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An Investigation of Stochastic Variance Reduction Algorithms for Relative Difference Penalized 3D PET Image

Robert Twyman, Simon Arridge, Zeljko Kereta

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    |August 31, 2022
    PubMed
    Summary
    This summary is machine-generated.

    Stochastic variance reduction gradient algorithms like SAGA and SVRG improve Positron Emission Tomography (PET) image reconstruction by converging faster and with less parameter tuning than BSREM, especially for low-count data.

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    Area of Science:

    • Medical Imaging
    • Computational Science
    • Applied Mathematics

    Background:

    • Penalised PET image reconstruction algorithms often use subsets for acceleration, but this can lead to limit cycle behaviour in later iterations.
    • Existing methods to achieve convergence, like relaxed step sizes, require heuristic parameter selection impacting image quality and convergence rates.

    Purpose of the Study:

    • To adapt and apply stochastic variance reduction gradient (SVRG) algorithms for Positron Emission Tomography (PET) image reconstruction.
    • To numerically compare the convergence performance of SAGA and SVRG algorithms against the popular BSREM algorithm.

    Main Methods:

    • Investigated SAGA (Stochastic Average Gradient) and SVRG (Stochastic Variance Reduced Gradient) algorithms for PET image reconstruction using a relative difference penalty.
    • Utilized Monte Carlo simulated data and a patient dataset for 3D PET acquisitions.
    • Explored the impact of subset number, preconditioning, and step size methods on convergence.

    Main Results:

    • SAGA and SVRG showed reduced voxel value variations and less reliance on step size hyper-parameter selection compared to BSREM when using constant preconditioning.
    • SAGA and SVRG demonstrated significantly faster convergence to the penalised maximum likelihood solution than BSREM.
    • These improvements were particularly notable in low-count data scenarios.

    Conclusions:

    • SAGA and SVRG are effective alternatives for PET image reconstruction, offering improved convergence speed and stability.
    • These algorithms reduce the sensitivity to parameter tuning, enhancing the reliability of PET image reconstruction, especially in challenging low-count situations.