Electronic noise compensation in iterative X-ray CT reconstruction

Electronic noise compensation can be important for low-dose x-ray CT applications where severe photon starvation occursi. For clinical x-ray CT systems utilisiing energy-integrating detectors, it has been shown that the detected x-ray intensity is compound Poisson distributed,^1-3 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 trackabie: instead of working with it directly, we formulate the problem in the expectation-maximisation (BM) 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, ./V1 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 (if similar approaches using the Poisson model^{4, 5} to the compound Poisson model.