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A collaborative framework for detecting the different sources in mixedsignals is presented in this paper. The approach is based on C-HiLasso, aconvex collaborative hierarchical sparse model, and proceeds as follows. First,we build a structured dictionary for mixed signals by concatenating a set ofsub-dictionaries, each one of them learned to sparsely model one of a set ofpossible classes. Then, the coding of the mixed signal is performed byefficiently solving a convex optimization problem that combines standardsparsity with group and collaborative sparsity. The present sources areidentified by looking at the sub-dictionaries automatically selected in thecoding. The collaborative filtering in C-HiLasso takes advantage of thetemporal/spatial redundancy in the mixed signals, letting collections ofsamples collaborate in identifying the classes, while allowing individualsamples to have different internal sparse representations. This collaborationis critical to further stabilize the sparse representation of signals, inparticular the class/sub-dictionary selection. The internal sparsity inside thesub-dictionaries, as naturally incorporated by the hierarchical aspects ofC-HiLasso, is critical to make the model consistent with the essence of thesub-dictionaries that have been trained for sparse representation of eachindividual class. We present applications from speaker and instrumentidentification and texture separation. In the case of audio signals, we usesparse modeling to describe the short-term power spectrum envelopes of harmonicsounds. The proposed pitch independent method automatically detects the numberof sources on a recording.

Collaborative Sources Identification in Mixed Signals via Hierarchical Sparse Modeling