabilization scheme to achieve stationary variance. The validation of the proposed methodology was performed with a physical phantom and clinical CT scans acquired with different configurations (kernels, doses, algorithms including iterative reconstruction). The results confirmed its suitability to enable comparisons with different doses, and acquisition protocols.

Partial Discreteness: A Novel Prior for Magnetic Resonance Image Reconstruction

An important factor influencing the quality of magnetic resonance (MR) images is the reconstruction method that is employed, and specifically, the type of prior knowledge that is exploited during reconstruction. In this work, we introduce a new type of prior knowledge, partial discreteness (PD), where a small number of regions in the image are assumed to be homogeneous and can be well represented by a constant magnitude. In particular, we mathematically formalize the partial discreteness property based on a Gaussian Mixture Model (GMM) and derive a partial discreteness image representation that characterizes the salient features of partially discrete images: a constant intensity in homogeneous areas and texture in heterogeneous areas. The partial discreteness representation is then used to construct a novel prior dedicated to the reconstruction of partially discrete MR images. The strength of the proposed prior is demonstrated on various simulated and real k-space data-based experiments with partially discrete images. Results demonstrate that the PD algorithm performs competitively with state-of-the-art reconstruction methods, being flexible and easy to implement.

SHAPE BASED IMAGE RECONSTRUCTION USING LINEARIZED DEFORMATIONS

We introduce a reconstruction framework that can account for shape related a priori information in ill-posed linear inverse problems in imaging. It is a variational scheme that uses a shape functional defined using deformable templates machinery from shape theory. As proof of concept, we apply the proposed shape based reconstruction to 2D tomography with very sparse measurements, and demonstrate strong empirical results.

Trace: a high-throughput tomographic reconstruction engine for large-scale datasets

BACKGROUND

Modern synchrotron light sources and detectors produce data at such scale and complexity that large-scale computation is required to unleash their full power. One of the widely used imaging techniques that generates data at tens of gigabytes per second is computed tomography (CT). Although CT experiments result in rapid data generation, the analysis and reconstruction of the collected data may require hours or even days of computation time with a medium-sized workstation, which hinders the scientific progress that relies on the results of analysis.

METHODS

We present Trace, a data-intensive computing engine that we have developed to enable high-performance implementation of iterative tomographic reconstruction algorithms for parallel computers. Trace provides fine-grained reconstruction of tomography datasets using both (thread-level) shared memory and (process-level) distributed memory parallelization. Trace utilizes a special data structure called replicated reconstruction object to maximize application performance. We also present the optimizations that we apply to the replicated reconstruction objects and evaluate them using tomography datasets collected at the Advanced Photon Source.

RESULTS

Our experimental evaluations show that our optimizations and parallelization techniques can provide 158× speedup using 32 compute nodes (384 cores) over a single-core configuration and decrease the end-to-end processing time of a large sinogram (with 4501 × 1 × 22,400 dimensions) from 12.5 h to <5 min per iteration.

CONCLUSION

The proposed tomographic reconstruction engine can efficiently process large-scale tomographic data using many compute nodes and minimize reconstruction times.

Recovering fine details from under-resolved electron tomography data using higher order total variation ℓ1 regularization

Over the last decade or so, reconstruction methods using ℓ₁ regularization, often categorized as compressed sensing (CS) algorithms, have significantly improved the capabilities of high fidelity imaging in electron tomography. The most popular ℓ₁ regularization approach within electron tomography has been total variation (TV) regularization. In addition to reducing unwanted noise, TV regularization encourages a piecewise constant solution with sparse boundary regions. In this paper we propose an alternative ℓ₁ regularization approach for electron tomography based on higher order total variation (HOTV). Like TV, the HOTV approach promotes solutions with sparse boundary regions. In smooth regions however, the solution is not limited to piecewise constant behavior. We demonstrate that this allows for more accurate reconstruction of a broader class of images - even those for which TV was designed for - particularly when dealing with pragmatic tomographic sampling patterns and very fine image features. We develop results for an electron tomography data set as well as a phantom example, and we also make comparisons with discrete tomography approaches.

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.