A method to solve the permutation problem in blind source deconvolution for audio signals based on phase linearity estimation

One approach to solve the blind source deconvolution (BSD) is to transform the observations into the frequency domain and apply common blind source separation (BSS) in each frequency bin. This approach is called frequency-domain blind source separation (FD-BSS). Generally FD-BSS has a problem with indeterminacy of the permutation of the separated signals in each frequency bin. Furthermore, even if the permutation problem is solved, we cannot avoid the degradation of quality of the estimated signals because of noise or statistical error. In this paper, we describe a new approach for BSS that utilizes the phase linearity not only to solve the permutation problem but also to tune each value of the elements of the separating matrices. To effectively detect multi- and ambiguous linearity, we propose the use of the Hough transform. To improve the signal-to-noise ratio (SNR), we propose not to persist in the independence, but to adopt the constraints of phase linearity. Simulation results for audio sources show the improvement of SNR with the proposed method.