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

Published

Journal Article

© 2015 Society for Industrial and Applied Mathematics. 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.

Full Text

Duke Authors

Cited Authors

  • Kaganovsky, Y; Han, S; Degirmenci, S; Politte, DG; Brady, DJ; O’Sullivan, JA; Carin, L

Published Date

  • September 30, 2015

Published In

Volume / Issue

  • 8 / 3

Start / End Page

  • 2087 - 2132

Electronic International Standard Serial Number (EISSN)

  • 1936-4954

Digital Object Identifier (DOI)

  • 10.1137/141000038

Citation Source

  • Scopus