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 applied on the transform domain coefficients. We formulate the problem as a search for a saddle point and derive algorithms through a primal-dual framework. We also discuss how to modify the primal-dual algorithms in order to derive a simpler heuristic scheme.