Least-squares and maximum-likelihood in computed tomography.

Purpose: Existing maximum-likelihood (ML) methods in computed tomography usually require significant computing resources to implement, and/or are limited to particular measurement noise models that are representative of the simplest theoretical archetypes. There is an absence of general procedures to produce rapid ML methods that account precisely for the noise model of a given experiment. We investigate a mathematical-computational procedure of producing constrained quadratic optimization reconstruction algorithms that fill this niche, requiring less computing resources than the exact (expectation-maximization) procedures and having comparable performance with least-squares iterative methods. This allows high-fidelity reconstructions to be practically achievable for largely arbitrary noise models. Approach: We identify a systematic mathematical procedure to produce constrained quadratic optimization methods that maximize tomogram likelihood under arbitrary noise models, which are tunable to specific characteristics of the experiment. This procedure is applied to a general theory of mixed Poisson-Gaussian noise in transmission tomography, and to a theory of invertible linear transformations of measurement intensity subject to Poisson noise. We perform tomographic reconstructions of a very highly attenuating two-dimensional object phantom and compare the speed and fidelity of reconstruction with alternative quadratic metrics ( ℓ 2 -minimization among others). Results: Quantitative metrics reveal that reconstructions under our systematically produced quadratic methods achieved significantly greater reconstruction fidelity with less computation than the optimized conventional, untuned quadratic metrics with a comparable procedure. Conclusion: Constrained quadratic optimization methods appear to apply sufficiently good approximations to achieve a high reconstruction fidelity with a simple quadratic metric amenable to a broad class of minimization methods. These preliminary simulation-based results are very promising and suggest that such methods may be used to produce high-fidelity reconstructions with less computation than many other statistical methods. By design, these quadratic methods are also explicit and quantitative in their description, allowing fine-tuning according to the specific uncertainties and noise model of the experiment. Further research is required to ascertain the full practical potential of these methods.

Dynamics of Lead Bioavailability and Speciation in Indoor Dust and X-ray Spectroscopic Investigation of the Link between Ingestion and Inhalation Pathways.

Lead (Pb) exposure from household dust is a major childhood health concern because of its adverse impact on cognitive development. This study investigated the absorption kinetics of Pb from indoor dust following a single dose instillation into C57BL/6 mice. Blood Pb concentration (PbB) was assessed over 24 h, and the dynamics of particles in the lung and gastro-intestinal (GI) tract were visualized using X-ray fluorescence (XRF) microscopy. The influence of mineralogy on Pb absorption and particle retention was investigated using X-ray absorption near-edge structure spectroscopy. A rapid rise in PbB was observed between 0.25 and 4 h after instillation, peaking at 8 h and slowly declining during a period of 24 h. Following clearance from the lungs, Pb particles were detected in the stomach and small intestine at 4 and 8 h, respectively. Analysis of Pb mineralogy in the residual particles in tissues at 8 h showed that mineral-sorbed Pb and Pb-phosphates dominated the lung, while organic-bound Pb and galena were the main phases in the small intestines. This is the first study to visualize Pb dynamics in the lung and GI tract using XRF microscopy and link the inhalation and ingestion pathways for metal exposure assessment from dust.

Towards a practical implementation of X-ray ghost imaging with synchrotron light.

An experimental procedure for transmission X-ray ghost imaging using synchrotron light is presented. Hard X-rays from an undulator were divided by a beamsplitter to produce two copies of a speckled incident beam. Both beams were simultaneously measured on an indirect pixellated detector and the intensity correlation between the two copies was used to retrieve the ghost image of samples placed in one of the two beams, without measuring the samples directly. Aiming at future practical uses of X-ray ghost imaging, the authors discuss details regarding data acquisition, image reconstruction strategies and measure the point-spread function of the ghost-imaging system. This approach may become relevant for applications of ghost imaging with X-ray sources such as undulators in storage rings, free-electron lasers and lower-coherence laboratory facilities.

Linear iterative near-field phase retrieval (LIPR) for dual-energy x-ray imaging and material discrimination.

Near-field x-ray refraction (phase) contrast is unavoidable in many lab-based micro-CT imaging systems. Quantitative analysis of x-ray refraction (a.k.a. phase retrieval) is in general an under-constrained problem. Regularizing assumptions may not hold true for interesting samples; popular single-material methods are inappropriate for heterogeneous samples, leading to undesired blurring and/or over-sharpening. In this paper, we constrain and solve the phase-retrieval problem for heterogeneous objects, using the Alvarez-Macovski model for x-ray attenuation. Under this assumption we neglect Rayleigh scattering and pair production, considering only Compton scattering and the photoelectric effect. We formulate and test the resulting method to extract the material properties of density and atomic number from single-distance, dual-energy imaging of both strongly and weakly attenuating multi-material objects with polychromatic x-ray spectra. Simulation and experimental data are used to compare our proposed method with the Paganin single-material phase-retrieval algorithm, and an innovative interpretation of the data-constrained modeling phase-retrieval technique.

Spiral scanning X-ray fluorescence computed tomography.

Scanning X-ray fluorescence tomography was once considered impractical due to prohibitive measurement time requirements but is now common for investigating metal distributions within small systems. A recent look-ahead to the possibilities of 4th-generation synchrotron light sources [J. Synchrotron. Radiat. 21, 1031 (2014)] raised the possibility of a spiral-scanning measurement scheme where motion overheads are almost completely eliminated. Here we demonstrate the spiral scanning measurement and use Fourier ring correlation analysis to interrogate sources of resolution degradation. We develop an extension to the Fourier ring correlation formalism that enables direct determination of resolution from the measured sinogram data, greatly enhancing its power as a diagnostic tool for computed tomography.

The index of dispersion as a metric of quanta - unravelling the Fano factor.

In statistics, the index of dispersion (or variance-to-mean ratio) is unity (σ2/〈x〉 = 1) for a Poisson-distributed process with variance σ2 for a variable x that manifests as unit increments. Where x is a measure of some phenomenon, the index takes on a value proportional to the quanta that constitute the phenomenon. That outcome might thus be anticipated to apply for an enormously wide variety of applied measurements of quantum phenomena. However, in a photon-energy proportional radiation detector, a set of M witnessed Poisson-distributed measurements {W1, W2,… WM} scaled so that the ideal expectation value of the quantum is unity, is generally observed to give σ2/〈W〉 < 1 because of detector losses as broadly indicated by Fano [Phys. Rev. (1947), 72, 26]. In other cases where there is spectral dispersion, σ2/〈W〉 > 1. Here these situations are examined analytically, in Monte Carlo simulations, and experimentally. The efforts reveal a powerful metric of quanta broadly associated with such measurements, where the extension has been made to polychromatic and lossy situations. In doing so, the index of dispersion's variously established yet curiously overlooked role as a metric of underlying quanta is indicated. The work's X-ray aspects have very diverse utility and have begun to find applications in radiography and tomography, where the ability to extract spectral information from conventional intensity detectors enables a superior level of material and source characterization.

Bayesian approach to time-resolved tomography.

Conventional X-ray micro-computed tomography (µCT) is unable to meet the need for real-time, high-resolution, time-resolved imaging of multi-phase fluid flow. High signal-to-noise-ratio (SNR) data acquisition is too slow and results in motion artefacts in the images, while fast acquisition is too noisy and results in poor image contrast. We present a Bayesian framework for time-resolved tomography that uses priors to drastically reduce the required amount of experiment data. This enables high-quality time-resolved imaging through a data acquisition protocol that is both rapid and high SNR. Here we show that the framework: (i) encompasses our previous, algorithms for imaging two-phase flow as limiting cases; (ii) produces more accurate results from imperfect (i.e. real) data, where it can be compared to our previous work; and (iii) is generalisable to previously intractable systems, such as three-phase flow.

Extending reference scan drift correction to high-magnification high-cone-angle tomography.

The reference scan method is a simple yet powerful method for measuring spatial drift of the x-ray spot during a low-cone-angle µ-CT experiment. As long as the drift is smooth, and occurring on a time scale that is long compared to the acquisition time of each projection, this method provides a way to compensate for the drift by applying 2D in-plane translations to the radiographs. Here we show that this compensation may be extended to the regime of high-magnification, high-cone-angle CT experiments where source drift perpendicular to the detector plane can cause significant magnification changes throughout the acquisition.

Dynamic tomography with a priori information.

We present "dynamic tomography" algorithms that allow for the high-resolution, time-resolved imaging of dynamic (i.e., continuously time evolving) complex systems at existing x-ray micro-CT facilities. The behavior of complex systems is constrained by the underlying physics. By exploiting a priori knowledge of the geometry of the physical process being studied to allow the use of sophisticated iterative reconstruction techniques that incorporate constraints, we improve on current frame rates by at least an order of magnitude. This allows time-resolved imaging of previously intractable processes, such as two-phase fluid flow. We present reconstructions from experimental data collected at the Australian National University x-ray micro-CT facility.

Stability of phase-contrast tomography.

Phase-contrast tomography (PCT) allows three-dimensional imaging of objects that display insufficient contrast for conventional absorption-based tomography. We prove that PCT is stable with respect to high-frequency noise in experimental phase-contrast data, unlike conventional tomography, which is known to be mildly unstable. We use known properties of the three-dimensional x-ray transform and transport-of-intensity equation to construct a matrix representation of the forward PCT operator. We then invert this formula to show that, under natural boundary conditions, the PCT reconstruction operator exists and leads to a unique solution. We show that the singular values s(n) of the reconstruction operator have asymptotic behavior s(n)=O(n(-3/2)), guaranteeing the mathematical stability of the reconstruction process.