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The underlying model and iterative image-reconstruction algorithm, based on maximum-likelihood estimation, is extended to consider finite x-ray beam width. Simulations are presented by maximum-likelihood images compared with filtered-backprojection images. The main conclusion of this study is that it is feasible to obtain a marked improvement in image clarity and reduction of artifacts: (1) There is an improvement in delineation of the boundaries of low-contrast soft-tissue substructures. There is an improvement in the capability of identifying at least one of the low-contrast soft-tissue substructures. (2) The algorithm is capable of reconstructing onto a discrete array of finer resolution, again with better delineation of substructures than the filtered-backprojection algorithm. (3) Maximum-likelihood images at an atypically low photon flux level are, at the very least, comparable in image quality to filtered-backprojection images at a much higher and more typical photon flux level. These observations imply that the diagnostic capability of x-ray computed tomography may be improved to a broader range of otherwise adverse conditions. It may be capable of much better visualization of soft-tissue regions that reside near dense regions (such as bone or metal prostheses), of visualizing finer spatial detail, and of use with much lower x-ray dosages.

We investigate the potential and present limitations of a maximum-likelihood (ML) approach to x-ray computed tomography that utilizes Poisson modeling and an iterative gradient-based algorithm. This model and algorithm incorporate the finite width of the x-ray beam, and they were extended from an approach originally proposed by Lange et al. [IEEE Trans. Med. Imaging MI-6, 106–114 (1987)]. Low-count data, obtained from an industrial computed-tomography scanner, are used to reconstruct an image of a concrete cube with metal reinforcing bars. We utilize both ML and filtered backprojection to reconstruct a cross section of the internal structure of the cube. In this initial evaluation with low-count data the images reconstructed by ML show several potential advantages over those reconstructed by filtered backprojection. The advantages shown are the following: (1) there are significantly reduced noise and streak artifacts in the ML image; (2) some of the known structural detail is more apparent in the ML image; (3) there is a closer quantitative fit, based on log-likelihood and residual calculations, between the ML image and the observed data; (4) the ML approach shows the potential to achieve finer spatial resolution than filtered backprojection. We observe two present, yet addressable, limitations of the ML approach. First, the ML image currently has a peripheral smoothing artifact that seems to disappear gradually with increasing iteration numbers. This smoothing is possibly caused by the slow rate of convergence of the algorithm and may be addressed by future acceleration strategies. Second, the finer spatial resolution achieved with the ML approach currently occurs at the expense of noise and edge artifacts. This limitation may be addressed by a number of extended ML and maximum a posteriori approaches that are currently under investigation in other modalities of imaging to address similar noise and edge artifacts.

We briefly describe a maximum likelihood (ML) approach to x-ray computed tomography (CT) based on the expectationmaximization (EM) algorithm. This work extends upon earlier theoretical studies by Lange and Carson. Our algorithm differs from that of Lange and Carson in that several simplifying approximations are introduced that make the maximization step (M-step) of the algorithm solvable. The results of computer simulations using noise-free and Poisson randomized projections are presented. The images obtained with the ML methods are compared to those reconstructed with filtered backprojection (FBP). Preliminary results show that there are potential advantages in the ML approaches in situations where a high-contrast object, such as bone, is embedded in soft tissue.

X-ray computed tomography (CT) is an important and powerful tool in industrial imaging for obtaining shape and dimensional information of industrial parts. It also serves to provide digital models of parts for inputs to new and emerging technologies in the manufacturing industry that have begun to embrace CT-assisted engineering and design. Since a large number of objects encountered in industrial CT are made either of a single homogenous material or a few homogenous materials, algorithms for discrete tomography should, in principle, yield CT images whose resolution and dimensional accuracy are superior to CT images obtained by conventional algorithms. This in turn should result in significant improvements in the accuracy of boundaries extracted from CT images for the creation of digital models of a large class of parts of interest in CT-assisted manufacturing. This chapter looks at some important applications in CT-assisted engineering and manufacturing that can benefit from the techniques of discrete tomography, and discuss some of the technical challenges faced in extracting boundaries with the degree of accuracy demanded for engineering and manufacturing applications.

We present experimental results for a maximum likelihood (ML) reconstruction algorithm for x-ray computed tomography (CT) which incorporates both the Poisson nature of photon counts and the finite width of the x-ray beam. Count data, obtained from an industrial CT scanner, are used to reconstruct an image of a concrete rebar-reinforced cube. The internal structure of the cube is reconstructed using both ML and filtered backprojection (FBP). We find that the ML method reduces noise and streak artifacts in the reconstructed image thus supporting our earlier work with simulated count data.