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Technical Note: Convergence analysis of a polyenergetic SART algorithm.

T Humphries1

  • 1Department of Mathematics, Oregon State University, Corvallis, Oregon 97331.

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Summary
This summary is machine-generated.

The polyenergetic simultaneous algebraic reconstruction technique (pSART) shows empirical promise but lacks mathematical convergence proof. Numerical experiments suggest pSART generally converges similarly to SART in practical CT imaging scenarios.

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Area of Science:

  • Medical Imaging
  • Computational Science
  • Image Reconstruction

Background:

  • The simultaneous algebraic reconstruction technique (SART) is a standard algorithm for image reconstruction.
  • A polyenergetic SART (pSART) was proposed, modifying SART by incorporating a polyenergetic forward projection.
  • Empirical results for pSART are promising, but its mathematical convergence is not established.

Purpose of the Study:

  • To mathematically analyze the convergence properties of the polyenergetic SART (pSART) algorithm.
  • To determine if pSART is guaranteed to converge under various conditions.
  • To compare the convergence of pSART with the original SART algorithm.

Main Methods:

  • pSART was analyzed as a nonlinear fixed point iteration.
  • The Jacobian of the iteration was explicitly computed.
  • A necessary condition for convergence (spectral radius < 1) was investigated.
  • Numerical examples and realistic CT system matrices were used for experiments.

Main Results:

  • pSART is not guaranteed to converge in all general cases.
  • The convergence of pSART depends on the system matrix and attenuation modeling.
  • A numerical example demonstrated a case where the spectral radius exceeded one.
  • Experiments with realistic CT data suggest convergence is likely in practice.

Conclusions:

  • While not mathematically guaranteed, pSART demonstrates practical convergence.
  • The convergence rate of pSART is comparable to SART for typical CT imaging systems.
  • pSART remains a valuable tool for reconstructing polyenergetic CT data.