Adaptive blind separation with an unknown number of sources

The blind source separation (BSS) problem with an unknown number of sources is an important practical issue that is usually skipped by assuming that the source number n is known and equal to the number m of sensors. This letter studies the general BSS problem satisfying m greater than or equal to n. First, it is shown that the mutual information of outputs of the separation network is a cost function for BSS, provided that the mixing matrix is of full column rank and the m x m separating matrix is nonsingular. The mutual information reaches its local minima at the separation points, where the m outputs consist of n desired source signals and m - n redundant signals. Second, it is proved that the natural gradient algorithm proposed primarily for complete BSS (m = n) can be generalized to deal with the overdetermined BSS problem (m > n), but it would diverge inevitably due to lack of a stationary point. To overcome this shortcoming, we present a modified algorithm, which can perform BSS steadily and provide the desired source signals at specified channels if some matrix is designed properly. Finally, the validity of the proposed algorithm is confirmed by computer simulations on artificially synthesized data.