Fast PET reconstruction with variance reduction and prior-aware preconditioning.

Area of Science:

• Medical Imaging
• Computational Science
• Nuclear Medicine

Background:

• Positron Emission Tomography (PET) image reconstruction is crucial for clinical diagnosis.
• Relative Difference Prior (RDP) regularization improves reconstruction quality over conventional methods.
• Fast and stable reconstruction is essential for clinical workflow efficiency.

Purpose of the Study:

• To investigate and optimize subset-based reconstruction methods for PET using RDP.
• To evaluate the impact of incorporating prior effects into the preconditioner on convergence speed and stability.
• To compare the performance of various stochastic optimization algorithms for PET reconstruction.

Main Methods:

• Evaluated subset-based optimization algorithms including Stochastic Gradient Descent (SGD), SAGA, and SVRG.
• Utilized simulated PET data and real brain PET scans from the PET Rapid Image Reconstruction Challenge (PETRIC) 2024.
• Assessed performance across varying noise levels (count statistics) and regularization strengths.

Main Results:

• Incorporating the prior effect into the preconditioner is critical for fast and stable convergence in RDP-regularized PET reconstruction.
• SVRG and SAGA algorithms demonstrated superior performance compared to SGD.
• SVRG exhibited a slight overall advantage in reconstruction speed and stability.

Conclusions:

• The study highlights the importance of preconditioner design for efficient PET image reconstruction.
• SVRG and SAGA are effective stochastic optimization methods for RDP-regularized PET reconstruction.
• The findings contributed to the development of winning algorithms in the PETRIC 2024 challenge.