Alternating minimization algorithm with automatic relevance determination for transmission tomography under poisson noise

Yan Kaganovsky, Shaobo Han, Soysal Degirmenci, David G. Politte, David J. Brady, Joseph A. O’Sullivan, Lawrence Carin

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We propose a globally convergent alternating minimization (AM) algorithm for image reconstruction in transmission tomography, which extends automatic relevance determination (ARD) to Poisson noise models with Beer’s law. The algorithm promotes solutions that are sparse in the pixel/voxel– difference domain by introducing additional latent variables, one for each pixel/voxel, and then learning these variables from the data using a hierarchical Bayesian model. Importantly, the proposed AM algorithm is free of any tuning parameters with image quality comparable to standard penalized likelihood methods. Our algorithm exploits optimization transfer principles which reduce the problem into parallel one-dimensional optimization tasks (one for each pixel/voxel), making the algorithm feasible for large-scale problems. This approach considerably reduces the computational bottleneck of ARD associated with the posterior variances. Positivity constraints inherent in transmission tomography problems are also enforced. We demonstrate the performance of the proposed algorithm for x-ray computed tomography using synthetic and real-world datasets. The algorithm is shown to have much better performance than prior ARD algorithms based on approximate Gaussian noise models, even for high photon flux. Sample code is available from http://www.yankaganovsky. com/#!code/c24bp.

Original languageEnglish (US)
Pages (from-to)2087-2132
Number of pages46
JournalSIAM Journal on Imaging Sciences
Issue number3
StatePublished - Sep 30 2015
Externally publishedYes


  • Alternating minimization
  • Automatic relevance determination
  • Optimization transfer
  • Poisson noise
  • Transmission tomography
  • X-ray CT

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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