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.

中文翻译：

---

通过去噪进行块坐标正则化

我们考虑使用仅使用图像降噪器指定的先验从其噪声测量重建图像的问题。最近关于即插即用先验 (PnP) 和去噪正则化 (RED) 的工作表明，在一系列成像问题中，在此类先验下图像重建算法的最先进性能。在这项工作中，我们开发了一种新的块坐标 RED 算法，该算法将大规模估计问题分解为对未知变量的小子集进行更新的序列。我们从理论上分析了算法的收敛性，并讨论了它与传统近端优化的关系。我们的分析补充并扩展了基于 RED 的估计方法的最新理论结果。我们使用几种去噪先验对我们的方法进行了数值验证，包括基于深度神经网络的那些。