We introduce a unified framework for the restoration of distorted audio data, leveraging the Image Inpainting concept and covering existing audio applications. In this framework, termed Audio Inpainting, the distorted data is considered missing and its location is assumed to be known. We further introduce baseline approaches based on sparse representations. For this new audio inpainting concept, we provide reproducible-research tools including: the handling of audio inpainting tasks as inverse problems, embedded in a frame-based scheme similar to patch-based image processing; several experimental settings; speech and music material; OMP-like algorithms, with two dictionaries, for general audio inpainting or specifically-enhanced declipping.