Estimating the Spectrum in Computed Tomography Via Kullback–Leibler Divergence Constrained Optimization

Purpose We study the problem of spectrum estimation from transmission data of a known phantom. The goal is to reconstruct an x‐ray spectrum that can accurately model the x‐ray transmission curves and reflects a realistic shape of the typical energy spectra of the CT system. Methods Spectrum estimation is posed as an optimization problem with x‐ray spectrum as unknown variables, and a Kullback–Leibler (KL)‐divergence constraint is employed to incorporate prior knowledge of the spectrum and enhance numerical stability of the estimation process. The formulated constrained optimization problem is convex and can be solved efficiently by use of the exponentiated‐gradient (EG) algorithm. We demonstrate the effectiveness of the proposed approach on the simulated and experimental data. The comparison to the expectation–maximization (EM) method is also discussed. Results In simulations, the proposed algorithm is seen to yield x‐ray spectra that closely match the ground truth and represent the attenuation process of x‐ray photons in materials, both included and not included in the estimation process. In experiments, the calculated transmission curve is in good agreement with the measured transmission curve, and the estimated spectra exhibits physically realistic looking shapes. The results further show the comparable performance between the proposed optimization‐based approach and EM. Conclusions Our formulation of a constrained optimization provides an interpretable and flexible framework for spectrum estimation. Moreover, a KL‐divergence constraint can include a prior spectrum and appears to capture important features of x‐ray spectrum, allowing accurate and robust estimation of x‐ray spectrum in CT imaging

Erosion and dilation of edges in dimensional X-ray computed tomography images

Dimensional X-ray Computed Tomography (CT) is a rapidly expanding field of research due to the numerous advantages this technique offers over conventional measurement technologies, most notably, the ability to measure internal features of a component. Tactile and optical Coordinate Measurement Machines (CMM), currently used in the manufacturing production industry, record points on the external surface of a workpiece by measuring the contact point of a physical probe or the reflection of projected light. X-ray CT has the ability to capture full volumetric data, since X-rays are transmitted through the entire object, revealing features which are otherwise invisible. Over the past five years, interest in this field has grown in the UK, with an increasing number of organisations in industry and research having access to X-ray CT machines and the wide range of manufacturers, offering new systems specifically designed for dimensional metrology applications.Despite this, the complexity of data acquisition required for dimensional measurement using X-ray CT has made it difficult to estimate the measurement uncertainty. This has hindered the generation of standards and full-scale adoption of this technique in industry. Due to the nature of X-ray imaging, a number of non-linear influence factors exist which have the potential to cause dimensional measurement error. These influences must be better understood to reduce and ideally, compensate error.In this doctoral thesis, the effects of the influence factors associated with CT data acquisition are studied, specifically, beam hardening and a finite X-ray source size. The effects these have on the quality of X-ray CT data are well understood; typically degrading the achievable contrast and spatial resolution of the CT image. However, the effects on dimensional measurement are less well understood due to the complexity of their interactions before reconstruction of the final image. These influences are modelled in a simulated CT acquisition to quantify any systematic effects on determination of edges in the CT image. The results are then validated by experimentally replicating the simulation set-up.In this work, it is found that beam hardening and a finite source diameter can lead to systematic errors in the edge position within the CT image. Beam hardening generally leads to dilation of the edge; where the edge position moves in the direction of the surface vector. In contrast, a finite source diameter can lead to erosion of the edge; where the edge position moves in an opposing direction to the surface vector.</div

Advances in dual-energy computed tomography imaging of radiological properties

Dual-energy computed tomography (DECT) has shown great potential in the reduction of uncertainties of proton ranges and low energy photon cross section estimation used in radiation therapy planning. The work presented herein investigated three contributions for advancing DECT applications. 1) A linear and separable two-parameter DECT, the basis vector model (BVM) was used to estimate proton stopping power. Compared to other nonlinear two-parameter models in the literature, the BVM model shows a comparable accuracy achieved for typical human tissues. This model outperforms other nonlinear models in estimations of linear attenuation coefficients. This is the first study to clearly illustrate the advantages of linear model not only in accurately mapping radiological quantities for radiation therapy, but also in providing a unique model for accurate linear forward projection modelling, which is needed by the statistical iterative reconstruction (SIR) and other advanced DECT reconstruction algorithms. 2) Accurate DECT requires knowledge of x-ray beam properties. Using the Birch-Marshall1 model and beam hardening correction coefficients encoded in a CT scanner’s sinogram header files, an efficient and accurate way to estimate the x-ray spectrum is proposed. The merits of the proposed technique lie in requiring no physical transmission measurement after a one-time calibration against an independently measured spectrum. This technique can also be used in monitoring the aging of x-ray CT tubes. 3) An iterative filtered back projection with anatomical constraint (iFBP-AC) algorithm was also implemented on a digital phantom to evaluate its ability in mitigating beam hardening effects and supporting accurate material decomposition for in vivo imaging of photon cross section and proton stopping power. Compared to iFBP without constraints, both algorithms demonstrate high efficiency of convergence. For an idealized digital phantom, similar accuracy was observed under a noiseless situation. With clinically achievable noise level added to the sinograms, iFBP-AC greatly outperforms iFBP in prediction of photon linear attenuation at low energy, i.e., 28 keV. The estimated mean errors of iFBP and iFBP-AC for cortical bone are 1% and 0.7%, respectively; the standard deviations are 0.6% and 5%, respectively. The achieved accuracy of iFBP-AC shows robustness versus contrast level. Similar mean errors are maintained for muscle tissue. The standard deviation achieved by iFBP-AC is 1.2%. In contrast, the standard deviation yielded by iFBP is about 20.2%. The algorithm of iFBP-AC shows potential application of quantitative measurement of DECT. The contributions in this thesis aim to improve the clinical performance of DECT