论文标题
插件图像重建是一种收敛正则化方法
Plug-and-Play image reconstruction is a convergent regularization method
论文作者
论文摘要
非唯一性和不稳定性是图像重建过程的特征。结果，有必要开发可用于计算可靠近似解决方案的正则化方法。正则化方法提供了稳定重建家族，随着噪声水平往往为零，该家族会收敛到无噪声问题的精确解决方案。标准正则化技术是由变异图像重建定义的，该技术可最大程度地减少正规器增强的数据差异。实际的数值实现利用了迭代方法，通常涉及正规器的近端映射。近年来，已开发出插件图像重建（PNP）是一种对基于更通用的图像DeOisers替换近端映射的变化方法的新的强大概括。虽然PNP迭代效果取得了出色的结果，但到目前为止，在正则化意义上均未研究稳定性和收敛性。在这项工作中，我们通过考虑PNP迭代的家庭，均伴有其自己的DeNoiser来扩展PNP的想法。作为我们的主要理论结果，我们表明这种PNP重建导致稳定和收敛的正则化方法。这首先表明PNP在数学上是合理的，用于鲁棒图像重建作为变异方法
Non-uniqueness and instability are characteristic features of image reconstruction processes. As a result, it is necessary to develop regularization methods that can be used to compute reliable approximate solutions. A regularization method provides of a family of stable reconstructions that converge to an exact solution of the noise-free problem as the noise level tends to zero. The standard regularization technique is defined by variational image reconstruction, which minimizes a data discrepancy augmented by a regularizer. The actual numerical implementation makes use of iterative methods, often involving proximal mappings of the regularizer. In recent years, Plug-and-Play image reconstruction (PnP) has been developed as a new powerful generalization of variational methods based on replacing proximal mappings by more general image denoisers. While PnP iterations yield excellent results, neither stability nor convergence in the sense of regularization has been studied so far. In this work, we extend the idea of PnP by considering families of PnP iterations, each being accompanied by its own denoiser. As our main theoretical result, we show that such PnP reconstructions lead to stable and convergent regularization methods. This shows for the first time that PnP is mathematically equally justified for robust image reconstruction as variational methods
