I have just finished presenting my portion of a PhD course here at Aalborg University, during which I talked for nearly 8 hours about sparse approximation for audio and music signals, as well as adaptive concatenative sound synthesis — which I consider to be another “dictionary-based method”. My slides are available in four parts here, under teaching.
Now I can focus on continuing my experiments from the past week, and in particular the interesting directions commenter Phil Schniter provides. For instance, in the sparse signals greedy methods fail to reconstruct from compressive measurements, do we see a lack of dynamic range in the non-zero coefficients? Are there too many active elements too close together? More experiments will tell!