Plug-and-play (PnP) prior is a well-known class of methods for solving imaging inverse problems by computing fixed-points of operators combining physical measurement models and learned image denoisers. While PnP methods have been extensively used for image recovery with known measurement operators, there is little work on PnP for solving blind inverse problems. We address this gap by presenting a new block-coordinate PnP (BC-PnP) method that efficiently solves this joint estimation problem by introducing learned denoisers as priors on both the unknown image and the unknown measurement operator. We present a new convergence theory for BC-PnP compatible with blind inverse problems by considering nonconvex data-fidelity terms and expansive denoisers. Our theory analyzes the convergence of BC-PnP to a stationary point of an implicit function associated with an approximate minimum mean-squared error (MMSE) denoiser. We numerically validate our method on two blind inverse problems: automatic coil sensitivity estimation in magnetic resonance imaging (MRI) and blind image deblurring. Our results show that BC-PnP provides an efficient and principled framework for using denoisers as PnP priors for jointly estimating measurement operators and images.

翻译：即插即用（Plug-and-Play, PnP）先验是一类著名的成像逆问题求解方法，通过计算结合物理测量模型与学习型图像去噪器的算子不动点来恢复图像。尽管PnP方法已广泛应用于已知测量算子的图像恢复任务，但针对盲逆问题的PnP研究仍较为匮乏。我们通过提出一种新的块坐标PnP（BC-PnP）方法填补了这一空白：该方法将学习型去噪器同时作为未知图像和未知测量算子的先验，从而高效求解这一联合估计问题。我们建立了兼容盲逆问题的BC-PnP新收敛理论，该理论能够处理非凸数据保真项与扩张型去噪器。理论分析表明，BC-PnP可收敛至与近似最小均方误差（MMSE）去噪器相关联的隐函数的稳定点。我们通过两个盲逆问题对方法进行数值验证：磁共振成像（MRI）中的自动线圈灵敏度估计与盲图像去模糊。结果表明，BC-PnP为使用去噪器作为PnP先验联合估计测量算子与图像提供了高效且规范化的框架。