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Convergent incremental optimization transfer algorithms: application to tomography.

Sangtae Ahn1, Jeffrey A Fessler, Doron Blatt

  • 1Electrical Engineering and Computer Science Department, University of Michigan, Ann Arbor 48109-2122, USA. sangtaea@usc.edu

IEEE Transactions on Medical Imaging
|March 10, 2006
PubMed
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This study introduces incremental optimization transfer, a new framework for transmission tomography image reconstruction. It presents the first convergent ordered subsets algorithm for penalized-likelihood reconstruction, accelerating convergence without relaxation parameters.

Area of Science:

  • Medical Imaging
  • Computational Science

Background:

  • Ordered subsets (OS) algorithms for transmission tomography image reconstruction lack convergence guarantees.
  • Existing convergent OS algorithms in emission tomography include relaxation parameters or incremental expectation-maximization (EM).

Purpose of the Study:

  • To develop a novel, convergent OS-type image reconstruction algorithm for transmission tomography.
  • To generalize the incremental EM approach for improved convergence and broader applicability.

Main Methods:

  • Introduced a general framework called "incremental optimization transfer."
  • Developed the first convergent OS-type algorithm for penalized-likelihood (PL) transmission image reconstruction using separable paraboloidal surrogates (SPS).
  • Proposed a hybrid approach combining OS with a large number of subsets and the new "transmission incremental optimization transfer (TRIOT)" algorithm.

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Main Results:

  • The proposed algorithms ensure global convergence without needing relaxation parameters.
  • The TRIOT algorithm demonstrates faster convergence in increasing the PL objective compared to nonincremental ordinary SPS and OS-SPS.
  • The use of separable paraboloidal surrogates (SPS) allows for closed-form maximization steps.

Conclusions:

  • Incremental optimization transfer provides a generalized framework for developing convergent OS algorithms.
  • The TRIOT algorithm is an effective and convergent method for penalized-likelihood transmission image reconstruction, offering accelerated convergence rates.