Blind source separation of acoustic signals in realistic environments based on ICA in the time-frequency domain

We present an approach for blind separation of acoustic sources produced from multiple speakers mixed in realistic room environments. We first transform recorded signals into the time-frequency domain to make mixing become instantaneous. We then separate the sources in each frequency bin based on an independent component analysis (ICA) algorithm. For the present paper, we choose the complex version of fixedpoint iteration (CFPI), i.e. the complex version of FastICA, as the algorithm. From the separated signals in the time-frequency domain, we reconstruct output-separated signals in the time domain. To solve the so-called permutation problem due to the indeterminacy of permutation in the standard ICA, we propose a method that applies a special property of the CFPI cost function. Generally, the cost function has several optimal points that correspond to the different permutations of the outputs. These optimal points are isolated by some non-optimal regions of the cost function. In different but neighboring bins, optimal points with the same permutation are at almost the same position in the space of separation parameters. Based on this property, if an initial separation matrix for a learning process in a frequency bin is chosen equal to the final separation matrix of the learning process in the neighboring frequency bin, the learning process automatically leads us to separated signals with the same permutation as that of the neighbor frequency bin. In each bin, but except the starting one, by chosen the initial separation matrix in such a way, the permutation problem in the time domain reconstruction can be avoided. We present the results of some simulations and experiments on both artificially synthesized speech data and real-world speech data, which show the effectiveness of our approach.