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Block Coordinate Regularization by Denoising

We consider the problem of reconstructing an image from its noisy measurements using a prior specified only with an image denoiser. Recent work on plug-and-play priors (PnP) and regularization by denoising (RED) has shown the state-of-the-art performance of image reconstruction algorithms under such priors in a range of imaging problems. 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 denoising priors, including those based on deep neural nets.