18 March 2008 Electronic noise compensation in iterative x-ray CT reconstruction
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Electronic noise compensation can be important for low-dose x-ray CT applications where severe photon starvation occurs. For clinical x-ray CT systems utilizing energy-integrating detectors, it has been shown that the detected x-ray intensity is compound Poisson distributed, instead of the Poisson distribution that is often studied in the literature. We model the electronic noise contaminated signal Z as the sum of a compound Poisson distributed random variable (r.v.) Y and a Gaussian distributed electronic noise N with known mean and variance. We formulate the iterative x-ray CT reconstruction problem with electronic noise compensation as a maximum-likelihood reconstruction problem. However the likelihood function of Z is not analytically trackable; instead of working with it directly, we formulate the problem in the expectation-maximization (EM) framework, and iteratively maximize the conditional expectation of the complete log-likelihood of Y. We further demonstrate that the conditional expectation of the surrogate function of the complete log-likelihood is a legitimate surrogate for the incomplete surrogate. Under certain linearity conditions on the surrogate function, a reconstruction algorithm with electronic noise compensation can be obtained by some modification of one previously derived without electronic noise considerations; the change incurred is simply replacing the unavailable, uncontaminated measurement Y by its conditional expectation E(Y|Z). The calculation of E(Y|Z) depends on the model of Y, N, and Z. We propose two methods for calculating this conditional expectation when Y follows a special compound Poisson distribution - the exponential dispersion model (ED). Our methods can be regarded as an extension of similar approaches using the Poisson model to the compound Poisson model.
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Jingyan Xu, Benjamin M. W. Tsui, "Electronic noise compensation in iterative x-ray CT reconstruction", Proc. SPIE 6913, Medical Imaging 2008: Physics of Medical Imaging, 69132H (18 March 2008); doi: 10.1117/12.772843; https://doi.org/10.1117/12.772843

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