Electronic noise modeling in statistical iterative reconstruction

  • Authors:

  • Jingyan Xu;Benjamin M. W. Tsui

  • Affiliations:

  • Johns Hopkins University, Baltimore, MD;Johns Hopkins University, Baltimore, MD

  • Venue:
  • IEEE Transactions on Image Processing
  • Year:
  • 2009

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Abstract

We consider electronic noise modeling in tomographic image reconstruction when the measured signal is the sum of a Gaussian distributed electronic noise component and another random variable whose log-likelihood function satisfies a certain linearity condition. Examples of such likelihood functions include the Poisson distribution and an exponential dispersion (ED) model that can approximate the signal statistics in integration mode X-ray detectors. We formulate the image reconstruction problem as a maximum-likelihood estimation problem. Using an expectation-maximization approach, we demonstrate that a reconstruction algorithm can be obtained following a simple substitution rule from the one previously derived without electronic noise considerations. To illustrate the applicability of the substitution rule, we present examples of a fully iterative reconstruction algorithm and a sinogram smoothing algorithm both in transmission CT reconstruction when the measured signal contains additive electronic noise. Our simulation studies show the potential usefulness of accurate electronic noise modeling in low-dose CT applications.