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In this article, we propose a slice-based interactive segmentation of spectral CT datasets using a bag of features method. The data are acquired from a MARS scanner that divides up the X-ray spectrum into multiple energy bins for imaging. In literature, most existing segmentation methods are limited to performing a specific task or tied to a particular imaging modality. Therefore, when applying generalized methods to MARS datasets, the additional energy information acquired from the scanner cannot be sufficiently utilized. We describe a new approach that circumvents this problem by effectively aggregating the data from multiple channels. Our method solves a classification problem to get the solution for segmentation. Starting with a set of labeled pixels, we partition the data using superpixels. Then, a set of local descriptors, extracted from each superpixel, are encoded into a codebook and pooled together to create a global superpixel-level descriptor (bag of features representation). We propose to use the vector of locally aggregated descriptors as our encoding/pooling strategy, as it is efficient to compute and leads to good results with simple linear classifiers. A linear support vector machine is then used to classify the superpixels into different labels. The proposed method was evaluated on multiple MARS datasets. Experimental results show that our method achieved an average of more than 10% increase in the accuracy over other state-of-the-art methods.

Assessment of disease burden and drug efficacy is achieved preclinically using high resolution micro computed tomography (CT). However, micro-CT is not applicable to clinical human imaging due to operating at high dose. In addition, the technology differences between micro-CT and standard clinical CT prevent direct translation of preclinical applications. The current proof-of-concept study presents spectral photon-counting CT as a clinically translatable, molecular imaging tool by assessing contrast uptake in an ex-vivo mouse model of pulmonary tuberculosis (TB). Iodine, a common contrast used in clinical CT imaging, was introduced into a murine model of TB. The excised mouse lungs were imaged using a standard micro-CT subsystem (SuperArgus) and the contrast enhanced TB lesions quantified. The same lungs were imaged using a spectral photoncounting CT system (MARS small-bore scanner). Iodine and soft tissues (water and lipid) were materially separated, and iodine uptake quantified. The volume of the TB infection quantified by spectral CT and micro-CT was found to be 2.96 mm3 and 2.83 mm3, respectively. This proof-of-concept study showed that spectral photon-counting CT could be used as a predictive preclinical imaging tool for the purpose of facilitating drug discovery and development. Also, as this imaging modality is available for human trials, all applications are translatable to human imaging. In conclusion, spectral photon-counting CT could accelerate a deeper understanding of infectious lung diseases using targeted pharmaceuticals and intrinsic markers, and ultimately improve the efficacy of therapies by measuring drug delivery and response to treatment in animal models and later in humans.

Images from MARS spectral CT scanners show that there is much diagnostic value from using small pixels and good energy data. MARS scanners use energy-resolving photon-counting CZT Medipix3RX detectors that measure the energy of photons on a five-point scale and with a spatial resolution of 110 microns. The energy information gives good material discrimination and quantification. The 3D reconstruction gives a voxel size of 70 microns. We present images of pre-clinical specimens, including excised atheroma, bone and joint samples, and nanoparticle contrast agents along with images from living humans. Images of excised human plaque tissue show the location and extent of lipid and calcium deposition within the artery wall. The presence of intraplaque haemorrhage, where the blood leaks into the artery wall following a rupture, has also been visualised through the detection of iron. Several clinically important bone and joint problems have been investigated including: site-specific bone mineral density, bone-metal interfaces (spectral CT reduces metal artefacts), cartilage health using ionic contrast media, gout and pseudogout crystals, and microfracture assessment using nanoparticles. Metallic nanoparticles have been investigated as a cellular marker visible in MARS images. Cell lines of different cancer types (Raji and SK-BR3) were incubated with monoclonal antibody-functionalised AuNPs (Herceptin and Rituximab). We identified and quantified the labelled AuNPs demonstrating that Herceptin-functionalised AuNPs bound to SK-BR3 breast cancer cells but not to the Raji lymphoma cells. In vivo human images show the bone microstructure. Fat, water, and calcium concentrations are quantifiable.

The aim is to perform qualitative and quantitative assessment of metal induced artefacts of small titanium biomaterials using photon counting spectral CT. The energy binning feature of some photon counting detectors enables the measured spectrum to be segmented into low, mid and high energy bins in a single exposure. In this study, solid and porous titanium implants submerged in different concentrations of calcium solution were scanned using the small animal MARS photon counting spectral scanner equipped with a polyenergetic X-ray source operated at 118 kVp. Five narrow energy bins (7-45 keV, 45-55 keV, 55-65 keV, 65-75 keV and 75-118 keV) in charge summing mode were utilised. Images were evaluated in the energy domain (spectroscopic images) as well as material domain (material segmentation and quantification). Results show that calcium solution outside titanium implants can be accurately quantified. However, there was an overestimation of calcium within the pores of the scaffold. This information is critical as it can severely limit the assessment of bone ingrowth within metal structures. The energy binning feature of the spectral scanner was exploited and a correction factor, based on calcium concentrations adjacent to and within metal structures, was used to minimise the variation. Qualitative and quantitative evaluation of bone density and morphology with and without titanium screw shows that photon counting spectral CT can assess bone-metal interface with less pronounced artefacts. Quantification of bone growth in and around the implants would help in orthopaedic applications to determine the effectiveness of implant treatment and assessment of fracture healing.

Treatment failure in cancer is often due to variation in tumour characteristics within the same tumour, or across tumour sites, or over time. At present, most cancers are staged with imaging; treatment is selected, then the patient is re-imaged to see if the treatment is working. We intend to transform that approach by using a novel non-invasive spectral imaging technology together with targeted and non-targeted gold nanoparticles to measure tumour burden as well as drug delivery. In this study, we report spectral CT imaging of four different cancer cell types (ovarian, breast, Raji cancer cells and Lewis lung carcinoma) using gold nanoparticles. We also report that drug labelled targeted gold nanoparticles can specifically target HER2+ breast cancer cells and can be quantified by a spectral scanner. MARS CT incorporated with Medipix3RX detector was used. For image acquisition, four energy thresholds were set between 18 to 118keV to detect the K-edge of gold nanoparticles. Reconstructed images in narrow energy bins were used for material decomposition. In the first study, two ovarian cancer cell lines (OVCAR5 and SKOV3) were incubated in four sizes of gold nanoparticles (18, 40, 60 and 80nm). Results indicated a high uptake of 18 and 80nm of the gold nanoparticle by SKOV3; OVCAR5 show less uptake for all four nanoparticle sizes. In the second study, Lewis lung carcinoma was implanted in C57BL mice, and 15nm non-functionalized gold nanoparticles were injected via tail vein. Gold nanoparticles were visualized and quantified (0.497mg) in the peripheral region of a tumour whilst showing tumour necrosis in the middle. The third study showed the successful cross-over experiment of gold nanoparticles labelled to two drugs, Rituximab, and Herceptin to target Raji, and breast cancer cells respectively. The findings demonstrated spectral CT has the potential to enable the imaging and quantification of nanoparticles to monitor biological or disease processes and drug delivery to specific cell types.

We describe a CMS-Medipix3RX neutron camera developed by adapting and modifying detector readout electronics developed at the University of Canterbury. The readout electronics are part of the MARS x-ray scanner used for imaging applications [1]. The neutron cameras will be used for the precise evaluation of complex radiation fields in and around the Compact Muon Solenoid (CMS) detector on the Large Hadron Collider (LHC) at CERN. This evaluation will help to ascertain the performance of various sub-systems installed in the cavern as well as to predict their useful lifetimes. Medipix3RX detector can deliver real-time images of the flux and spectral composition of different particles, including slow and fast neutrons. In this neutron camera, slow neutrons are detected using a lithium fluoride conversion layer and fast neutrons by a polypropylene layer. These produce charged particles, which are then detected by a semiconductor sensor material, silicon. We modelled the mixed-field radiation at seven Medipix detector locations in the cavern by scoring the particle travelling through the detector location using FOCUS, a Monte-Carlo simulation tool, analysing the energy as well as their angular distributions of neutrons from the result of simulations.A good agreement was observed between the average flux predicted by standard FLUKA methods and those obtained from FOCUS output data integrated over time. Also, the response function of the Medipix detectors was modelled and simulated for different thicknesses of the neutron conversion layer. An algorithm was developed for track reconstruction and recognition using cluster analysis techniques. This labels and determines the density of clusters formed by groups of particles. The CMS-Medipix detectors with their conversion layers were calibrated in the CERN neutron facility and installed in the CMS cavern at the beginning of 2018. This paper discusses the calibration of the detector installation and presents early results of radiation measurements from 2018 run.

This study aims to demonstrate that spectral CT imaging can identify and quantify inflammatory components of unstable plaque such as iron, calcium and lipid in phantoms and excised human atherosclerotic plaques. Spectral CT acquisition protocol was optimised using the MARS spectral scanner. A phantom with multiple concentrations of ferric nitrate (25, 50, 100, 200 and 400 mg/ml), hydroxyapatite (104.3, 402.3, and 603.3 mg/cm3), iodine (9 and 18 mg/ml), lipid and water was scanned followed by blood clots and excised human plaques using energy thresholds 20, 28, 36 and 44 keV at 80 kVp, 55 µA tube current and 100 ms exposure time. CT images were reconstructed in narrow energy bins. Differences in linear attenuation coefficients between different concentrations of ferric nitrate and hydroxyapatite were compared using the receiver operating characteristic (ROC) curve and considered successful if AUC≥0.8. Differentiation between iron and calcium was successful at 400mg/ml ferric nitrate and 100mg/ml hydroxyapatite (AUC≥0.9; 99% correct material identification). The optimised calibrations were implemented in blood clots and plaque scans, which successfully identified iron signal within the clots, and areas of intraplaque haemorrhage and calcification in the carotid plaque specimens.

The aim of the present study is to show that non-invasive MARS imaging can differentiate between infected and healthy pulmonary tissue using an iodine-based contrast agent at high resolution. One C57BL/6J mouse with chronic tuberculosis (TB) was euthanized with CO2 and the pulmonary tissue excised. The TB lungs were incubated in 3% iodine solution. Mouse pulmonary tissue free of TB was also excised and incubated in the iodine solution for control purposes. Calibration of the MARS scanner involved scanning a phantom containing four concentrations of iodine along with water (soft tissue) and lipid (fat). The calibration phantom, control, and TB infected tissue were imaged at four threshold energy levels (20, 27, 34, 45 keV) at a constant 60 kVp tube voltage and 90 µA tube current. Following analysis of the calibration phantom, material decomposition (MD) was applied to the pulmonary tissue samples and iodine to obtain material images. MARS Vision software was used to visualize the materials to produce 3D material images. TB granulomas are visible within the lung lobes due to the iodine uptake. The amount of iodine uptake can be measured in mg by analysis of the material images using MARS Vision. MARS imaging was able to better differentiate between infected and healthy tissue. The present study demonstrated non-invasive, photon-counting CT is capable of differentiating between infected and healthy tissue. Future studies will consider development of TB markers, or drug markers labelled with gold nanoparticles, to enhance the understanding of the basic biology and mechanisms underpinning TB, and its relevance to the phenomenon of persistence in the infected host during therapy.

This paper outlines image domain material decomposition algorithms that have been routinely used in MARS spectral CT systems. These algorithms (known collectively as MARS-MD) are based on a pragmatic heuristic for solving the under-determined problem where there are more materials than energy bins. This heuristic contains three parts: (1) splitting the problem into a number of possible sub-problems, each containing fewer materials; (2) solving each sub-problem; and (3) applying rejection criteria to eliminate all but one sub-problem's solution. An advantage of this process is that different constraints can be applied to each sub-problem if necessary. In addition, the result of this process is that solutions will be sparse in the material domain, which reduces crossover of signal between material images. Two algorithms based on this process are presented: the Segmentation variant, which uses segmented material classes to define each sub-problem; and the Angular Rejection variant, which defines the rejection criteria using the angle between reconstructed attenuation vectors. This paper outlines image domain material decomposition algorithms that have been routinely used in MARS spectral CT systems. These algorithms (known collectively as MARS-MD) are based on a pragmatic heuristic for solving the under-determined problem where there are more materials than energy bins. This heuristic contains three parts: (1) splitting the problem into a number of possible sub-problems, each containing fewer materials; (2) solving each sub-problem; and (3) applying rejection criteria to eliminate all but one sub-problem's solution. An advantage of this process is that different constraints can be applied to each sub-problem if necessary. In addition, the result of this process is that solutions will be sparse in the material domain, which reduces crossover of signal between material images. Two algorithms based on this process are presented: the Segmentation variant, which uses segmented material classes to define each sub-problem; and the Angular Rejection variant, which defines the rejection criteria using the angle between reconstructed attenuation vectors.

Previous work has investigated the feasibility of using Eigenimage-based enhancement tools to highlight abnormalities on chest X-rays (Butler et al in J Med Imaging Radiat Oncol 52:244-253, 2008). While promising, this approach has been limited by computational restrictions of standard clinical workstations, and uncertainty regarding what constitutes an adequate sample size. This paper suggests an alternative mathematical model to the above referenced singular value decomposition method, which can significantly reduce both the required sample size and the time needed to perform analysis. Using this approach images can be efficiently separated into normal and abnormal parts, with the potential for rapid highlighting of pathology.

A new algorithm is presented which aims to solve problems from compressed sensing - under-determined problems where the solution vector is known a priori to be sparse. Upper bounds on the solution vector are found so that the problem can be reformulated as a box-constrained quadratic programme. A sparse solution is sought using a Barzilai-Borwein type projection algorithm. New insight into the choice of step length is provided through a study of the special structure of the underlying problem together with upper bounds on the step length. Numerical experiments are conducted and results given, comparing this algorithm with a number of other current algorithms.

Wulbert and Meir have each obtained a Korovkin theorem for weak convergence of operators on an L1 space. Here we prove a result which includes both of these theorems and which provides a general setting for weak Korovkin type L1 convergence of operators which are not assumed positive.

Spectral molecular imaging is a new imaging technique able to discriminate and quantify different components of tissue simultaneously at high spatial and high energy resolution. Our MARS scanner is an x-ray based small animal CT system designed to be used in the diagnostic energy range (20 to 140 keV). In this paper, we demonstrate the use of the MARS scanner, equipped with the Medipix3RX spectroscopic photon-processing detector, to discriminate fat, calcium, and water in tissue. We present data collected from a sample of lamb meat including bone as an illustrative example of human tissue imaging. The data is analyzed using our 3D Algebraic Reconstruction Algorithm (MARS-ART) and by material decomposition based on a constrained linear least squares algorithm. The results presented here clearly show the quantification of lipid-like, water-like and bone-like components of tissue. However, it is also clear to us that better algorithms could extract more information of clinical interest from our data. Because we are one of the first to present data from multi-energy photon-processing small animal CT systems, we make the raw, partial and fully processed data available with the intention that others can analyze it using their familiar routines. The raw, partially processed and fully processed data of lamb tissue along with the phantom calibration data can be found at [http://hdl.handle.net/10092/8531]., Comment: 11 pages, 6 figs

A segmentation algorithm that assists material analysis in multi-energy computed tomography is presented. Segmentation is typically used in conjunction with quantitative material analysis algorithms (known as material decomposition) to increase the total number of materials which can be discriminated and quantified. The algorithm illustrated here identifies voxels (in the image domain) with one of three material classes: air, soft tissues and dense tissue or contrast pharmaceuticals. Two soft tissue materials are chosen (the most and the least attenuating soft tissues) to define the boundaries between the different material classes. The intensity (calculated from the multi-energy representation using the Euclidean norm) of each voxel is compared to the two boundary materials to determine which material class it belongs to. Unlike other intensity based segmentation methods this algorithm checks, using multi-variate confidence intervals (ellipsoids), whether each voxel is statistically distinguishable from the two boundary materials. If the voxels are not distinguishable then they are defaulted to the soft tissue class. An advantage of this segmentation method is that noise which passes through to the binary representations of each material class typically resemble salt and pepper noise, which is easily removed with a median filter. Simulations demonstrate that the algorithm can correctly allocate a variety of medically relevant soft tissue and non soft tissue materials to their correct material classes and that segmentation using multi-energy information can handle noisier data than when using single-energy information. The proposed algorithm is also successfully applied to a multi-energy CT scan taken using the MARS (Medipix All Resolution System) scanner.

The Medipix All Resolution System (MARS) system is a commercial spectral/multi-energy micro-CT scanner designed and assembled by the MARS Bioimaging, Ltd. in New Zealand. This system utilizes the state-of-the-art Medipix photon-counting, energy-discriminating detector technology developed by a collaboration based at European Organization for Nuclear Research (CERN). In this paper, we report our preliminary experimental results using this system, including geometrical alignment, photon energy characterization, protocol optimization, and spectral image reconstruction. We produced our scan datasets with a multi-material phantom, and then applied ordered subset-simultaneous algebraic reconstruction technique (OS-SART) to reconstruct images in different energy ranges and principal component analysis (PCA) to evaluate spectral deviation between the energy ranges.

In many applications involving image reconstruction, signal observation time is limited. This emphasizes the requirement for optimal observation selection algorithms. A selection criterion using the trace of a matrix forms the basis of two existing algorithms, the Sequential Backward Selection and Sequential Forward Selection algorithms. Neither is optimal although both generally perform well. Here we introduce a trace row-exchange criterion to further improve the quality of the selected subset and introduce another observation selection criterion based upon the determinant of a matrix.

The study of the conformal group in $R^{p,q}$ usually involves the conformal compactification of $R^{p,q}$. This allows the transformations to be represented by linear transformations in $R^{p+1,q+1}$. So, for example, the conformal group of Minkowski space, $R^{1,3}$ leads to its isomorphism with $SO(2,4)$. This embedding into a higher dimensional space comes at the expense of the geometric properties of the transformations. This is particularly a problem in $R^{1,3}$ where we might well prefer to keep the geometric nature of the various types of transformations in sight. In this note, we show that this linearization procedure can be achieved with no loss of geometric insight, if, instead of using this compactification, we let the conformal transformations act on two copies of the associated Clifford algebra. Although we are mostly concerned with the conformal group of Minkowski space (where the geometry is clearest), generalization to the general case is straightforward.

The stabilized Poincare-Heisenberg algebra (SPHA) is the Lie algebra of quantum relativistic kinematics generated by fifteen generators. It is obtained from imposing stability conditions after attempting to combine the Lie algebras of quantum mechanics and relativity which by themselves are stable, however not when combined. In this paper we show how the sixteen dimensional Clifford algebra CL(1,3) can be used to generate the SPHA. The Clifford algebra path to the SPHA avoids the traditional stability considerations, relying instead on the fact that CL(1,3) is a semi-simple algebra and therefore stable. It is therefore conceptually easier and more straightforward to work with a Clifford algebra. The Clifford algebra path suggests the next evolutionary step toward a theory of physics at the interface of GR and QM might be to depart from working in space-time and instead to work in space-time-momentum., 14 pages

An image whose region of support is smaller than its bounding rectangle can, in principle, be reconstructed from a subset of the Nyquist samples. However, determining such a sampling set that gives a stable reconstruction is a difficult and computationally intensive problem. An algorithm is developed for determining periodic nonuniform sampling patterns that is orders of magnitude faster than existing algorithms. The speedup is achieved by using a sequential selection algorithm and heuristic metrics for the quality of sampling sets that are fast to compute, as opposed to the more rigorous linear algebraic metrics that have been used previously. Simulations show that the sampling sets determined using the new algorithm give image reconstructions that are of accuracy comparable with those determined by other slower algorithms.

This paper discusses methods for reducing beam hardening effects and metal artefacts using spectral x-ray information in biomaterial samples. A small-animal spectral scanner was operated in the 15 to 80 keV x-ray energy range for this study. We use the photon-processing features of a CdTe-Medipix3RX ASIC in charge summing mode to reduce beam hardening and associated artefacts. We present spectral data collected for metal alloy samples, its analysis using algebraic 3D reconstruction software and volume visualisation using a custom volume rendering software. The cupping effect and streak artefacts are quantified in the spectral datasets. The results show reduction in beam hardening effects and metal artefacts in the narrow high energy range acquired using the spectroscopic detector. A post-reconstruction comparison between CdTe-Medipix3RX and Si-Medipix3.1 is discussed. The raw data and processed data are made available (http://hdl.handle.net/10092/8851) for testing with other software routines. Refereed/Peer-reviewed

We consider the recovery of localised structure from signals consisting of a piecewise constant structure and sparse components. A new algorithm is presented which aims to reconstruct signals of this type from a limited set of observed data. The algorithm is broken down into two subproblems which both involve minimisation of an $l_1$-regularised least squares problem. Numerical results are presented which demonstrate the effectiveness and efficiency of the proposed method. References M. V. Afonso, J. M. Bioucas-Dias, and M. A. T. Figueiredo. A Fast Algorithm for the Constrained Formulation of Compressive Image Reconstruction and Other Linear Inverse Problems. IEEE International Conference on Acoustics Speech and Signal Processing , pages 4034--4037, 2010. doi:10.1109/ICASSP.2010.5495758 R. L. Broughton, I. D. Coope, P. F. Renaud, and R. E. H. Tappenden. A Box Constrained Gradient Projection Algorithm for Compressed Sensing. Signal Processing , 91(8):1985--1992, August 2011. doi:10.1016/j.sigpro.2011.03.003 E. Candes, J. Romberg, and T. Tao. Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information. IEEE Transactions on Information Theory , 52(2):489--509, 2004. doi:10.1109/TIT.2005.862083 E. J. Candes. Compressive Sampling. In Proceedings of the International Congress of Mathematics , pages 1433--1452, Madrid, Spain, 2006. European Mathematical Society. E. J. Candes and T. Tao. Near-Optimal Signal Recovery From Random Projections and Universal Encoding Strategies. IEEE Transactions on Information Theory , 52(12):5406--5425, December 2006. doi:10.1109/TIT.2006.885507 D. L. Donoho. Compressed Sensing. IEEE Transactions on Information Theory , 52(4):1289--1306, 2006. doi:10.1109/TIT.2006.871582 M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright. Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems. IEEE Journal of Selected Topics in Signal Processing , 1(4):586--597, December 2007. doi:10.1109/JSTSP.2007.910281 G. H. Golub and C. F. Van Loan. Matrix Computations . The Johns Hopkins University Press, 3 edition, 1996. A. Griffin and P. Tsakalides. Compressed sensing of audio signals using multiple sensors. Lausanne, Switzerland, 25--29 August 2008. EUSIPCO08. P. C. Hansen. {Rank-Deficient and Discrete Ill-Posed Problems} . SIAM, 1998. M. Lustig, D. Donoho, and J. Pauly. Sparse MRI: The Application of Compressed Sensing for Rapid MR Imaging. Magnetic Resonance in Imaging , 58(6):1182--1195, December 2007. doi:10.1002/mrm.21391 J. Provost and F. Lesage. The Application fo Compressed Sensing for Photo-Acoustic Tomography. IEEE Transactions on Medical Imaging , 28(4), April 2009. doi:10.1109/TMI.2008.2007825 J. L. Starck and J. Bobin. Astronomical Data Analysis and Sparsity: From Wavelets to Compressed Sensing. Proceedings of the IEEE , 98(6):1021--1030, 2010. doi:10.1109/JPROC.2009.2025663 H. Yu and G. Wang. Compressed sensing based interior tomography. Physics in Medicine and Biology , pages 2791--2805, 2009. doi:10.1088/0031-9155/54/9/014

Introduction. In his paper, On all kinds of homogeneous spaces, Ungar proves the following: If G is either a compact metric space or a locally compact, locally connected, separable metric space which is, uniquely homogeneous, then G is an abelian topological group, and the group of topological automorphisms of G is trivial. He showed that such a finite dimensional G would be a Lie group and thus have too many homeomorphisms to be uniquely homogeneous. Using topological arguments together with some structure theorems for topological groups, it is possible to show there are no uniquely homogeneous continua at all. This completely answers a question to this effect posed by Burgess at the 1955 Wisconsin topology conference. Alternatively one uses the following result about topological groups. RESULT. Let G be a T2 locally compact topological group with Aut(G) = {id}. Then G = {0} or Z2. PROOF. All inner automorphisms of G are trivial so G is abelian; and x -> x is trivial so all elements have order 2. By Zorn's lemma it is easy to show that an automorphism of any open subgroup extends to all of G. Since G is torsion and locally compact it contains a compact open subgroup H. By the extension result, Aut(H) must be trivial. Let X be the character group of H. X is discrete and Aut(X) is trivial (anti-isomorphic with Aut(H)). Now X must be {0} or Z2 otherwise it contains an open subgroup isomorphic to Z2 X Z2 which has nontrivial automorphisms. So H is Z2 or (0), G must be discrete, so G = {0} or Z2