Adaptive blind separation of independent sources: a deflation approach
Signal Processing
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
A blind source separation technique using second-order statistics
IEEE Transactions on Signal Processing
Blind separation of instantaneous mixtures of nonstationary sources
IEEE Transactions on Signal Processing
Complex random vectors and ICA models: identifiability, uniqueness, and separability
IEEE Transactions on Information Theory
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
ICA over finite fields-Separability and algorithms
Signal Processing
Fast communication: The modified MEXICO for ICA over finite fields
Signal Processing
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We consider Independent Component Analysis (ICA) for the case of binary sources, where addition has the meaning of the boolean "Exclusive Or" (XOR) operation. Thus, each mixture-signal is given by the XOR of one or more of the source-signals. While such mixtures can be considered linear transformations over the finite Galois Field of order 2, they are certainly nonlinear over the field of real-valued numbers, so classical ICA principles may be inapplicable in this framework. Nevertheless, we show that if none of the independent random sources is uniform (i.e., neither one has probability 0.5 for 1/0), then any invertible mixing is identifiable (up to permutation ambiguity). We then propose a practical deflation algorithm for source separation based on entropy minimization, and present empirical performance results by simulation.