A Feedback Approach and Its Learning Algorithm for Over Complete Blind Source Separation

In blind source separation (BSS) applications, the number of the signal sources is not known. When the number of the sensors is less than that of the signal sources, this problem is called over complete BSS´ (OC-BSS), which is a difficult problem due to lack of information in observations. In this paper, a feedback approach and its learning algorithm are proposed for the OC-BSS. The number of the outputs of an umixing block is set to be equal to that of the sensors. By assuming some condition, at least one output can separate a single signal source. This output is fed back to the inputs of the unmixing block, and is subtracted from the observations, in order to reduce the number of equivalent signal sources. Two kinds of feedback methods are proposed. One of them is direct subtraction and the other is sample elimination based on histogram of the feedback signal and the observed signals. The modified observations are further separated. The same process is repeated until all signal sources are separated. Performance of the proposed method is evaluated through computer simulation. The proposed method can improve a signal to interference ratio by the several dB compared to the conventional methods