Electronic noise compensation in iterative x-ray CT reconstruction

Jingyan Xu; Benjamin M. W. Tsui

doi:10.1117/12.772843

Abstract

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.

Citation Download Citation

Jingyan Xu, Jingyan Xu, Benjamin M. W. Tsui, 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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