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We introduce a stochastic framework into the open--source Core Imaging Library (CIL) which enables easy development of stochastic algorithms. Five such algorithms from the literature are developed, Stochastic Gradient Descent, Stochastic Average Gradient (-Am\'elior\'e), (Loopless) Stochastic Variance Reduced Gradient. We showcase the functionality of the framework with a comparative study against a deterministic algorithm on a simulated 2D PET dataset, with the use of the open-source Synergistic Image Reconstruction Framework. We observe that stochastic optimisation methods can converge in fewer passes of the data than a standard deterministic algorithm.

This article presents the algorithms developed by the Core Imaging Library (CIL) developer team for the Helsinki Tomography Challenge 2022. The challenge focused on reconstructing 2D phantom shapes from limited-angle computed tomography (CT) data. The CIL team designed and implemented five reconstruction methods using CIL (https://ccpi.ac.uk/cil/), an open-source Python package for tomographic imaging. The CIL team adopted a model-based reconstruction strategy, unique to this challenge with all other teams relying on deep-learning techniques. The CIL algorithms showcased exceptional performance, with one algorithm securing the third place in the competition. The best-performing algorithm employed careful CT data pre-processing and an optimization problem with single-sided directional total variation regularization combined with isotropic total variation and tailored lower and upper bounds. The reconstructions and segmentations achieved high quality for data with angular ranges down to 50 degrees, and in some cases acceptable performance even at 40 and 30 degrees. This study highlights the effectiveness of model-based approaches in limited-angle tomography and emphasizes the importance of proper algorithmic design leveraging on available prior knowledge to overcome data limitations. Finally, this study highlights the flexibility of CIL for prototyping and comparison of different optimization methods., Comment: 20 pages, 14 figures

Here we apply hyperspectral bright field imaging to collect computed tomographic images with excellent energy resolution (800 eV), applying it for the first time to map the distribution of stain in a fixed biological sample through its characteristic K-edge. Conventionally, because the photons detected at each pixel are distributed across as many as 200 energy channels, energy-selective images are characterised by low count-rates and poor signal-to-noise ratio. This means high X-ray exposures, long scan times and high doses are required to image unique spectral markers. Here, we achieve high quality energy-dispersive tomograms from low dose, noisy datasets using a dedicated iterative reconstruction algorithm. This exploits the spatial smoothness and inter-channel structural correlation in the spectral domain using two carefully chosen regularisation terms. For a multi-phase phantom, a reduction in scan time of 36 times is demonstrated. Spectral analysis methods including K-edge subtraction and absorption step-size fitting are evaluated for an ex vivo, single (iodine)-stained biological sample, where low chemical concentration and inhomogeneous distribution can affect soft tissue segmentation and visualisation. The reconstruction algorithms are available through the open-source Core Imaging Library. Taken together, these tools offer new capabilities for visualisation and elemental mapping, with promising applications for multiply-stained biological specimens., Comment: 13 pages, 5 figures

Time-of-flight neutron imaging offers complementary attenuation contrast to X-ray computed tomography (CT), coupled with the ability to extract additional information from the variation in attenuation as a function of neutron energy (time of flight) 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 exposure 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., Comment: 22 pages, 11 figures

We present evidence of 1D S=1/2 anisotropic XY ferromagnetism in the paramagnetic phase of the cyanido-bridged chain complex [Tb(pzam)3(H2O)M(CN)8]H2O, with M=W(V), based upon the measurement of the specific heat, the uniform susceptibility and the magnetization curve on a powder sample. Both the specific heat and the susceptibility exhibit a transition peak to long-range ferromagnetism, mediated by the residual interchain couplings, at a critical temperature Tc=1.15 K. Yet in the temperature range T > Tc the specific heat exhibits a broad Schottky anomaly which can be very well fitted by the exact result for the 1D S=1/2 XY model with strong anisotropy in the XY plane (Jx = 1.89 K, Jy=2Jx). For the analysis of the susceptibility and magnetization, not directly accessible theoretically via the exact solution of the XY model, we resort to numerically exact quantum Monte Carlo simulations. Very good agreement is found between the powder-sample data and the Monte Carlo data using an effective average g-factor., Comment: 6 pages, 6 figures, journal paper