论文标题
插件ISTA与内核Denoiser收敛
Plug-and-play ISTA converges with kernel denoisers
论文作者
论文摘要
插件播放（PNP）方法是图像正则化的最新范例，其中迭代算法中的近端运算符（与某些给定的正规器相关联）被强大的DeNoiser替换。从算法上讲，这涉及重复反转（正向模型），并降解直至收敛。值得注意的是，PNP正则化为多种恢复应用带来了令人鼓舞的结果。但是，在这方面的一个基本问题是PNP迭代的理论收敛性，因为该算法并非严格源自优化框架。这个问题已在最近的作品中进行了调查，但是仍然存在许多未解决的问题。例如，如果我们在ISTA框架（PNP-ISTA）中使用通用的内核Deoisiser（例如非局部均值），则不知道是否可以保证收敛。我们证明，在合理的假设下，PNP-AISTA的固定点收敛确实可以保证在诸如deblurring，inpherting和reprassolution等线性的反相反问题（假设可以证明对内化）。我们将我们的理论发现与现有结果进行比较，以数值验证它们，并解释其实际相关性。
Plug-and-play (PnP) method is a recent paradigm for image regularization, where the proximal operator (associated with some given regularizer) in an iterative algorithm is replaced with a powerful denoiser. Algorithmically, this involves repeated inversion (of the forward model) and denoising until convergence. Remarkably, PnP regularization produces promising results for several restoration applications. However, a fundamental question in this regard is the theoretical convergence of the PnP iterations, since the algorithm is not strictly derived from an optimization framework. This question has been investigated in recent works, but there are still many unresolved problems. For example, it is not known if convergence can be guaranteed if we use generic kernel denoisers (e.g. nonlocal means) within the ISTA framework (PnP-ISTA). We prove that, under reasonable assumptions, fixed-point convergence of PnP-ISTA is indeed guaranteed for linear inverse problems such as deblurring, inpainting and superresolution (the assumptions are verifiable for inpainting). We compare our theoretical findings with existing results, validate them numerically, and explain their practical relevance.
