Blind Source Separation Based on Time-Domain Optimization of a Frequency-Domain Independence Criterion

Abstract

Abstract-A

Use of bimodal coherence to resolve the permutation problem in convolutive BSS

“…Convolutive BSS can be directly performed in the time domain [23][24][25] by deconvolution, but the computational complexity is high especially when the mixing filters have long taps. Based on the short-time stationarity of the speech signals and the linear time-invariance of the mixing process, an alternative is to perform convolutive BSS in the frequency domain by applying the short-time Fourier transform (STFT) to the observations.…”

“…Under the framework of independent component analysis (ICA) [17], the BSS problems have been extensively studied and many classical algorithms have been proposed for the instantaneous mixing model such as the ''J-H'' algorithm [18], JADE [19], Infomax [20], SOBI [21] and FastICA [22] algorithms. For the more complex convolutive mixing model, one can apply either the time domain deconvolution algorithms [23][24][25] or the frequency domain separation algorithms [12][13][14][15][26][27][28][29][30][31], which often suffer from the permutation and scaling ambiguity problems. Considering the bimodal nature of human speech, we could potentially improve the separation of the source signals from their audio mixtures utilizing the audiovisual coherence obtained by the integration of visual speech.…”

Blind source separation for convolutive mixtures based on the joint diagonalization of power spectral density matrices

“…Firstly, source signals must be nonstationary, whether the sources are colored or not does not matter. Secondly, the joint optimization of IDIFs is with respect to the timedomain parameters of the separation system rather than the frequency-domain parameters, this implies that the length of HðnÞ is predetermined and it sets a smoothness constraint on the corresponding frequency-domain parameters Hðe jo Þ, just like that in [21][22][23], so the permutation issue can be avoided effectively. Thirdly, the number of the IDIFs involved in the joint optimization is equal to or greater than the number of sources.…”

“…In [23], integration is applied to the frequencydomain defined Kullback-Leibler divergence and leads to BSS of convolutive mixtures where no local permutations take place.…”

“…It is different from the one in [21] in that it directly finds the unmixing system based on a group of entirely different objective functions, and it differs from the one in [22] in that it looks at general nonstationary processes instead of looking at colored stationary ones. It is also different from [23] as it exploits nonstationarity instead of nonGaussianity. As the separation is performed by a MIMO system in the time domain whose coefficients are the optimizing variables, the proposed approach does not have the local permutation ambiguity disadvantage.…”