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2014 | Book

Quantum-Source Independent Component Analysis and Related Statistical Blind Qubit Uncoupling Methods Read chapter Read first chapter

Blind Source Separation

Advances in Theory, Algorithms and Applications

Editors: Ganesh R. Naik, Wenwu Wang

Publisher: Springer Berlin Heidelberg

Book Series : Signals and Communication Technology

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

Blind Source Separation intends to report the new results of the efforts on the study of Blind Source Separation (BSS). The book collects novel research ideas and some training in BSS, independent component analysis (ICA), artificial intelligence and signal processing applications. Furthermore, the research results previously scattered in many journals and conferences worldwide are methodically edited and presented in a unified form. The book is likely to be of interest to university researchers, R&D engineers and graduate students in computer science and electronics who wish to learn the core principles, methods, algorithms and applications of BSS.

Dr. Ganesh R. Naik works at University of Technology, Sydney, Australia; Dr. Wenwu Wang works at University of Surrey, UK.

Table of Contents

Frontmatter
Erratum to: Performance Study for Complex Independent Component Analysis
Benedikt Loesch, Bin Yang

Theory, Algorithms, and Extensions

Frontmatter
Chapter 1. Quantum-Source Independent Component Analysis and Related Statistical Blind Qubit Uncoupling Methods
Abstract
Quantum Information Processing (QIP) is an emerging field which yields new capabilities beyond classical, i.e., non-quantum, information processing. QIP methods manipulate quantum bit (qubit) states instead of classical bit values. Undesired coupling between these individual quantum states is expected, in the same way as classical systems involve undesired signal coupling. Methods for recovering individual quantum states from their coupled version are therefore required. To solve this problem, we recently introduced the field of Quantum Source Separation (QSS). We showed how to convert qubit states with cylindrical-symmetry Heisenberg coupling into classical-form data, mixed according to a specific nonlinear model, which was not previously studied in the literature. We therefore started to develop methods for unmixing such data. While we restricted ourselves to nonblind QSS methods and a basic blind approach in those previous works, we here proceed much further for the more difficult, i.e., blind, case: we introduce the concept of Quantum-Source Independent Component Analysis (QSICA), and we develop related QSS methods using various statistical signal processing tools, namely mutual information, likelihood and moments. The performance of the proposed approaches is validated by means of numerical tests. This especially shows the attractiveness of our method focused on second-order moments.
Yannick Deville, Alain Deville
Chapter 2. Blind Source Separation Based on Dictionary Learning: A Singularity-Aware Approach
Abstract
This chapter surveys recent works in applying sparse signal processing techniques, in particular, dictionary learning algorithms to solve the blind source separation problem. For the proof of concepts, the focus is on the scenario where the number of mixtures is not less than that of the sources. Based on the assumption that the sources are sparsely represented by some dictionaries, we present a joint source separation and dictionary learning algorithm (SparseBSS) to separate the noise corrupted mixed sources with very little extra information. We also discuss the singularity issue in the dictionary learning process, which is one major reason for algorithm failure. Finally, two approaches are presented to address the singularity issue.
Xiaochen Zhao, Guangyu Zhou, Wei Dai, Wenwu Wang
Chapter 3. Performance Study for Complex Independent Component Analysis
Abstract
The goal of independent component analysis (ICA) is to decompose observed signals into components as independent as possible. In linear instantaneous blind source separation, ICA is used to separate linear instantaneous mixtures of source signals into signals that are as close as possible to the original signals. In the estimation of the so-called demixing matrix one has to distinguish two different factors:
1.
Variance of the estimated inverse mixing matrix in the noiseless case due to randomness of the sources.
 
2.
Bias of the demixing matrix from the inverse mixing matrix:
 
This chapter studies both factors for circular and noncircular complex mixtures. It is important to note that the complex case is not directly equivalent to the real case of twice larger dimension. In the derivations, we aim to clearly show the connections and differences between the complex and real cases. In the first part of the chapter, we derive a closed-form expression for the CRB of the demixing matrix for instantaneous noncircular complex mixtures. We also study the CRB numerically for the family of noncircular complex generalized Gaussian distributions (GGD) and compare it to simulation results of several ICA estimators. In the second part, we consider a linear noisy noncircular complex mixing model and derive an analytic expression for the demixing matrix of ICA based on the Kullback-Leibler divergence (KLD). We show that for a wide range of both the shape parameter and the noncircularity index of the GGD, the signal-to-interference-plus-noise ratio (SINR) of KLD-based ICA is close to that of linear MMSE estimation. Furthermore, we show how to extend our derivations to the overdetermined case (\(M>N\)) with circular complex noise.
Benedikt Loesch, Bin Yang
Chapter 4. Subband-Based Blind Source Separation and Permutation Alignment
Abstract
The aim of this chapter is to present the fundamental ideas of subband-based convolutive blind source separation (BSS) employing filter banks, in particular with a focus on the inherent permutation alignment problem associated with this approach, and bring attention to the most recent developments in this area, including the joint BSS approach in solving the convolutive mixing problem.
Bo Peng, Wei Liu
Chapter 5. Frequency Domain Blind Source Separation Based on Independent Vector Analysis with a Multivariate Generalized Gaussian Source Prior
Abstract
Independent vector analysis (IVA) is designed for retaining the dependency contained in each source vector, while removing the dependency between different source vectors during the source separation process. It can theoretically avoid the permutation problem inherent to independent component analysis (ICA). The dependency in each source vector is maintained by adopting a multivariate source prior instead of a univariate source prior. In this chapter, a multivariate generalized Gaussian distribution is proposed to be the source prior, which can exploit the energy correlation within each source vector. It can preserve the dependency between different frequency bins better to achieve an improved separation performance, and is suitable for the whole family of IVA algorithms. Experimental results on real speech signals confirm the advantage of adopting the new source prior on three types of IVA algorithms.
Yanfeng Liang, Syed Mohsen Naqvi, Wenwu Wang, Jonathon A. Chambers
Chapter 6. Sparse Component Analysis: A General Framework for Linear and Nonlinear Blind Source Separation and Mixture Identification
Abstract
In this chapter, we consider two closely related data processing tasks. The first one is Blind Source Separation (BSS), which consists in estimating a set of unknown source data (one-dimensional signals, images, ...) from observed mixtures of these data, while the mixing operator has unknown parameter values. The second task is Blind Mixture Identification (BMI), which aims at estimating these unknown parameter values of the mixing operator. We provide a unified view and describe the latest extensions of the general framework that we have been developing for BSS and BMI since the beginning of the 2000s. This framework yields a wide range of BSS/BMI methods applicable to various types of sources (one-dimensional signals, images, ...) mixed according to various models (linear instantaneous, anechoic, full convolutive, nonlinear and especially linear-quadratic), possibly with non-negativity or sum-to-one constraints. This framework is based on the concept of joint sparsity of the source data, considered in various domains (original temporal or spatial domain, transformed representation in time-frequency or time-scale/wavelet domain, ...). More precisely, the proposed methods essentially require a few tiny zones, in mixed signals or in their transformed versions, where only one of the source “signals” is active, i.e., nonzero. They therefore set very limited constraints on source sparsity and could then be considered as “quasi-non-sparse component analysis” methods. Besides, unlike Independent Component Analysis methods, they are suited to correlated sources. We also discuss their application to various data processing functions, ranging from audio signal separation to unmixing of hyperspectral remote sensing images.
Yannick Deville
Chapter 7. Underdetermined Audio Source Separation Using Laplacian Mixture Modelling
Abstract
The problem of underdetermined audio source separation has been explored in the literature for many years. The instantaneous \(K\)-sensors, \(L\)-sources mixing scenario (where \(K<L\)) has been tackled by many different approaches, provided the sources remain quite distinct in the virtual positioning space spanned by the sensors. In this case, the source separation problem can be solved as a directional clustering problem along the source position angles in the mixture. The use of Laplacian Mixture Models in order to cluster and thus separate sparse sources in underdetermined mixtures will be explained in detail in this chapter. The novel Generalised Directional Laplacian Density will be derived in order to address the problem of modelling multidimensional angular data. The developed scheme demonstrates robust separation performance along with low processing time.
Nikolaos Mitianoudis
Chapter 8. Itakura-Saito Nonnegative Matrix Two-Dimensional Factorizations for Blind Single Channel Audio Separation
Abstract
A new blind single channel source separation method is presented. The proposed method does not require training knowledge and the separation system is based on nonuniform time-frequency (TF) analysis and feature extraction. Unlike conventional researches that concentrate on the use of spectrogram or its variants, we develop our separation algorithms using an alternative TF representation based on the gammatone filterbank. In particular, we show that the monaural mixed audio signal is considerably more separable in this nonuniform TF domain. We also provide the analysis of signal separability to verify this finding. In addition, we derive two new algorithms that extend the recently published Itakura-Saito nonnegative matrix factorization to the case of convolutive model for the nonstationary source signals. These formulations are based on the Quasi-EM framework and the Multiplicative Gradient Descent (MGD) rule, respectively. Experimental tests have been conducted which show that the proposed method is efficient in extracting the sources’ spectral–temporal features that are characterized by large dynamic range of energy, and thus lead to significant improvement in source separation performance.
Bin Gao, Wai Lok Woo
Chapter 9. Source Localization and Tracking: A Sparsity-Exploiting Maximum a Posteriori Based Approach
Abstract
In this work, we explore the potential of sparse recovery algorithms for localization and tracking the direction-of-arrivals (DOA) of multiple targets using a limited number of noisy time samples collected from a small number of sensors. In target tracking problems, the targets are assumed to be moving with a small random angular acceleration. We show that the target tracking problem can be posed as a problem of recursively reconstructing a sequence of sparse signals where the support of the signals changing slowly with time. Here, one can use the support of last signal as a priori information to estimate the behavior of current signal. In particular, we propose a maximum a posteriori (MAP)-based approach to deal with the sparse recovery problem arising in tracking and detection of DOAs. We consider both narrowband and broadband scenarios. Numerical simulations demonstrate the effectiveness of the proposed algorithm. We found that the proposed algorithm can resolve and track closely spaced DOAs with a small number of sensors.
Md Mashud Hyder, Kaushik Mahata

Applications

Frontmatter
Chapter 10. Statistical Analysis and Evaluation of Blind Speech Extraction Algorithms
Abstract
In this chapter, a problem of blind source separation for speech applications operated under real acoustic environments is addressed. In particular, we focus on a blind spatial subtraction array (BSSA) consisting of a noise estimator based on independent component analysis (ICA) for efficient speech enhancement. First, it is theoretically and experimentally pointed out that ICA is proficient in noise estimation rather than in speech estimation under a nonpoint-source noise condition. Next, motivated by the above-mentioned fact, we introduce a structure-generalized parametric BSSA, which consists of an ICA-based noise estimator and post-filtering based on generalized spectral subtraction. In addition, we perform its theoretical analysis via higher-order statistics. Comparing a parametric BSSA and a parametric channelwise BSSA, we reveal that a channelwise BSSA structure is recommended for listening but a conventional BSSA is more suitable for speech recognition.
Hiroshi Saruwatari, Ryoichi Miyazaki
Chapter 11. Speech Separation and Extraction by Combining Superdirective Beamforming and Blind Source Separation
Abstract
Blind source separation (BSS) and beamforming are two well-known multiple microphone techniques for speech separation and extraction in cocktail-party environments. However, both of them perform limitedly in highly reverberant and dynamic scenarios. Emulating human auditory systems, this chapter proposes a combined method for better separation and extraction performance, which uses superdirective beamforming as a preprocessor of frequency-domain BSS. Based on spatial information only, superdirective beamforming presents abilities of dereverberation and noise reduction and performs robustly in time-varying environments. Using it as a preprocessor can mitigate the inherent “circular convolution approximation problem” of the frequency-domain BSS and enhances its robustness in dynamic environments. Meanwhile, utilizing statistical information only, BSS can further reduce the residual interferences after beamforming efficiently. The combined method can exploit both spatial information and statistical information about microphone signals and hence performs better than using either BSS or beamforming alone. The proposed method is applied to two specific challenging tasks, namely a separation task in highly reverberant environments with the positions of all sources known, and a target speech extraction task in highly dynamic cocktail-party environments with only the position of the target known. Experimental results prove the effectiveness of the proposed method.
Lin Wang, Heping Ding, Fuliang Yin
Chapter 12. On the Ideal Ratio Mask as the Goal of Computational Auditory Scene Analysis
Abstract
The ideal binary mask (IBM) is widely considered to be the benchmark for time–frequency-based sound source separation techniques such as computational auditory scene analysis (CASA). However, it is well known that binary masking introduces objectionable distortion, especially musical noise. This can make binary masking unsuitable for sound source separation applications where the output is auditioned. It has been suggested that soft masking reduces musical noise and leads to a higher quality output. A previously defined soft mask, the ideal ratio mask (IRM), is found to have similar properties to the IBM, may correspond more closely to auditory processes, and offers additional computational advantages. Consequently, the IRM is proposed as the goal of CASA. To further support this position, a number of studies are reviewed that show soft masks to provide superior performance to the IBM in applications such as automatic speech recognition and speech intelligibility. A brief empirical study provides additional evidence demonstrating the objective and perceptual superiority of the IRM over the IBM.
Christopher Hummersone, Toby Stokes, Tim Brookes
Chapter 13. Monaural Speech Enhancement Based on Multi-threshold Masking
Abstract
The ideal binary mask (IBM) has been assigned as a computational goal in computational auditory scene analysis (CASA) algorithms. Only time–frequency (T-F) units with local signal-to-noise ratio (SNR) exceeding a local criterion (LC) are assigned the binary value 1 in the binary mask. However, there are two problems with employing IBM in source separation applications. First, an optimum LC for a certain SNR may not be appropriate for other SNRs. Second, binary weighting may cause some parts or regions of the synthesized speech to be discarded at the output. If one employs variable weights, as opposed to the hard limiting weights (i.e., 0 or 1) taken in IBM, the above-mentioned problems can be solved considerably. In this chapter, a novel auditory-based mask, called ideal multi-threshold mask (IMM) is proposed which can be used in source separation applications. To show the potential capabilities of the new mask, a minimum mean-square error (MMSE)-based method is proposed to estimate IMM in the framework of monaural speech enhancement system. Various objective and subjective evaluation criteria show the superior performance of the new speech enhancement system as compared to a recently introduced enhancement technique.
Masoud Geravanchizadeh, Reza Ahmadnia
Chapter 14. REPET for Background/Foreground Separation in Audio
Abstract
Repetition is a fundamental element in generating and perceiving structure. In audio, mixtures are often composed of structures where a repeating background signal is superimposed with a varying foreground signal (e.g., a singer overlaying varying vocals on a repeating accompaniment or a varying speech signal mixed up with a repeating background noise). On this basis, we present the REpeating Pattern Extraction Technique (REPET), a simple approach for separating the repeating background from the non-repeating foreground in an audio mixture. The basic idea is to find the repeating elements in the mixture, derive the underlying repeating models, and extract the repeating background by comparing the models to the mixture. Unlike other separation approaches, REPET does not depend on special parameterizations, does not rely on complex frameworks, and does not require external information. Because it is only based on repetition, it has the advantage of being simple, fast, blind, and therefore completely and easily automatable.
Zafar Rafii, Antoine Liutkus, Bryan Pardo
Chapter 15. Nonnegative Matrix Factorization Sparse Coding Strategy for Cochlear Implants
Abstract
With the development of new speech processors and algorithms, the majority of cochlear implant (CI) users benefit from their device, however, the average performance of most CI users still falls below normal hearing (NH) listeners, and speech quality and intelligibility generally deteriorate in the presence of background noise. Cochlear implants require efficient speech processing to maximize information transfer to the brain, especially in noise. Our current work is to improve the performance of CIs in noisy environments by developing new speech processing strategies. In this chapter, a nonnegative matrix factorization (NMF)-based speech coding strategy is introduced, where the speech is first transferred to the time–frequency domain via a 22-channel filter bank and the envelope in each frequency channel is extracted; and then the NMF SPARSE strategy is applied on these envelopes. The algorithm was evaluated by objective and subjective experiments, and the results were compared to the standard CI speech processing strategy (Advanced Combination Encoder, ACE). A vocoder simulation study with six participants showed that the proposed sparse NMF strategy can outperform ACE, especially at low SNR for both speech intelligibility and quality.
Hongmei Hu, Guoping Li, Mark E. Lutman, Stefan Bleeck
Chapter 16. Exploratory Analysis of Brain with ICA
Abstract
This chapter introduces the use of independent component analysis (ICA) in the study of electroencephalographic (EEG) data. Though the main application of ICA is in the context of denoising, we prefer to focus our attention to the independent components of artifacts-free EEG data. The interpretation of these independent components is still controversial, and we outline the more accepted alternatives. An introduction to the results obtained when applying ICA to evoked potentials (EPs) and event-related potentials (ERPs) is presented, as well as an explanation of the ICA of natural images and its relationship with models of visual cortex is also presented. This chapter is written as a general introduction to the subject for those who want to get started in the main topics.
Rubén Martín-Clemente
Chapter 17. Supervised Normalization of Large-Scale Omic Datasets Using Blind Source Separation
Abstract
Biotechnological advances in genomics have heralded in a new era of quantitative molecular biology whereby it is now possible to routinely measure over tens of thousands of molecular features (e.g., gene expression levels) in hundreds if not thousands of patient samples. A key statistical challenge in the analysis of such large omic datasets is the presence of confounding sources of variation, which are often either unknown or only known with error. In this chapter, we present a supervised normalization method in which Blind Source Separation (BSS) is applied to identify the sources of variation, and demonstrate that this leads to improved statistical inference in subsequent supervised analyses. The statistical framework presented here will be of interest to biologists, bioinformaticians and signal processing experts alike.
Andrew E. Teschendorff, Emilie Renard, Pierre A. Absil
Chapter 18. FebICA: Feedback Independent Component Analysis for Complex Domain Source Separation of Communication Signals
Abstract
In this chapter, an effective blind source separation (BSS) algorithm is applied to solve the co-channel interference problem in wireless communication systems. Algorithms developed for this purpose must not only have the capability of working in the complex domain and improving output signal to interference plus noise ratio (SINR), but also have relatively low computational complexity. We propose a fast Fourier transform (FFT)-based algorithm called feedback independent component analysis (FebICA) that is able to blindly separate complex modulated digital signals. By applying this algorithm to communication signals, it is observed that it has the advantages of SINR gain improvement as well as low computational complexity. The performance of the FebICA algorithm is shown to be better than the joint approximate diagonalization of eigen-matrices (JADE) algorithm in terms of the output SINR and requires lower computational complexity than the analytical constant modulus algorithm (ACMA). The algorithm is also shown to be more robust with increasing number of sources compared to other algorithms. The separation performance by using the collected field data has also been demonstrated.
A. K. Kattepur, F. Sattar
Chapter 19. Semi-blind Functional Source Separation Algorithm from Non-invasive Electrophysiology to Neuroimaging
Abstract
Neuroimaging, investigating how specific brain sources play a particular role in a definite cognitive or sensorimotor process, can be achieved from non-invasive electrophysiological (EEG, EMG, MEG) and multimodal (concurrent EEG-fMRI) recordings. However, especially for the non-invasive electrophysiological techniques, the signals measured at the scalp are a mixture of the contributions from multiple generators or sources added to background activity and system noise, meaning that it is often difficult to identify the dynamic activity of generators of interest starting from the electrode/sensor recordings. Although the most common method of overcoming this limitation is time-domain averaging with or without source localization, blind source separation (BSS) algorithms are becoming increasingly widely accepted as a way of extracting the different neuronal sources that contribute to the measured scalp signals without trial exclusion. The advantage of BSS or semi-blind source separation (semi-BSS) techniques compared to methods such as time-domain averaging lies in their ability to extract sources exploring the whole time evolving data. Taking into account the whole signal without averaging, it also provides a means suitable to investigate non-phase locked oscillatory processes and single-trial behaviour. This characteristic becomes a crucial issue when investigating combined EEG-fMRI data, particularly when the focus is on neurovascular coupling definitely dependent on single trial variability of the two datasets. In this context, this chapter describes a semi-BSS technique, Functional Source Separation (FSS), which is a tool to identify cerebral sources by exploiting a priori knowledge, such as spectral or evoked activity, which cannot be expressed by sources other than the one to be identified (functional fingerprint). In other words, FSS allows the identification of specific neuronal pools on the bases of their functional roles, independent of their spatial position.
Camillo Porcaro, Franca Tecchio
Metadata
Title
Blind Source Separation
Editors
Ganesh R. Naik
Wenwu Wang
Copyright Year
2014
Publisher
Springer Berlin Heidelberg
Electronic ISBN
978-3-642-55016-4
Print ISBN
978-3-642-55015-7
DOI
https://doi.org/10.1007/978-3-642-55016-4