Block Coordinate Regularization by Denoising
This work addresses computational scalability in imaging tasks for researchers and practitioners, but it is incremental as it builds on existing RED methods.
The authors tackled the problem of large-scale vector estimation from noisy measurements using denoising-based priors, by developing a block coordinate RED algorithm that decomposes the problem into smaller updates, and they theoretically analyzed its convergence and validated it numerically with CNN denoisers.
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.