Fast PET Reconstruction with Variance Reduction and Prior-Aware Preconditioning.

Area of Science:

• Medical Imaging
• Computational Science
• Optimization Algorithms

Background:

• Positron Emission Tomography (PET) image reconstruction is crucial for clinical diagnosis.
• Relative Difference Prior (RDP) regularization improves PET image quality over conventional methods like OSEM.
• The PET Rapid Image Reconstruction Challenge (PETRIC) 2024 focused on accelerating RDP-regularized PET reconstruction.

Purpose of the Study:

• To investigate and optimize subset-based methods for RDP-regularized PET image reconstruction.
• To evaluate the impact of incorporating prior information into preconditioners for convergence speed and stability.
• To compare the performance of various stochastic optimization algorithms for PET reconstruction.

Main Methods:

• Simulation experiments and analysis of real brain PET scans from PETRIC 2024.
• Comparison of Stochastic Gradient Descent (SGD), Stochastic Averaged Gradient Amelioré (SAGA), and Stochastic Variance Reduced Gradient (SVRG) algorithms.
• Evaluation under varying data noise levels (count statistics) and regularization strengths.

Main Results:

• Incorporating the RDP into the preconditioner is essential for achieving rapid and stable convergence.
• SVRG and SAGA algorithms demonstrated superior performance compared to SGD.
• SVRG showed a slight overall advantage in reconstruction speed and stability.

Conclusions:

• Effective PET image reconstruction relies on optimizing the interplay between regularization priors and algorithmic preconditioners.
• Stochastic optimization methods, particularly SVRG, offer significant improvements for accelerated RDP-regularized PET reconstruction.
• The findings directly informed the development of the winning algorithms for the PETRIC 2024 challenge.