Alternating minimization algorithm with iteratively reweighted quadratic penalties for compressive transmission tomography

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

We propose an alternating minimization (AM) algorithm for estimating attenuation functions in X-ray transmission tomography using priors that promote sparsity in the pixel/voxel differences domain. As opposed to standard maximum-a-posteriori (MAP) estimation, we use the automatic relevance determination (ARD) framework. In the ARD approach, sparsity (or compressibility) is promoted by introducing latent variables which serve as the weights of quadratic penalties, with one weight for each pixel/voxel; these weights are then automatically learned from the data. This leads to an algorithm where the quadratic penalty is reweighted in order to effectively promote sparsity. In addition to the usual object estimate, ARD also provides measures of uncertainty (posterior variances) which are used at each iteration to automatically determine the trade-off between data fidelity and the prior, thus potentially circumventing the need for any tuning parameters. We apply the convex decomposition lemma in a novel way and derive a separable surrogate function that leads to a parallel algorithm. We propose an extension of branchless distance-driven forward/back-projections which allows us to considerably speed up the computations associated with the posterior variances. We also study the acceleration of the algorithm using ordered subsets.

Original languageEnglish
Title of host publicationMedical Imaging 2015
Subtitle of host publicationImage Processing
EditorsMartin A. Styner, Sebastien Ourselin
PublisherSPIE
ISBN (Electronic)9781628415032
DOIs
StatePublished - Jan 1 2015
EventMedical Imaging 2015: Image Processing - Orlando, United States
Duration: Feb 24 2015Feb 26 2015

Publication series

NameProgress in Biomedical Optics and Imaging - Proceedings of SPIE
Volume9413
ISSN (Print)1605-7422

Conference

ConferenceMedical Imaging 2015: Image Processing
CountryUnited States
CityOrlando
Period02/24/1502/26/15

Keywords

  • Alternating minimization algorithms
  • automatic relevance determination
  • edge preserving priors
  • helical CT
  • image reconstruction
  • posterior variance estimation
  • reweighted L2
  • separable surrogates

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