Convolutive Blind Source Separation Methods

In this chapter, we provide an overview of existing algorithms for blind source separation of convolutive audio mixtures. We provide a taxonomy, wherein many of the existing algorithms can be organized, and we present published results from those algorithms that have been applied to real-world audio separation tasks

Polynomial matrix eigenvalue decomposition techniques for multichannel signal processing

Polynomial eigenvalue decomposition (PEVD) is an extension of the eigenvalue decomposition (EVD) for para-Hermitian polynomial matrices, and it has been shown to be a powerful tool for broadband extensions of narrowband signal processing problems. In the context of broadband sensor arrays, the PEVD allows the para-Hermitian matrix that results from the calculation of a space-time covariance matrix of the convolutively mixed signals to be diagonalised. Once the matrix is diagonalised, not only can the correlation between different sensor signals be removed but the signal and noise subspaces can also be identified. This process is referred to as broadband subspace decomposition, and it plays a very important role in many areas that require signal separation techniques for multichannel convolutive mixtures, such as speech recognition, radar clutter suppression, underwater acoustics, etc. The multiple shift second order sequential best rotation (MS-SBR2) algorithm, built on the most established SBR2 algorithm, is proposed to compute the PEVD of para-Hermitian matrices. By annihilating multiple off-diagonal elements per iteration, the MS-SBR2 algorithm shows a potential advantage over its predecessor (SBR2) in terms of the computational speed. Furthermore, the MS-SBR2 algorithm permits us to minimise the order growth of polynomial matrices by shifting rows (or columns) in the same direction across iterations, which can potentially reduce the computational load of the algorithm. The effectiveness of the proposed MS-SBR2 algorithm is demonstrated by various para-Hermitian matrix examples, including randomly generated matrices with different sizes and matrices generated from source models with different dynamic ranges and relations between the sources’ power spectral densities. A worked example is presented to demonstrate how the MS-SBR2 algorithm can be used to strongly decorrelate a set of convolutively mixed signals. Furthermore, the performance metrics and computational complexity of MS-SBR2 are analysed and compared to other existing PEVD algorithms by means of numerical examples. Finally, two potential applications of theMS-SBR2 algorithm, includingmultichannel spectral factorisation and decoupling of broadband multiple-input multiple-output (MIMO) systems, are demonstrated in this dissertation

Complex Independent Component Analysis of Frequency-Domain Electroencephalographic Data

Independent component analysis (ICA) has proven useful for modeling brain and electroencephalographic (EEG) data. Here, we present a new, generalized method to better capture the dynamics of brain signals than previous ICA algorithms. We regard EEG sources as eliciting spatio-temporal activity patterns, corresponding to, e.g., trajectories of activation propagating across cortex. This leads to a model of convolutive signal superposition, in contrast with the commonly used instantaneous mixing model. In the frequency-domain, convolutive mixing is equivalent to multiplicative mixing of complex signal sources within distinct spectral bands. We decompose the recorded spectral-domain signals into independent components by a complex infomax ICA algorithm. First results from a visual attention EEG experiment exhibit (1) sources of spatio-temporal dynamics in the data, (2) links to subject behavior, (3) sources with a limited spectral extent, and (4) a higher degree of independence compared to sources derived by standard ICA.Comment: 21 pages, 11 figures. Added final journal reference, fixed minor typo

A frequency-based BSS technique for speech source separation.

Ngan Lai Yin.Thesis (M.Phil.)--Chinese University of Hong Kong, 2003.Includes bibliographical references (leaves 95-100).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Blind Signal Separation (BSS) Methods --- p.4Chapter 1.2 --- Objectives of the Thesis --- p.6Chapter 1.3 --- Thesis Outline --- p.8Chapter 2 --- Blind Adaptive Frequency-Shift (BA-FRESH) Filter --- p.9Chapter 2.1 --- Cyclostationarity Properties --- p.10Chapter 2.2 --- Frequency-Shift (FRESH) Filter --- p.11Chapter 2.3 --- Blind Adaptive FRESH Filter --- p.12Chapter 2.4 --- Reduced-Rank BA-FRESH Filter --- p.14Chapter 2.4.1 --- CSP Method --- p.14Chapter 2.4.2 --- PCA Method --- p.14Chapter 2.4.3 --- Appropriate Choice of Rank --- p.14Chapter 2.5 --- Signal Extraction of Spectrally Overlapped Signals --- p.16Chapter 2.5.1 --- Simulation 1: A Fixed Rank --- p.17Chapter 2.5.2 --- Simulation 2: A Variable Rank --- p.18Chapter 2.6 --- Signal Separation of Speech Signals --- p.20Chapter 2.7 --- Chapter Summary --- p.22Chapter 3 --- Reverberant Environment --- p.23Chapter 3.1 --- Small Room Acoustics Model --- p.23Chapter 3.2 --- Effects of Reverberation to Speech Recognition --- p.27Chapter 3.2.1 --- Short Impulse Response --- p.27Chapter 3.2.2 --- Small Room Impulse Response Modelled by Image Method --- p.32Chapter 3.3 --- Chapter Summary --- p.34Chapter 4 --- Information Theoretic Approach for Signal Separation --- p.35Chapter 4.1 --- Independent Component Analysis (ICA) --- p.35Chapter 4.1.1 --- Kullback-Leibler (K-L) Divergence --- p.37Chapter 4.2 --- Information Maximization (Infomax) --- p.39Chapter 4.2.1 --- Stochastic Gradient Descent and Stability Problem --- p.41Chapter 4.2.2 --- Infomax and ICA --- p.41Chapter 4.2.3 --- Infomax and Maximum Likelihood --- p.42Chapter 4.3 --- Signal Separation by Infomax --- p.43Chapter 4.4 --- Chapter Summary --- p.45Chapter 5 --- Blind Signal Separation (BSS) in Frequency Domain --- p.47Chapter 5.1 --- Convolutive Mixing System --- p.48Chapter 5.2 --- Infomax in Frequency Domain --- p.52Chapter 5.3 --- Adaptation Algorithms --- p.54Chapter 5.3.1 --- Standard Gradient Method --- p.54Chapter 5.3.2 --- Natural Gradient Method --- p.55Chapter 5.3.3 --- Convergence Performance --- p.56Chapter 5.4 --- Subband Adaptation --- p.57Chapter 5.5 --- Energy Weighting --- p.59Chapter 5.6 --- The Permutation Problem --- p.61Chapter 5.7 --- Performance Evaluation --- p.63Chapter 5.7.1 --- De-reverberation Performance Factor --- p.63Chapter 5.7.2 --- De-Noise Performance Factor --- p.63Chapter 5.7.3 --- Spectral Signal-to-noise Ratio (SNR) --- p.65Chapter 5.8 --- Chapter Summary --- p.65Chapter 6 --- Simulation Results and Performance Analysis --- p.67Chapter 6.1 --- Small Room Acoustics Modelled by Image Method --- p.67Chapter 6.2 --- Signal Sources --- p.68Chapter 6.2.1 --- Cantonese Speech --- p.69Chapter 6.2.2 --- Noise --- p.69Chapter 6.3 --- De-Noise and De-Reverberation Performance Analysis --- p.69Chapter 6.3.1 --- Speech and White Noise --- p.73Chapter 6.3.2 --- Speech and Voice Babble Noise --- p.76Chapter 6.3.3 --- Two Female Speeches --- p.79Chapter 6.4 --- Recognition Accuracy Performance Analysis --- p.83Chapter 6.4.1 --- Speech and White Noise --- p.83Chapter 6.4.2 --- Speech and Voice Babble Noise --- p.84Chapter 6.4.3 --- Two Cantonese Speeches --- p.85Chapter 6.5 --- Chapter Summary --- p.87Chapter 7 --- Conclusions and Suggestions for Future Research --- p.88Chapter 7.1 --- Conclusions --- p.88Chapter 7.2 --- Suggestions for Future Research --- p.91Appendices --- p.92A The Proof of Stability Conditions for Stochastic Gradient De- scent Algorithm (Ref. (4.15)) --- p.92Bibliography --- p.9

Design of FIR paraunitary filter banks for subband coding using a polynomial eigenvalue decomposition

The problem of paraunitary filter bank design for subband coding has received considerable attention in recent years, not least because of the energy preserving property of this class of filter banks. In this paper, we consider the design of signal-adapted, finite impulse response (FIR), paraunitary filter banks using polynomial matrix EVD (PEVD) techniques. Modifications are proposed to an iterative, time-domain PEVD method, known as the sequential best rotation (SBR2) algorithm, which enables its effective application to the problem of FIR orthonormal filter bank design for efficient subband coding. By choosing an optimisation scheme that maximises the coding gain at each stage of the algorithm, it is shown that the resulting filter bank behaves more and more like the infiniteorder principle component filter bank (PCFB). The proposed method is compared to state-of-the-art techniques, namely the iterative greedy algorithm (IGA), the approximate EVD (AEVD), standard SBR2 and a fast algorithm for FIR compaction filter design, called the window method (WM). We demonstrate that for the calculation of the subband coder, the WM approach offers a low-cost alternative at lower coding gains, while at moderate to high complexity, the proposed approach outperforms the benchmarkers. In terms of run-time complexity, AEVD performs well at low orders, while the proposed algorithm offers a better coding gain than the benchmarkers at moderate to high filter order for a number of simulation scenarios