A Novel Blind Source Separation Algorithm Based on Projected Natural Gradient

The behavior of over-determined blind source separation(ODBSS) algorithm with unknown number of sources, proposed by Cichocki et al. is analyzed. It is found it is the redundant movement of demixing matrix among an equivalent class that causes the divergence of the algorithm. We cancel the redundant component among natural gradient, which corresponding to the redundant movement of the demixing matrix, in an orthogonal projection approach, such that the projected nature gradient is orthogonal to the equivalent class mentioned above. For being free of redundant movement, the proposed projected natural gradient algorithm will converge stably. A practical redundancy detection method based on separating matrix is proposed. By embedding it into algorithm, the redundant outputs can be canceled simultaneously in separation process. Simulations show the proposed novel algorithm can perform the ODBSS with unknown and dynamically changing source number successfully and converge stably without redundant outputs. What's more, as some sources are added (removed), the algorithmneed not be restarted, the separated sources will be held in the original channels, only the add sources will appear in another channels (the removed sources will disappear).