Underdetermined noisy blind separation using dual matching pursuits

Underdetermined blind source separation is a key application in audio where it is desirable to extract multiple sources from a stereo recording. A new variant on the stereo matching pursuit, the dual matching pursuit, is presented whereby independent matching pursuits are run on both channels of a stereo mixture of greater than two sources. By identifying correlating atoms from each decomposition, a histogram plot is applied to identify the position of each source in the stereo image and the atoms grouped to recover the original signals. To improve the atomic correlation between channels, a fixed overcomplete representation for each of the signal types present in a mixture is obtained by applying a learning algorithm to existing sources of that type and reducing the redundancy in the resulting basis set via a correlation-based algorithm. The resulting dictionaries are then used as a time-frequency basis for the independent matching pursuits. The results show improved separation quality compared to the dual matching pursuit with mathematical time-frequency dictionaries. The noise immunity of this method due to the use of overcomplete representations is also demonstrated showing that the system can withstand mixture signal-to-noise ratios down to 30 dB.