Faster PET reconstruction with non-smooth priors by randomization and preconditioning

Area of Science:

• Medical Imaging
• Computational Science
• Optimization Theory

Background:

• Positron emission tomography (PET) data is large, posing computational challenges.
• Non-smooth optimization problems are difficult to solve for large-scale clinical PET data.
• Existing algorithms for non-smooth problems do not scale effectively.

Purpose of the Study:

• To develop and validate advanced randomized optimization algorithms for PET image reconstruction.
• To address the computational challenges of non-smooth priors in clinical PET data.
• To enable the clinical translation of advanced mathematical imaging tools.

Main Methods:

• Utilized big data machine learning-inspired randomized optimization algorithms.
• Applied algorithms to solve PET reconstruction problems with various non-smooth priors (e.g., total variation).
• Employed random data subset selection for variable updates, demonstrating convergence properties.

Main Results:

• The proposed algorithm efficiently solves non-smooth optimization problems for large PET datasets.
• Demonstrated convergence for proper subset selection in randomized optimization.
• Showed that approximately ten projections and backprojections are sufficient for MAP optimization on real PET data.

Conclusions:

• Advanced randomized optimization algorithms can effectively handle large-scale, non-smooth PET reconstruction problems.
• The developed algorithm is computationally efficient, facilitating routine clinical practice.
• This work bridges the gap between advanced mathematical imaging and clinical PET data analysis.