New Approaches for Solving Permutation Indeterminacy and Scaling Ambiguity in Frequency Domain Separation of Convolved Mixtures

Permutation indeterminacy and scaling ambiguity occur in ICA and they are particularly problematic in time-frequency domain separation of convolutive mixtures. The quality of separation is severely degraded if these two problems are not well addressed. In this paper, we propose new approaches to solve the permutation indeterminacy and scaling ambiguity in the separation of convolutive mixture in frequency domain. We first apply Short Time Fourier Transform to the observed signals in order to transform the convolutive mixing in time domain to instantaneous mixing in time-frequency domain. A fixed-point algorithm with test of saddle point is adopted to derive the separated components in each frequency bin. To solve the permutation problem, we propose a new matching algorithm for this purpose. First we use discrete Haar Wavelet Transform to extract the feature vectors from the magnitude waveforms of the separated components and use Singular Value Decomposition to achieve dimension reduction. The permutation problem is solved by clustering the feature vectors using the new matching algorithm which is a combination of basic K-means and Hungarian algorithm. To solve the scaling ambiguity problem, we treat it as an overcomplete problem and realize it by maximizing the posterior of the scaling factor. Finally, experiments are conducted using benchmark data to present the effectiveness and performance of our proposed algorithms.