用数据驱动先验提升线性逆问题的熵最大解法，理论更稳健。
Data-Driven Priors in the Maximum Entropy on the Mean Method for Linear Inverse Problems
- 基于数据训练先验，改进熵最大方法在逆问题中的表现
- 证明了经验均值几乎必然收敛，且给出不同先验解的误差估计
- 适用于图像去噪，尤其适合有高质量数据集的场景
我们建立了在近似（数据驱动）先验下，求解线性逆问题的最大熵于均值（MEM）方法的理论框架。证明了经验均值的几乎必然收敛性，并基于对数矩生成函数的上图距离，推导出不同先验μ与ν对应的MEM解之间的通用误差估计。该估计进一步给出了经验均值在期望意义下的收敛速率。我们在MNIST和Fashion-MNIST数据集上的去噪任务中验证了所提方法的有效性。
原文摘要 · Abstract (English)
We establish the theoretical framework for implementing the maximumn entropy on the mean (MEM) method for linear inverse problems in the setting of approximate (data-driven) priors. We prove a.s. convergence for empirical means and further develop general estimates for the difference between the MEM solutions with different priors $μ$ and $ν$ based upon the epigraphical distance between their respective log-moment generating functions. These estimates allow us to establish a rate of convergence in expectation for empirical means. We illustrate our results with denoising on MNIST and Fashion-MNIST data sets.
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