Evelina Ametova

Spectral computed tomography has received considerable interest in recent years since spectral measurements contain much richer information about the object of interest. In spectral computed tomography, we are interested in the energy channel-wise reconstructions of the object. However, such reconstructions suffer from a low signal-to-noise ratio and share the challenges of conventional low-dose computed tomography such as ring artifacts. Ring artifacts arise from errors in the flat fields and can significantly degrade the quality of the reconstruction. We propose an extended flat-field model that exploits high correlation in the spectral flat fields to reduce ring artifacts in channel-wise reconstructions. The extended model relies on the assumption that the spectral flat fields can be well-approximated by a low-rank matrix. Our proposed model works directly on the spectral flat fields and can be combined with any existing reconstruction model, e.g. filtered back projection and iterative methods. The proposed model is validated on a neutron data set. The results show that our method successfully diminishes ring artifacts and improves the quality of the reconstructions. Moreover, the results indicate that our method is robust; it only needs a single spectral flat-field image, whereas existing methods need multiple spectral flat-field images to reach a similar level of ring reduction.

Point by point strain scanning is often used to map the residual stress (strain) in engineering materials and components. However, the gauge volume and, hence, spatial resolution are limited by the beam defining apertures and can be anisotropic for very low and high diffraction (scattering) angles. Alternatively, wavelength resolved neutron transmission imaging has a potential to retrieve information tomographically about residual strain induced within materials through measurement in transmission of Bragg edges—crystallographic fingerprints whose locations and shapes depend on microstructure and strain distribution. In such a case, the spatial resolution is determined by the geometrical blurring of the measurement setup and the detector point spread function. Mathematically, reconstruction of the strain tensor field is described by the longitudinal ray transform; this transform has a non-trivial null-space, making direct inversion impossible. A combination of the longitudinal ray transform with physical constraints was used to reconstruct strain tensor fields in convex objects. To relax physical constraints and generalize reconstruction, a recently introduced concept of histogram tomography can be employed. Histogram tomography relies on our ability to resolve the distribution of strain in the beam direction, as we discuss in the paper. More specifically, Bragg edge strain tomography requires extraction of the second moment (variance about zero) of the strain distribution, which has not yet been demonstrated in practice. In this paper, we verify experimentally that the second moment can be reliably measured for a previously well characterized aluminum ring and plug sample. We compare experimental measurements against numerical calculation and further support our conclusions by rigorous uncertainty quantification of the estimated mean and variance of the strain distribution.

We present a concept for propagating uncertainty in x-ray computed tomography (CT) using a Monte Carlo reconstruction (MCR) technique, comprising repeated reconstructions with varying input parameters. The proposed technique follows the framework for model-based x-ray CT uncertainty assessment per the Monte Carlo method (JCGM 101), although it provides several advantages over the conventional implementation, which relies on simulating all individual steps in the x-ray CT measurement procedure and is therefore considered to be impractical due to its high computational demand. The proposed method requires only a single set of simulated projections. For each Monte Carlo trial, the instrument geometrical parameters in a filtered back projection reconstruction algorithm are randomly sampled from specified uncertainty distributions. The output is a four-dimensional volumetric model where each voxel, defined by its three-dimensional indices, is represented by a distribution of reconstructed gray values. We reduce the four-dimensional volumetric model to three single-gray-value voxel models by calculating descriptive statistics: a voxel-wise lower gray value confidence limit, a central gray value, and an upper gray value confidence limit. Bi-directional length measurements performed on the surfaces determined from each single-gray-value model provide insight into the effect of uncertainty in the instrument geometry. The proposed approach requires significantly fewer computations and data storage per Monte Carlo trial and provides a straightforward way to relate uncertainties in reconstructed gray values to uncertainties in subsequent dimensional measurements. This, in turn, facilitates the practical application of the Monte Carlo method in x-ray CT. We implement MCR to determine uncertainty distributions in the simulated x-ray CT measurement of a simple cube and an impeller due to uncertainties in the instrument geometry. Possible extension of MCR to other sources of uncertainty in the x-ray CT measurement process is discussed.

The newly developed core imaging library (CIL) is a flexible plug and play library for tomographic imaging with a specific focus on iterative reconstruction. CIL provides building blocks for tailored regularized reconstruction algorithms and explicitly supports multichannel tomographic data. In the first part of this two-part publication, we introduced the fundamentals of CIL. This paper focuses on applications of CIL for multichannel data, e.g. dynamic and spectral. We formalize different optimization problems for colour processing, dynamic and hyperspectral tomography and demonstrate CIL’s capabilities for designing state-of-the-art reconstruction methods through case studies and code snapshots. This article is part of the theme issue ‘Synergistic tomographic image reconstruction: part 2’.

We present the Core Imaging Library (CIL), an open-source Python framework for tomographic imaging with particular emphasis on reconstruction of challenging datasets. Conventional filtered back-projection reconstruction tends to be insufficient for highly noisy, incomplete, non-standard or multi-channel data arising for example in dynamic, spectral and in situ tomography. CIL provides an extensive modular optimization framework for prototyping reconstruction methods including sparsity and total variation regularization, as well as tools for loading, preprocessing and visualizing tomographic data. The capabilities of CIL are demonstrated on a synchrotron example dataset and three challenging cases spanning golden-ratio neutron tomography, cone-beam X-ray laminography and positron emission tomography. This article is part of the theme issue ‘Synergistic tomographic image reconstruction: part 2’.

Long synonymous with medical imaging, x-ray computed tomography (CT) is proving its worth in industrial applications such as material characterization, defect analysis, and dimensional inspection e.g. of manufactured components. Since 2005, when the first purpose-built industrial x-ray CT instrument was made commercially available, there have been significant efforts to understand just how reliable x-ray CT dimensional measurements are. In metrology, the ultimate measure of confidence is metrological traceability—a clearly-defined but often not well-understood property of a measurement result. Metrological traceability places measurements on a comparable scale and provides a quantitative indication of measurement quality in the form of an uncertainty statement. From a practical perspective, achieving traceability can be divided into two tasks: (a) ensuring traceability of the scale with which the measurements are made and (b) assessing uncertainty in the resulting quantity assigned to the measurand. Based on this breakdown of the traceability problem, we provide a high-level discussion about traceability of x-ray CT dimensional measurements, review relevant work in understanding x-ray CT measurement uncertainty, and propose a framework for model-based uncertainty assessment per the Monte Carlo Simulation method and instrument scale calibration as a unified approach to traceability.

Time-of-flight (ToF) neutron imaging offers complementary attenuation contrast to x-ray computed tomography, coupled with the ability to extract additional information from the variation in attenuation as a function of neutron energy (ToF) at every point (voxel) in the image. In particular, Bragg edge positions provide crystallographic information and therefore enable the identification of crystalline phases directly. Here we demonstrate Bragg edge tomography with high spatial and spectral resolution. We propose a new iterative tomographic reconstruction method with a tailored regularisation term to achieve high quality reconstruction from low-count data, where conventional filtered back-projection (FBP) fails. The regularisation acts in a separated mode for spatial and spectral dimensions and favours characteristic piece-wise constant and piece-wise smooth behaviour in the respective dimensions. The proposed method is compared against FBP and a state-of-the-art regulariser for multi-channel tomography on a multi-material phantom. The proposed new regulariser which accommodates specific image properties outperforms both conventional and state-of-the-art methods and therefore facilitates Bragg edge fitting at the voxel level. The proposed method requires significantly shorter exposures to retrieve features of interest. This in turn facilitates more efficient usage of expensive neutron beamline time and enables the full utilisation of state-of-the-art high resolution detectors.

The newly developed Core Imaging Library (CIL) is a flexible plug and play library for tomographic imaging with a specific focus on iterative reconstruction. CIL provides building blocks for tailored regularised reconstruction algorithms and explicitly supports multichannel tomographic data. In the first part of this two-part publication, we introduced the fundamentals of CIL. This paper focuses on applications of CIL for multichannel data, e.g., dynamic and spectral. We formalise different optimisation problems for colour processing, dynamic and hyperspectral tomography and demonstrate CIL's capabilities for designing state of the art reconstruction methods through case studies and code snapshots.

We present the Core Imaging Library (CIL), an open-source Python framework for tomographic imaging with particular emphasis on reconstruction of challenging datasets. Conventional filtered back-projection reconstruction tends to be insufficient for highly noisy, incomplete, non-standard or multi-channel data arising for example in dynamic, spectral and in situ tomography. CIL provides an extensive modular optimisation framework for prototyping reconstruction methods including sparsity and total variation regularisation, as well as tools for loading, preprocessing and visualising tomographic data. The capabilities of CIL are demonstrated on a synchrotron example dataset and three challenging cases spanning golden-ratio neutron tomography, cone-beam X-ray laminography and positron emission tomography.

Synchrotron X-ray imaging is a powerful method to investigate internal structures down to the micro and nanoscopic scale. Fast cameras recording thousands of frames per second allow time-resolved studies with a high temporal resolution. Fast image reconstruction is essential to provide the synchrotron instrumentation with the imaging information required to track and control the process under study. Traditionally Filtered Back Projection algorithm is used for tomographic reconstruction. In this article, we discuss how to implement the algorithm on nowadays GPGPU architectures efficiently. The key is to achieve balanced utilization of available GPU subsystems. We present two highly optimized algorithms to perform back projection on parallel hardware. One is relying on the texture engine to perform reconstruction, while another one utilizes the Core computational units of the GPU. Both methods outperform current state-of-the-art techniques found in the standard reconstructions codes significantly. Finally, we propose a hybrid approach combining both algorithms to better balance load between G PU subsystems. It further boosts the performance by about 30 % on NVIDIA Pascal micro-architecture.