Résumé : We propose the Audio Inpainting framework that recovers audio intervals distorted due to impairments such as impulsive noise, clipping, and packet loss. In this framework, the distorted samples are treated as missing, and the signal is decomposed into overlapping time-domain frames. The restoration problem is then formulated as an inverse problem per audio frame. Sparse representation modeling is employed per frame, and each inverse problem is solved using the Orthogonal Matching Pursuit algorithm together with a discrete cosine or a Gabor dictionary. The performance of this algorithm is shown to be comparable or better than state-of-the-art methods when blocks of samples of variable durations are missing. We also demonstrate that the size of the block of missing samples, rather than the overall number of missing samples, is a crucial parameter for high quality signal restoration. We further introduce a constrained Matching Pursuit approach for the special case of audio declipping that exploits the sign pattern of clipped audio samples and their maximal absolute value, as well as allowing the user to specify the maximum amplitude of the signal. This approach is shown to outperforms state-of-the-art and commercially available methods for audio declipping.