Primal-dual algorithms for audio decomposition using mixed norms

We consider the problem of decomposing audio into components that have different time frequency characteristics. For this, we model the components using different transforms and mixed norms. While recent works concentrate on the synthesis prior formulation, we consider both the analysis and synthesis prior formulations. We derive algorithms for both formulations through a primal-dual framework. We also discuss how to modify the primal-dual algorithms in order to derive a simpler heuristic scheme.