Extrapolated Plug-and-Play Three-Operator Splitting Methods for Nonconvex Optimization with Applications to Image Restoration
<|reference_start|>Extrapolated Plug-and-Play Three-Operator Splitting Methods for Nonconvex Optimization with Applications to Image Restoration: This paper investigates the convergence properties and applications of the three-operator splitting method, also known as Davis-Yin splitting (DYS) method, integrated with extrapolation and Plug-and-Play (PnP) denoiser within a nonconvex framework. We first propose an extrapolated DYS method to effectively solve a class of structural nonconvex optimization problems that involve minimizing the sum of three possible nonconvex functions. Our approach provides an algorithmic framework that encompasses both extrapolated forward-backward splitting and extrapolated Douglas-Rachford splitting methods. To establish the convergence of the proposed method, we rigorously analyze its behavior based on the Kurdyka-{\L}ojasiewicz property, subject to some tight parameter conditions. Moreover, we introduce two extrapolated PnP-DYS methods with convergence guarantee, where the traditional regularization prior is replaced by a gradient step-based denoiser. This denoiser is designed using a differentiable neural network and can be reformulated as the proximal operator of a specific nonconvex functional. We conduct extensive experiments on image deblurring and image super-resolution problems, where our results showcase the advantage of the extrapolation strategy and the superior performance of the learning-based model that incorporates the PnP denoiser in terms of achieving high-quality recovery images.<|reference_end|>
@article{wu2024extrapolated,
    title={Extrapolated Plug-and-Play Three-Operator Splitting Methods for
  Nonconvex Optimization with Applications to Image Restoration},
    author={Zhongming Wu, Chaoyan Huang, Tieyong Zeng},
    journal={arXiv preprint arXiv:2403.01144},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.01144},
    primaryClass={math.NA cs.NA}
}