Electronic noise compensation in iterative X-ray CT reconstruction

Xu Jingyan, Benjamin M.W. Tsui

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


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 model4, 5 to the compound Poisson model.

Original languageEnglish (US)
Title of host publicationMedical Imaging 2008 - Physics of Medical Imaging
StatePublished - May 14 2008
EventMedical Imaging 2008 - Physics of Medical Imaging - San Diego, CA, United States
Duration: Feb 18 2008Feb 21 2008

Publication series

NameProgress in Biomedical Optics and Imaging - Proceedings of SPIE
ISSN (Print)1605-7422


OtherMedical Imaging 2008 - Physics of Medical Imaging
Country/TerritoryUnited States
CitySan Diego, CA


  • Computed tomography
  • Electronic noise compensation
  • Expectation-maximization
  • Iterative reconstruction
  • Poisson likelihood

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Biomaterials
  • Atomic and Molecular Physics, and Optics
  • Radiology Nuclear Medicine and imaging


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