Range condition and ML-EM checkerboard artifacts

Jiangsheng You, Jing Wang, Zhengrong Liang

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


The expectation maximization (EM) algorithm for the maximum likelihood (ML) image reconstruction criterion generates severe checkerboard artifacts in the presence of noise. A classical remedy is to impose an a priori constraint for a penalized ML or maximum a posteriori probability solution. The penalty reduces the checkerboard artifacts and also introduces uncertainty because a priori information is usually unknown in clinic. Recent theoretical investigation reveals that the noise can be divided into two components: one is called null-space noise and the other is range-space noise. The null-space noise can be numerically estimated using filtered backprojection (FBP) algorithm. By the FBP algorithm, the null-space noise annihilates in the reconstruction while the range-space noise propagates into the reconstructed image. The aim of this work is to investigate the relation between the null-space noise and the checkerboard artifacts in the ML-EM reconstruction from noisy projection data. Our study suggests that removing the null-space noise from the projection data could improve the signal-to-noise ratio of the projection data and, therefore, reduce the checkerboard artifacts in the ML-EM reconstructed images. This study reveals an in-depth understanding of the different noise propagations in analytical and iterative image reconstructions, which may be useful to single photon emission computed tomography, where the noise has been a major factor for image degradation. The reduction of the ML-EM checkerboard artifacts by removing the null-space noise avoids the uncertainty of using a priori penalty.

Original languageEnglish (US)
Pages (from-to)1696-1702
Number of pages7
JournalIEEE Transactions on Nuclear Science
Issue number5
StatePublished - Oct 2007


  • Attenuated Radon transform
  • Computed tomography
  • Consistent condition
  • Noise analysis

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Nuclear Energy and Engineering
  • Electrical and Electronic Engineering


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