Sparsity in signal representation requires two aspects: a large dictionary of potential basis functions that can be adapted to a variety of waveforms, and an efficient means of selecting these functions and reconstructing the corresponding signal representation. In this talk we introduce a family of time-frequency systems termed superposition frames that enable adaptivity and also, in contrast to many adaptive analysis systems, admit the property of fast overlap-add reconstruction. We prove several properties of this family and discuss specific examples of adaptation criteria in the context of sparse audio processing.
(Joint work with Daniel Rudoy and Prabahan Basu.)