物理信息在即插即用（PnP）方法中的作用：基于MMSE和神经网络去噪器的恢复保证
Physics Matters in PnP: Recovery Guarantees with the MMSE and NN Denoisers
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中文总结 AI 辅助
该研究针对线性不适定问题，改进即插即用（PnP）方法，结合MMSE估计器或神经网络去噪器，推导恢复保证，证明去噪器选择需依赖正向模型，拓展了PnP方法的理论分析。
中文摘要 AI 辅助
我们研究针对线性不适定问题的即插即用（Plug and Play, PnP）方法的前向-后向拆分版本，该方法以最小均方误差（Minimum Mean Square Error, MMSE）估计器作为去噪器。与现有文献不同，我们考虑专门针对（退化）高斯噪声的估计器，这类噪声可能具有非对角协方差矩阵。我们还偏离经典迭代方式，用将观测噪声与MMSE估计器噪声关联的线性算子替代下降步骤的部分内容。在温和假设下，我们推导了去噪器的若干性质，并证明了该迭代在逐点意义及潜在概率分布的Wasserstein距离下的恢复保证。关键是，我们的分析表明，去噪器不能以与物理无关的方式选择，即不能独立于正向模型。我们将结果扩展到MMSE去噪器由神经网络参数化的情况，并推导了相应的恢复界。
英文摘要
We investigate the forward-backward-splitting version of the Plug and Play (PnP) method for linear ill-posed problems with MMSE estimators as denoisers. In contrast to existing literature, we consider estimators which are specialized for (degenerate) Gaussian noise with possibly non-diagonal covariance matrices. We further deviate from the classical iteration by replacing parts of the descent step with a linear operator that relates the observation noise to that of the MMSE estimator. Under mild assumptions, we derive several properties of the denoiser and prove recovery guarantees of the iteration both pointwise and in the Wasserstein distance of the underlying probability distributions. Crucially, our analysis shows that the denoiser cannot be chosen in a physics-agnostic way, that is, independently of the forward model. We extend our results to the case where the MMSE denoiser is parametrized by a neural network and derive the corresponding recovery bounds.
