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 modelbased 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.

Positron emission tomography (PET) provides quantitative functional imaging of biomarkers unavailable in other modalities, however, images are of relatively low resolution compared to modalities such as magnetic resonance imaging (MRI). A typical approach is to reconstruct to a higher resolution and regularize using a structural image, but there are practical limitations to this approach. Alternatively, post-reconstruction approaches involve image-based correction, but typically rely on a segmentation which may be difficult or even ambiguous to find, depending on the anatomical region or deformities. Here, we perform super-resolution by utilising iterative deconvolution, regularized by minimizing shared directional total variation (dTV) with an anatomical MRI image. We present results on synthetic and clinical data. For the former, PET acquisitions were simulated using an analytic PET simulation. The Gaussian blurring model parameters for deconvolution were optimized on a simplistic phantom simulation with a total variation prior. This model was then applied to deconvolve realistic synthetic data using dTV, which was synthesized to include PET-unique lesions. The model was also applied to a single 18F-florbetaben study acquired over 10 minutes. Gray matter-white matter contrast increased using dTV compared with baseline, however, where an accurate segmentation is available, traditional partial volume correction techniques are superior. Hence, dTV-regularised deconvolution can perform PVC and super-resolution in situations where a reliable segmentation cannot be achieved. With appropriate hyper-parameter selection, dTV deconvolution can preserve PET-unique features.

We introduce a method for fast estimation of data-adapted, spatio-temporally dependent regularization parameter-maps for variational image reconstruction, focusing on total variation (TV)-minimization. Our approach is inspired by recent developments in algorithm unrolling using deep neural networks (NNs), and relies on two distinct sub-networks. T he first sub-network estimates the regularization parameter-map from the input data. The second sub-network unrolls T iterations of an iterative algorithm which approximately solves the corresponding TV-minimization problem incorporating the previously estimated regularization parameter-map. The overall network is trained end-to-end in a supervised learning fashion using pairs of clean-corrupted data but crucially without the need of having access to labels for the optimal regularization parameter-maps. We prove consistency of the unrolled scheme by showing that the unrolled energy functional used for the supervised learning Γ-converges as T tends to infinity, to the corresponding functional that incorporates the exact solution map of the TV-minimization problem. We apply and evaluate our method on a variety of large scale and dynamic imaging problems in which the automatic computation of such parameters has been so far challenging: 2D dynamic cardiac MRI reconstruction, quantitative brain MRI reconstruction, low-dose CT and dynamic image denoising. The proposed method consistently improves the TV-reconstructions using scalar parameters and the obtained parameter-maps adapt well to each imaging problem and data by leading to the preservation of detailed features. Although the choice of the regularization parameter-maps is data-driven and based on NNs, the proposed algorithm is entirely interpretable since it inherits the properties of the respective iterative reconstruction method from which the network is implicitly defined.

SIRF is a powerful PET/MR image reconstruction research tool for processing data and developing new algorithms. In this research, new developments to SIRF are presented, with focus on motion estimation and correction. SIRF’s recent inclusion of the adjoint of the resampling operator allows gradient propagation through resampling, enabling the MCIR technique. Another enhancement enabled registering and resampling of complex images, suitable for MRI. Furthermore, SIRF’s integration with the optimization library CIL enables the use of novel algorithms. Finally, SPM is now supported, in addition to NiftyReg, for registration. Results of MR and PET MCIR reconstructions are presented, using FISTA and PDHG, respectively. These demonstrate the advantages of incorporating motion correction and variational and structural priors.

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.

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.

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.

Here we apply hyperspectral bright field imaging to collect computed tomographic images with excellent energy resolution (  1 keV), 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.

We are interested in a spatial-temporal variational model for image sequences. The model involves a fitting data term adapted to different modalities, such as denoising, deblurring, or emission tomography. The regularizing term acts as an infimal-convolution type operator that takes into account the respective influence of space and time variables in a separate mode. We give existence and uniqueness results and provide optimality conditions via duality analysis.

The aim of this paper is to test and analyse a novel technique for image reconstruction in positron emission tomography, which is based on (total variation) regularization on both the image space and the projection space. We formulate our variational problem considering both total variation penalty terms on the image and on an idealized sinogram to be reconstructed from a given Poisson distributed noisy sinogram. We prove existence, uniqueness and stability results for the proposed model and provide some analytical insight into the structures favoured by joint regularization. For the numerical solution of the corresponding discretized problem we employ the split Bregman algorithm and extensively test the approach in comparison to standard total variation regularization on the image. The numerical results show that an additional penalty on the sinogram performs better on reconstructing images with thin structures.

The aim of this paper is to test and analyse a novel technique for image reconstruction in positron emission tomography, which is based on (total variation) regularization on both the image space and the projection space. We formulate our variational problem considering both total variation penalty terms on the image and on an idealized sinogram to be reconstructed from a given Poisson distributed noisy sinogram. We prove existence, uniqueness and stability results for the proposed model and provide some analytical insight into the structures favoured by joint regularization. For the numerical solution of the corresponding discretized problem we employ the split Bregman algorithm and extensively test the approach in comparison to standard total variation regularization on the image. The numerical results show that an additional penalty on the sinogram performs better on reconstructing images with thin structures.

We propose a method for fast and automatic estimation of spatially dependent regularization maps for total variation-based (TV) tomography reconstruction. The estimation is based on two distinct sub-networks, with the first sub-network estimating theregularization parameter-map from the input data while the second one unrolling T iterations of the Primal-Dual Three-Operator Split-ting (PD3O) algorithm. The latter approximately solves the corresponding TV-minimization problem incorporating the previously estimated regularization parameter-map. The overall network is then trained end-to-end in a supervised learning fashion using pairs of clean-corrupted data but crucially without the need of havingaccess to labels for the optimal regularization parameter-maps.

We propose a method for estimating spatio–temporal regularization parameter-maps to be used for dynamic cardiac MRI image reconstruction using total variation TV-minimization. Based on recent developments in algorithm un–rolling using Neural Networks (NNs), our approach uses two sub–networks. The first one predicts a spatio-temporal regularization parameter-map from an input image. Then, a second sub-network approximately solves a TV–reconstruction problem which is formulated with the estimated registration parameter–map. We show that the proposed method significantly improves the TV-reconstructions using only a single scalar regularization parameter and that the obtained parameter–maps match the problem-specific exppectations in terms of local features.

The Synergistic Image Reconstruction Framework (SIRF) is a research tool for reconstructing data from multiple imaging modalities, currently most prominently PET and MR. Included are acquisition models, reconstruction algorithms, registration tools, and regularisation models. In this work, we demonstrate the capabilities added since SIRF 2.0. PET/MR cardiac imaging results are presented with estimation of respiratory motion from the MR data, and motion compensation combined with various regularisation strategies used for both MR and PET reconstruction. The use of SIRF to facilitate this work enabled a range of techniques to be compared quickly and efficiently.

Time-of-flight (ToF) energy-dispersive neutron tomography is complimentary to X-ray tomographic imaging method aimed at the reconstruction of wavelength-dependent material response in every three-dimensional volume element. ToF neutron tomography has already demonstrated great potential for both mapping of crystallographic properties and elemental composition in micrometer scale. However, available neutron beams have inherently low fluxes and high ToF resolution comes at the cost of prohibitively long exposure times. In this paper we investigate application of advanced iterative reconstruction algorithms with both spatial and spectral regularisation to reduce exposure time. The capability of advanced reconstruction algorithms is demonstrated on a specifically designed multi-material sample.