### Abstract

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.

Original language | English (US) |
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Title of host publication | Medical Imaging 2008 - Physics of Medical Imaging |

DOIs | |

State | Published - May 14 2008 |

Event | Medical Imaging 2008 - Physics of Medical Imaging - San Diego, CA, United States Duration: Feb 18 2008 → Feb 21 2008 |

### Publication series

Name | Progress in Biomedical Optics and Imaging - Proceedings of SPIE |
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Volume | 6913 |

ISSN (Print) | 1605-7422 |

### Other

Other | Medical Imaging 2008 - Physics of Medical Imaging |
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Country | United States |

City | San Diego, CA |

Period | 2/18/08 → 2/21/08 |

### Keywords

- 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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## Cite this

*Medical Imaging 2008 - Physics of Medical Imaging*[69132H] (Progress in Biomedical Optics and Imaging - Proceedings of SPIE; Vol. 6913). https://doi.org/10.1117/12.772843