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：即插即用先验是一类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求解成像逆问题的著名方法。尽管PnP方法已被广泛用于已知测量算子的图像恢复，但针对求解盲逆问题的PnP研究尚为空白。为填补这一空白，我们提出一种新的块坐标PnP方法，该方法通过引入学习型去噪器作为未知图像和未知测量算子的联合先验，有效解决了这一联合估计问题。我们提出了与盲逆问题兼容的BC-PnP新收敛理论，该理论可处理非凸数据保真项与膨胀型去噪器。该理论分析了BC-PnP收敛到某近似最小均方误差去噪器关联隐函数驻点的过程。我们在两个盲逆问题上进行了数值验证：磁共振成像中的自动线圈灵敏度估计与盲图像去模糊。实验结果表明，BC-PnP为利用去噪器作为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。