Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications [#265081] of Guillermo Sapiro

Papers Published

  1. Sprechmann, P; Ramirez, I; Cancela, P; Sapiro, G, Collaborative sources identification in mixed signals via hierarchical sparse modeling, IEEE International Conference on Acoustics Speech and Signal Processing (2011), pp. 5816-5819, ISSN 1520-6149 [doi]
    (last updated on 2017/12/11)

    A collaborative framework for detecting the different sources in mixed signals is presented in this paper. The approach is based on C-HiLasso, a convex collaborative hierarchical sparse model, and proceeds as follows. First, we build a structured dictionary for mixed signals by concatenating a set of sub-dictionaries, each one of them learned to sparsely model one of a set of possible classes. Then, the coding of the mixed signal is performed by efficiently solving a convex optimization problem that combines standard sparsity with group and collaborative sparsity. The present sources are identified by looking at the sub-dictionaries automatically selected in the coding. The collaborative filtering in C-HiLasso takes advantage of the temporal/spatial redundancy in the mixed signals, letting collections of samples collaborate in identifying the classes, while allowing individual samples to have different internal sparse representations. This collaboration is critical to further stabilize the sparse representation of signals, in particular the class/sub-dictionary selection. The internal sparsity inside the sub-dictionaries, as naturally incorporated by the hierarchical aspects of C-HiLasso, is critical to make the model consistent with the essence of the sub-dictionaries that have been trained for sparse representation of each individual class. We present applications from speaker and instrument identification and texture separation. In the case of audio signals, we use sparse modeling to describe the short-term power spectrum envelopes of harmonic sounds. The proposed pitch independent method automatically detects the number of sources on a recording. © 2011 IEEE.
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320