Plug-and-play priors (PnP) is a methodology for regularized image reconstruction that specifies the prior through an image denoiser. While PnP algorithms are well understood for denoisers performing maximum a posteriori probability (MAP) estimation, they have not been analyzed for the minimum mean squared error (MMSE) denoisers. This letter addresses this gap by establishing the first theoretical convergence result for the iterative shrinkage/thresholding algorithm (ISTA) variant of PnP for MMSE denoisers. We show that the iterates produced by PnP-ISTA with an MMSE denoiser converge to a stationary point of some global cost function. We validate our analysis on sparse signal recovery in compressive sensing by comparing two types of denoisers, namely the exact MMSE denoiser and the approximate MMSE denoiser obtained by training a deep neural net.

中文翻译：

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即插即用先验与 MMSE 降噪器的可证明收敛

即插即用先验 (PnP) 是一种用于正则化图像重建的方法，它通过图像降噪器指定先验。虽然 PnP 算法对于执行最大后验概率 (MAP) 估计的降噪器很好理解，但尚未针对最小均方误差 (MMSE) 降噪器对​​其进行分析。这封信通过为 MMSE 降噪器的 PnP 的迭代收缩/阈值算法 (ISTA) 变体建立第一个理论收敛结果来解决这一差距。我们展示了由带有 MMSE 降噪器的 PnP-ISTA 产生的迭代收敛到某个全局成本函数的驻点。我们通过比较两种类型的降噪器，即精确 MMSE 降噪器和通过训练深度神经网络获得的近似 MMSE 降噪器，验证了我们对压缩感知中稀疏信号恢复的分析。