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An accelerated preconditioned proximal gradient algorithm with a generalized Nesterov momentum for PET image

Yizun Lin1, Yongxin He1, C Ross Schmidtlein2

  • 1Department of Mathematics, Jinan University, Guangzhou 510632, China.

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Summary

This study introduces an accelerated preconditioned proximal gradient algorithm (APPGA) for positron emission tomography (PET) image reconstruction. APPGA demonstrates faster convergence rates and superior performance compared to existing methods, enhancing PET imaging analysis.

Keywords:
accelerated preconditioned proximal gradient algorithmimage reconstructionpositron emission tomographytotal variation

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Area of Science:

  • Medical Imaging
  • Computational Science
  • Optimization Theory

Background:

  • Positron Emission Tomography (PET) image reconstruction requires efficient algorithms to handle complex models.
  • Differentiable regularizers are crucial for improving PET image quality but pose optimization challenges.
  • Existing methods may lack the convergence speed and efficiency needed for high-order regularization models.

Purpose of the Study:

  • To develop and analyze an accelerated preconditioned proximal gradient algorithm (APPGA) for PET image reconstruction.
  • To establish the convergence properties of APPGA using the generalized Nesterov (GN) momentum scheme.
  • To enhance the algorithm's efficiency for higher-order isotropic total variation (ITV) regularized PET models.

Main Methods:

  • Development of an Accelerated Preconditioned Proximal Gradient Algorithm (APPGA).
  • Theoretical analysis of APPGA convergence rates using generalized Nesterov (GN) momentum.
  • Application of APPGA to a smoothed higher-order isotropic total variation (ITV) regularized PET model.

Main Results:

  • APPGA converges to a minimizer with rates of o(1/k^(2ω)) for function value and o(1/k^ω) for iterate distance.
  • Increasing the GN momentum power parameter (ω) progressively accelerates APPGA convergence.
  • APPGA significantly outperforms preconditioned proximal gradient and Krasnoselskii-Mann algorithms.

Conclusions:

  • APPGA offers an efficient and effective solution for PET image reconstruction with differentiable regularizers.
  • The GN momentum scheme enhances convergence speed, particularly for higher-order ITV regularized models.
  • The proposed framework can be extended to more complex optimization problems with multiple non-differentiable terms.