What I mean more generally is this: To what extent can I expect a specific
sparse approximation process and dictionary to hinder the separation of several sources from a mixture decomposed into atoms? Will a sparse approximation
of a mixture make impossible an agglomeration
of atoms into the separated sources? More specifically, can I
expect to take a
matching pursuit decomposition of a speech and
music mixture using an overcomplete scale-time-frequency dictionary, and reconstruct the two sources using disjoint subsets of the
book? This is like taking a jigsaw puzzle of a nature scene and building up
just the trees, or just the clouds, from the pieces.
It is a naive assumption that each atom belongs to either the speech or music signal, especially for greedy pursuits that are prone to represent errors made in the model rather than anything real in the signal. But I wonder how bad of an assumption it is. Looks like I have got a new reading list for Paper of the Day (Po’D) next week!
N. Cho, Y. Shiu, and C.-C. J. Kuo, “Audio source separation with
matching pursuit and content-adaptive dictionaries (MP-CAD),” in Proc.
IEEE Workshop Appl. Signal Process. Audio Acoust., (New Paltz, NY),
pp. 287-290, Oct. 2007.
B. V. Gowreesunker and A. H. Tewfik, “Blind source separation using
monochannel overcomplete dictionaries,” in Proc. IEEE Int. Conf.
Acoust., Speech, Signal Process., (Las Vegas, NV), pp. 33-36, Mar. 2008.
R. Gribonval, “Sparse decomposition of stereo signals with matching pursuit and application to blind separation of more than two sources from a stereo mixture,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., vol. 3, (Orlando, FL), pp. 3057-3060, May 2002.
S. Lesage, S. Krstulovic, and R. Gribonval, “Underdetermined source
separation: Comparison of two approaches based on sparse
decompositions,” in Proc. Int. Conf. Independent Component Analysis
Blind Source Separation, (Charleston, South Carolina), pp. 633-640, Mar.
P. Sugden and N. Canagarajah, “Underdetermined noisy blind separation using dual matching pursuits,” in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Process., (Montreal, Quebec, Canada), pp. 557-560, May 2004.