  Plug-and-play priors (PnP) is a powerful framework for regularizing imaging
inverse problems by using advanced denoisers within an iterative algorithm.
Recent experimental evidence suggests that PnP algorithms achieve
state-of-the-art performance in a range of imaging applications. In this paper,
we introduce a new online PnP algorithm based on the iterative
shrinkage/thresholding algorithm (ISTA). The proposed algorithm uses only a
subset of measurements at every iteration, which makes it scalable to very
large datasets. We present a new theoretical convergence analysis, for both
batch and online variants of PnP-ISTA, for denoisers that do not necessarily
correspond to proximal operators. We also present simulations illustrating the
applicability of the algorithm to image reconstruction in diffraction
tomography. The results in this paper have the potential to expand the
applicability of the PnP framework to very large and redundant datasets.
