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A row-action alternative to the EM algorithm for maximizing likelihood in emission tomography.

J Browne1, A B de Pierro

  • 1Adv. Res. & Appl. Corp., Sunnyvale, CA.

IEEE Transactions on Medical Imaging
|January 1, 1996
PubMed
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A new Row-Action Maximum Likelihood Algorithm (RAMLA) significantly speeds up image reconstruction in emission computed tomography (ECT) compared to the standard Expectation Maximization (EM) algorithm, requiring fewer iterations for comparable results.

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Area of Science:

  • Medical Imaging
  • Nuclear Medicine
  • Computational Science

Background:

  • Maximum Likelihood (ML) estimation is preferred for radioactive distribution imaging in Emission Computed Tomography (ECT) due to superior image quality over Filtered Backprojection (FBP).
  • The Expectation Maximization (EM) algorithm is a common iterative ML method in ECT, but suffers from slow convergence, demanding extensive computation.
  • Slow convergence of EM necessitates computationally intensive processing for acceptable image reconstruction in ECT.

Purpose of the Study:

  • To introduce a novel Row-Action Maximum Likelihood Algorithm (RAMLA) as a faster alternative to the EM algorithm for Poisson likelihood maximization in ECT.
  • To analyze the convergence properties of RAMLA and compare its performance against the standard EM algorithm using computer simulations.
  • To investigate the relationship between RAMLA and modified Ordered Subsets EM (OS-EM) algorithms, and assess convergence to a Maximum Likelihood solution.

Main Methods:

  • Development and theoretical deduction of convergence properties for the Row-Action Maximum Likelihood Algorithm (RAMLA).
  • Computer simulations using simulated brain phantoms to compare RAMLA and Expectation Maximization (EM) algorithm performance in terms of likelihood increase and radionuclide uptake measurement.
  • Presentation and analysis of a modified fast Ordered Subsets EM (OS-EM) algorithm, demonstrating RAMLA as a special case and evaluating convergence properties.

Main Results:

  • RAMLA demonstrates an order of magnitude faster increase in Poisson likelihood in ECT compared to the standard EM algorithm in early iterations.
  • Early iterations (1-4) of RAMLA achieve performance in radionuclide uptake measurement comparable to significantly later iterations (45-80) of the EM algorithm.
  • RAMLA achieves likelihood values comparable to much later iterations of the EM algorithm within its initial iterations.
  • RAMLA is identified as a special case of a modified OS-EM algorithm, and this modification is shown to converge to a Maximum Likelihood solution, unlike standard OS-EM.

Conclusions:

  • RAMLA offers a substantial computational advantage over the EM algorithm for ECT image reconstruction, achieving faster convergence.
  • The proposed RAMLA provides a more efficient approach to obtaining high-quality images in ECT, reducing the need for extensive computation.
  • RAMLA's convergence to a Maximum Likelihood solution, unlike standard OS-EM, highlights its robustness and potential for improved diagnostic accuracy in ECT.