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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.
© 1994 Optical Society of America
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