Research Of Convolutive Blind Separation In The Frequency Domain

Blind source separation of convolutive mixtures (CMBSS) is a hotspot of modern signal processing. It has been widely used in many fields, such as tele-communications, audio signal separation, biomedical signal processing and image processing. Convolutive blind separation could be implemented in either temporal domain (TDCMBSS) or frequency domain (FDCMBSS). Since convolutive mixture can be simplified into instantaneous mixture in frequency domain by Short Time Fourier Transform (STFT), more and more attention is paid for FDCMBSS and a lot of algorithms are proposed in the past few years.Despite extensive efforts so far, there are still many open issues that deteriorate the separation performance and need further investigation. How to remove the Permutation indeterminacy, how to suppress the difference between circular and partial convolution and how to introduce the across frequency independence are three key issues. The research of this thesis will focus on these three aspects to improve the separation performance.The main contributions of this thesis are as following:1) To suppress the difference between circular and partial convolution, we propose two preprocessing approach for the existed FDCMBSS method, i.e. Temporal Filter and Weighted Modified Discrete Fourier Transform (WMDFT). Temporal Filter treats the STFT coefficients as a noisy-instantaneous mixture, and employs multi-inconsecutive-frames moving average to suppress the noise introduced by the difference between circular and partial convolution. WMDFT is an optimal transform whose coefficients approximates to the noise-free instantaneous mixture of source spectrum in a weighted least square sense, which is equivalent to suppress the difference between circular and partial convolution. The experiments results show that the proposed two preprocessing techniques are effective.2) Based on the independence between sources on different frequency bins, a cross-frequency-based approach is proposed for the convolutive blind source separation. The information on the adjacent frequency bins is used to estimate the separating matrix on each frequency bin. By incorporating the cross frequency independence in its cost function, the cross-frequency-based approach specifies the property of separating matrix more precisely than the existed FDCMBSS methods, and possesses a higher separation performance with faster convergence speed. The validity of this proposed method is confirmed by the simulation results.3) Based on the derived signal reconstruction algorithm with dense spectrum on one frequency bin, a single-bin-based approach is proposed for convolutive blind separation in the frequency domain. Since it can implement convolutive separation with only one frequency bin, there's no permutation indetermincy in single-bin-based approach, which improves the performance of proposed single-bin-based approach. The simulation results show the correctness and effectiveness of this method.4) To remove the permutation indetermincy, a general formulation for thetime-domain optimization of frequency-domain Independence Criterion is proposed. It's able to convert the existed learning rule of frequency domain separating matrix into learning rule of time domain separating filters. The permutation problem of the proposed cross-frequency-based approach is removed by this general formulation.The principle and algorithms of FDCMBSS are studied in this thesis. Theproposed methods expand the application of FDCMBSS with practical and theoreticalsignificance.