Bayesian image reconstruction for improving detection performance of muon tomography

Guobao Wang, Larry J. Schultz, Jinyi Qi

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


Muon tomography is a novel technology that is being developed for detecting high-Z materials in vehicles or cargo containers. Maximum likelihood methods have been developed for reconstructing the scattering density image from muon measurements. However, the instability of maximum likelihood estimation often results in noisy images and low detectability of high-Z targets. In this paper, we propose using regularization to improve the image quality of muon tomography. We formulate the muon reconstruction problem in a Bayesian framework by introducing a prior distribution on scattering density images. An iterative shrinkage algorithm is derived to maximize the log posterior distribution. At each iteration, the algorithm obtains the maximum a posteriori update by shrinking an unregularized maximum likelihood update. Inverse quadratic shrinkage functions are derived for generalized Laplacian priors and inverse cubic shrinkage functions are derived for generalized Gaussian priors. Receiver operating characteristic studies using simulated data demonstrate that the Bayesian reconstruction can greatly improve the detection performance of muon tomography.

Original languageEnglish (US)
Pages (from-to)1080-1089
Number of pages10
JournalIEEE Transactions on Image Processing
Issue number5
StatePublished - 2009


  • Bayesian estimation
  • Expectation maximization
  • Image reconstruction
  • Muon tomography
  • ROC analysis
  • Shrinkage algorithm

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software


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