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) regularisation, 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.
翻译:解决成像逆差问题的方法通常将明确的数据概率功能与先前的分布方法结合起来,而前者则明确模拟了解决办法的预期特性。文献中探讨了许多前科,从表达当地特性的简单前科到更多涉及的在非局部规模上利用图像冗余的前科;由于偏离明确的建模,最近的一些工作提议并研究使用由图像去除算法界定的隐含前科。这种方法通常被称为“Plug & Play(PnP)”规范化,可以产生非常准确的结果,特别是当与基于共生神经网络的先进储量器相结合时。然而,对PnP Bayesian模型和算法的理论分析很困难,而关于这一专题的工作往往依赖不切实际的假设,即图像去除器的特性。本论文研究Bayesian模型和PnPps(PPP)先前的模型的最大估计值。我们首先考虑与存在、稳定性和充分定位有关的问题,然后为PnPstochaci 梯度模型下的数据计算结果的一致证据。