  We consider the problem of estimating a vector from its noisy measurements
using a prior specified only through a denoising function. Recent work on
plug-and-play priors (PnP) and regularization-by-denoising (RED) has shown the
state-of-the-art performance of estimators under such priors in a range of
imaging tasks. In this work, we develop a new block coordinate RED algorithm
that decomposes a large-scale estimation problem into a sequence of updates
over a small subset of the unknown variables. We theoretically analyze the
convergence of the algorithm and discuss its relationship to the traditional
proximal optimization. Our analysis complements and extends recent theoretical
results for RED-based estimation methods. We numerically validate our method
using several denoiser priors, including those based on convolutional neural
network (CNN) denoisers.
