论文标题
大约运算符，并应用于音频介入
Approximal operator with application to audio inpainting
论文作者
论文摘要
Lieb and Stark（2018）在最近对音频表示的时频表示和结构化的稀疏方法的评估中，将特定的映射用作近端操作员。该操作员是迭代数值求解器的基本部分。但是，它们的映射是不当合理的。本文证明，它们的映射确实是近端运营商，并且还提供了适当的对应物。此外，可以将Lieb和Stark的操作员理解为适当映射的近似值是合理的。令人惊讶的是，在大多数情况下，与其适当的对应物相比，这种近似值（称为近似运算符）在音频插入方面提供了更好的数值结果，同时在计算上更有效。
In their recent evaluation of time-frequency representations and structured sparsity approaches to audio inpainting, Lieb and Stark (2018) have used a particular mapping as a proximal operator. This operator serves as the fundamental part of an iterative numerical solver. However, their mapping is improperly justified. The present article proves that their mapping is indeed a proximal operator, and also derives its proper counterpart. Furthermore, it is rationalized that Lieb and Stark's operator can be understood as an approximation of the proper mapping. Surprisingly, in most cases, such an approximation (referred to as the approximal operator) is shown to provide even better numerical results in audio inpainting compared to its proper counterpart, while being computationally much more effective.
