发表机构
University of California, San Diego（加利福尼亚大学圣地亚哥分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文阐明学习近端网络的理论基础，扩展激活函数类别，并研究平均与缩放两种控制学习先验的机制，刻画平均诱导正则化器并开发缩放近端算子的收敛评估方法。
AI 中文摘要
即插即用（PnP）方法用学习得到的去噪器替代近端算子，虽然能产生最先进的重建质量，但牺牲了近端方法的变分解释和收敛保证。学习近端网络（LPNs）通过设计去噪器架构使其恰好为正则化器的近端算子来解决这一问题。在这项工作中，我们阐明了LPNs的理论基础，并将框架扩展到更广泛的激活函数类别。随后，我们研究了控制学习先验的两种实用机制：（i）将LPN与恒等映射进行平均，这是PnP方法中常见的启发式方法，以及（ii）直接缩放由近端算子隐式诱导的正则化器。特别地，我们刻画了由平均操作诱导的正则化器，并开发了一种用于评估缩放近端算子的收敛方法。
英文摘要
Plug-and-Play (PnP) methods replace proximal operators with learned denoisers, which produce state-of-the-art reconstruction quality, but sacrifice the variational interpretation and convergence guarantees of proximal methods. Learned Proximal Networks (LPNs) address this problem by designing the denoiser architecture so that it is exactly the proximal operator of a regularizer. In this work, we clarify the theoretical foundations of LPNs and extend the framework to a broader class of activation functions. We then study two practical mechanisms for controlling the learned prior: (i) averaging the LPN with the identity, a common heuristic in PnP methods, and (ii) directly scaling the implicit regularizer induced by the proximal operator. In particular, we characterize the regularizer induced by averaging and develop a convergent method for evaluating the scaled proximal operator.
