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The contrast function remains to be an open problem in blind source separation (BSS) when the number of source signals is unknown and/or dynamically changed. The paper studies this problem and proves that the mutual information is still the contrast function for BSS if the mixing matrix is of full column rank. The mutual information reaches its minimum at the separation points, where the random outputs of the BSS system are the scaled and permuted source signals, while the others are zero outputs. Using the property that the transpose of the mixing matrix and a matrix composed by m observed signals have the indentical null space with probability one, a practical method, which can detect the unknown number of source signals n, ulteriorly traces the dynamical change of the sources number with a few of data, is proposed. The effectiveness of the proposed theorey and the developed novel algorithm is verified by adaptive BSS simulations with unknown and dynamically changing number of source signals.
The contrast function remains to be an open problem in blind source separation (BSS) when the number of source signals is unknown and / or dynamically changed. The paper studies this problem and proves that the mutual information is still the contrast function for BSS if the The mutual information reaches its minimum at the separation points, where the random outputs of the scaled and permuted source signals, while the others are zero outputs. Using the property that the transpose of the mixing matrix and a matrix composed of m observed signals have the indentical null space with probability one, a practical method, which can detect the unknown number of source signals n, ulteriorly traces the dynamical change of the sources number with a few of data, is proposed. The effectiveness of the proposed theorey and the developed novel algorithm is verified by adaptive BSS simulations with unknown and dynamically changing number of source signals.