Plug-and-play image reconstruction meets stochastic variance-reduced gradient methods

Plug-and-play (PnP) methods have recently emerged as a powerful framework for image reconstruction that can flexibly combine different physics-based observation models with data-driven image priors in the form of denoisers, and achieve state-of-the-art image reconstruction quality in many applications. In this paper, we aim to further improve the computational efficacy of PnP methods by designing a new algorithm that makes use of stochastic variance-reduced gradients (SVRG), a nascent idea to accelerate runtime in stochastic optimization. Compared with existing PnP methods using batch gradients or stochastic gradients, the new algorithm, called PnP-SVRG, achieves comparable or better accuracy of image reconstruction at a much faster computational speed. Extensive numerical experiments are provided to demonstrate the benefits of the proposed algorithm through the application of compressive imaging using partial Fourier measurements in conjunction with a wide variety of popular image denoisers.