  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.
