  We propose a unified modeling and algorithmic framework for audio restoration
problem. It encompasses analysis sparse priors as well as more classical
synthesis sparse priors, and regular sparsity as well as various forms of
structured sparsity embodied by shrinkage operators (such as social shrinkage).
The versatility of the framework is illustrated on two restoration scenarios:
denoising, and declipping. Extensive experimental results on these scenarios
highlight both the speedups of 20% or even more offered by the analysis sparse
prior, and the substantial declipping quality that is achievable with both the
social and the plain flavor. While both flavors overall exhibit similar
performance, their detailed comparison displays distinct trends depending
whether declipping or denoising is considered.
