Abstract 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.

中文翻译：

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应用于音频修复的近似算子

摘要 Lieb 和 Stark (2018) 在他们最近对时频表示和结构化稀疏方法进行音频修复的评估中使用了一个特定的映射作为近端算子。该运算符用作迭代数值求解器的基本部分。然而，他们的映射是不正确的。本文证明了它们的映射确实是一个近端算子，并且还推导出了其适当的对应物。此外，可以将 Lieb 和 Stark 的算子理解为正确映射的近似值是合理的。令人惊讶的是，在大多数情况下，这种近似（称为近似算子）与其适当的对应物相比，可以在音频修复中提供更好的数值结果，同时在计算上更有效。