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

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.