On Maximum a Posteriori Estimation with Plug & Play Priors and Stochastic Gradient Descent
On Maximum a Posteriori Estimation with Plug & Play Priors and Stochastic Gradient Descent
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DOI：
10.1007/s10851-022-01134-7
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发表时间：
2023-01-18
影响因子：
2
通讯作者：
Pereyra, Marcelo
中科院分区：
文献类型：
--
作者：
Laumont, Remi;De Bortoli, Valentin;Pereyra, Marcelo
贝叶斯方法解决成像逆问题通常结合联合收割机一个明确的数据似然函数与先验分布，明确模型的预期性能的解决方案。在文献中已经探索了许多种先验，从简单的表示局部属性的先验到更多涉及的在非局部尺度上利用图像冗余的先验。在偏离显式建模，最近的几个作品提出并研究了使用的图像去噪算法定义的隐式先验。这种方法通常被称为即插即用（Plug & Play，简称PSTO）正则化，可以提供非常准确的结果，特别是当与基于卷积神经网络的最先进的去噪器相结合时。然而，Pestrian贝叶斯模型和算法的理论分析是困难的，并且对该主题的工作往往依赖于对图像去噪器的属性的不切实际的假设。本文研究了具有Pennsylvania先验的贝叶斯模型的最大后验（MAP）估计。我们首先考虑相关的问题的存在性，稳定性和适定性，然后提出了一个收敛证明MAP计算PnP随机梯度下降（PnP-SGD）在现实的假设下使用的去噪。我们报告了一系列的成像实验证明PnP-SGD以及与其他PnP-SGD计划的比较。
Bayesian methods to solve imaging inverse problems usually combine an explicit data likelihood function with a prior distribution that explicitly models expected properties of the solution. Many kinds of priors have been explored in the literature, from simple ones expressing local properties to more involved ones exploiting image redundancy at a non-local scale. In a departure from explicit modelling, several recent works have proposed and studied the use of implicit priors defined by an image denoising algorithm. This approach, commonly known as Plug & Play (PnP) regularization, can deliver remarkably accurate results, particularly when combined with state-of-the-art denoisers based on convolutional neural networks. However, the theoretical analysis of PnP Bayesian models and algorithms is difficult and works on the topic often rely on unrealistic assumptions on the properties of the image denoiser. This papers studies maximum a posteriori (MAP) estimation for Bayesian models with PnP priors. We first consider questions related to existence, stability and well-posedness and then present a convergence proof for MAP computation by PnP stochastic gradient descent (PnP-SGD) under realistic assumptions on the denoiser used. We report a range of imaging experiments demonstrating PnP-SGD as well as comparisons with other PnP schemes.