A Novel and Fast Algorithm for Solving Permutation in Convolutive BSS, Based on Real and Imaginary Decomposition

In this paper, a new fast method for solving the permutation problem in convolutive BSS is presented. Typically, by transferring signals to the frequency domain, the convolutive BSS problem is converted to an instantaneous BSS, and deconvolution takes place in each frequency bin. However, another major problem arises which is permutation ambiguity in the frequency domain. Solving the permutation ambiguity for N sources in frequency domain needs N! comparisons between adjacent frequency bins. This drastically increases the overall computational complexity of the convolutive BSS. In our new approach, the complex-valued signals are decomposed into real and imaginary parts in each frequency bin. We show that the ideal mixing matrix has to possess a simple and symmetric structure. Accordingly, the structure can be exploited for solving the permutation ambiguity in frequency domain. Although separation in subband is accomplished by the FastICA algorithm, the proposed method requires modification of the separation algorithm, and a new structure is imposed on the mixing matrix. After that signals are separated by means of the FastICA, the permutation correction takes place only by N comparisons, decreasing the computational complexity. Comparing to five competitive methods, we experimentally demonstrate that permutation ambiguity is resolved accurately by this very fast approach while substantially decreasing the order of calculations. In terms of the separation performance and signal quality, the proposed method is superior to four of the compared methods and almost similar to the best of them.