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Gregor J, Fessler JA. Comparison of SIRT and SQS for Regularized Weighted Least Squares Image Reconstruction. IEEE Trans Comput Imaging. 2015;1(1):44-55doi: 10.1109/TCI.2015.2442511.
Gregor, J., & Fessler, J. A. (2015). Comparison of SIRT and SQS for Regularized Weighted Least Squares Image Reconstruction. IEEE transactions on computational imaging, 1(1), 44-55. https://doi.org/10.1109/TCI.2015.2442511
Gregor, Jens, and Fessler, Jeffrey A. "Comparison of SIRT and SQS for Regularized Weighted Least Squares Image Reconstruction." IEEE transactions on computational imaging vol. 1,1 (2015): 44-55. doi: https://doi.org/10.1109/TCI.2015.2442511
Gregor J, Fessler JA. Comparison of SIRT and SQS for Regularized Weighted Least Squares Image Reconstruction. IEEE Trans Comput Imaging. 2015 Mar;1(1):44-55. doi: 10.1109/TCI.2015.2442511. Epub 2015 Jun 05. PMID: 26478906; PMCID: PMC4608542.
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IEEE Trans Comput Imaging. 2015 Mar;1(1):44-55. doi: 10.1109/TCI.2015.2442511. Epub 2015 Jun 05.

Comparison of SIRT and SQS for Regularized Weighted Least Squares Image Reconstruction.

IEEE transactions on computational imaging

Jens Gregor, Jeffrey A Fessler

Affiliations

  1. Dept. of Electrical Engr. & Computer Science, Univ. of Tennessee, Knoxville, TN 37996.
  2. Dept. of Electrical Engr. & Computer Science, Univ. of Michigan, Ann Arbor, MI 48109.

PMID: 26478906 PMCID: PMC4608542 DOI: 10.1109/TCI.2015.2442511

Abstract

Tomographic image reconstruction is often formulated as a regularized weighted least squares (RWLS) problem optimized by iterative algorithms that are either inherently algebraic or derived from a statistical point of view. This paper compares a modified version of SIRT (Simultaneous Iterative Reconstruction Technique), which is of the former type, with a version of SQS (Separable Quadratic Surrogates), which is of the latter type. We show that the two algorithms minimize the same criterion function using similar forms of preconditioned gradient descent. We present near-optimal relaxation for both based on eigenvalue bounds and include a heuristic extension for use with ordered subsets. We provide empirical evidence that SIRT and SQS converge at the same rate for all intents and purposes. For context, we compare their performance with an implementation of preconditioned conjugate gradient. The illustrative application is X-ray CT of luggage for aviation security.

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