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Blind signal separation (BSS) aims at recovering unknown source signals from the observed sensor signals where the mixing process is also unknown. As a popular method to solve this problem, independent component analysis (ICA) maximizes the mutual independence among, or equivalently the non-Gaussianity of, the signals and has been very successful especially when the unknown mixing process is instantaneous. In most realistic situations, however, there are time delay and reverberations which involve long filter lengths in the time domain. Such convolutive BSS problems are often tackled in the frequency domain, or short-time Fourier transform (STFT) domain, mainly because the convolutive mixture model can be approximated to bin-wise instantaneous mixtures given the frame size is long enough to cover the main part of the convolved impulse responses. While the bin-wise instantaneous mixtures can be separated by the ICA algorithms for complex-valued variables, there are several factors that have significant influence on the final separation performance, which are the permutation problem, incomplete bin-wise separation, and noise. Permutation problem refers to the random alignment of the STFT components that are separated by ICA. It is due to the permutation indeterminacy of ICA and it hinders proper reconstruction of the original time-domain signals. To solve this problem, a multidimensional ICA framework that is called independent vector analysis (IVA) has been proposed. IVA exploits the mutual dependence among the STFT components originating from the same source and employs a multivariate dependence model. In this thesis, various dependence models and methods are proposed in the framework of IVA to solve the convolutive BSS problem, which include Lp-norm invariant joint densities, density functions represented by overlapped cliques in graphical models, Newton's update optimization, and an EM algorithm using a mixture of multivariate Gaussians prior where Gaussian noise is added in the model. While IVA is an effective framework to solve the convolutive BSS, the high dimensionality in the STFT domain makes it difficult to model the joint probability density function (PDF) of the fullband STFT components. On the other hand, bin-wise separation is a simpler task for which a permutation correction algorithm has to follow. For permutation correction, overall measures of magnitude correlation have been popular. However, the positive correlation is stronger between STFT components that are close to each other and correlation is a measure computed pair-wise. Thus, in this thesis, subband likelihood functions are proposed for the permutation correction which is fast to obtain and robust in solving the permutation problem.
Edited by the people who were forerunners in creating the field, together with contributions from 34 leading international experts, this handbook provides the definitive reference on Blind Source Separation, giving a broad and comprehensive description of all the core principles and methods, numerical algorithms and major applications in the fields of telecommunications, biomedical engineering and audio, acoustic and speech processing. Going beyond a machine learning perspective, the book reflects recent results in signal processing and numerical analysis, and includes topics such as optimization criteria, mathematical tools, the design of numerical algorithms, convolutive mixtures, and time frequency approaches. This Handbook is an ideal reference for university researchers, R&D engineers and graduates wishing to learn the core principles, methods, algorithms, and applications of Blind Source Separation. Covers the principles and major techniques and methods in one book Edited by the pioneers in the field with contributions from 34 of the world’s experts Describes the main existing numerical algorithms and gives practical advice on their design Covers the latest cutting edge topics: second order methods; algebraic identification of under-determined mixtures, time-frequency methods, Bayesian approaches, blind identification under non negativity approaches, semi-blind methods for communications Shows the applications of the methods to key application areas such as telecommunications, biomedical engineering, speech, acoustic, audio and music processing, while also giving a general method for developing applications
The field of blind source separation (BSS) is a well studied discipline within the signal processing community due to its applicability to a variety of problems when the data observation model is poorly known or difficult to model. For example, in the study of the human brain with functional magnetic resonance imaging (fMRI), a neuroimaging sensor, BSS algorithms are able to provide medical researchers and practitioners with a decomposition of a three-dimensional `movie' of the brain that is amenable to analysis. BSS algorithms achieve this decomposition with only a few justifiable assumptions; this is contrary to methods based on the general linear model, which require prespecified models of the expected or desired response to achieve analysis of fMRI data.
A comprehensive introduction to ICA for students and practitioners Independent Component Analysis (ICA) is one of the most exciting new topics in fields such as neural networks, advanced statistics, and signal processing. This is the first book to provide a comprehensive introduction to this new technique complete with the fundamental mathematical background needed to understand and utilize it. It offers a general overview of the basics of ICA, important solutions and algorithms, and in-depth coverage of new applications in image processing, telecommunications, audio signal processing, and more. Independent Component Analysis is divided into four sections that cover: * General mathematical concepts utilized in the book * The basic ICA model and its solution * Various extensions of the basic ICA model * Real-world applications for ICA models Authors Hyvarinen, Karhunen, and Oja are well known for their contributions to the development of ICA and here cover all the relevant theory, new algorithms, and applications in various fields. Researchers, students, and practitioners from a variety of disciplines will find this accessible volume both helpful and informative.
Im Mittelpunkt dieses modernen und spezialisierten Bandes stehen adaptive Strukturen und unüberwachte Lernalgorithmen, besonders im Hinblick auf effektive Computersimulationsprogramme. Anschauliche Illustrationen und viele Beispiele sowie eine interaktive CD-ROM ergänzen den Text.
Unsupervised Signal Processing: Channel Equalization and Source Separation provides a unified, systematic, and synthetic presentation of the theory of unsupervised signal processing. Always maintaining the focus on a signal processing-oriented approach, this book describes how the subject has evolved and assumed a wider scope that covers several topics, from well-established blind equalization and source separation methods to novel approaches based on machine learning and bio-inspired algorithms. From the foundations of statistical and adaptive signal processing, the authors explore and elaborate on emerging tools, such as machine learning-based solutions and bio-inspired methods. With a fresh take on this exciting area of study, this book: Provides a solid background on the statistical characterization of signals and systems and on linear filtering theory Emphasizes the link between supervised and unsupervised processing from the perspective of linear prediction and constrained filtering theory Addresses key issues concerning equilibrium solutions and equivalence relationships in the context of unsupervised equalization criteria Provides a systematic presentation of source separation and independent component analysis Discusses some instigating connections between the filtering problem and computational intelligence approaches. Building on more than a decade of the authors’ work at DSPCom laboratory, this book applies a fresh conceptual treatment and mathematical formalism to important existing topics. The result is perhaps the first unified presentation of unsupervised signal processing techniques—one that addresses areas including digital filters, adaptive methods, and statistical signal processing. With its remarkable synthesis of the field, this book provides a new vision to stimulate progress and contribute to the advent of more useful, efficient, and friendly intelligent systems.
This book constitutes the refereed proceedings of the 6th International Conference on Independent Component Analysis and Blind Source Separation, ICA 2006, held in Charleston, SC, USA, in March 2006. The 120 revised papers presented were carefully reviewed and selected from 183 submissions. The papers are organized in topical sections on algorithms and architectures, applications, medical applications, speech and signal processing, theory, and visual and sensory processing.
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.
In many situations found both in Nature and in human-built systems, a set of mixed signals is observed (frequently also with noise), and it is of great scientific and technological relevance to be able to isolate or separate them so that the information in each of the signals can be utilized. Blind source separation (BSS) research is one of the more interesting emerging fields now a days in the field of signal processing. It deals with the algorithms that allow the recovery of the original sources from a set of mixtures only. The adjective "blind" is applied because the purpose is to estimate the original sources without any a priori knowledge about either the sources or the mixing system. Most of the models employed in BSS assume the hypothesis about the independence of the original sources. Under this hypothesis, a BSS problem can be considered as a particular case of independent component analysis(ICA), a linear transformation technique that, starting from a multivariate representation of the data, minimizes the statistical dependence between the components of the representation. It can be claimed that most of the advances in ICA have been motivated by the search for solutions to the BSS problem and, the other way around, advances in ICA have been immediately applied to BSS. ICA and BSS algorithms start from a mixture model, whose parameters are estimated from the observed mixtures. Separation is achieved by applying the inverse mixture model to the observed signals(separating or unmixing model). Mixturem- els usually fall into three broad categories: instantaneous linear models, convolutive models and nonlinear models, the?rstone being the simplest but, in general, not near realistic applications. The development and test of the algorithms can be accomplished through synthetic data or with real-world data. Obviously, the most important aim(and most difficult) is the separation of real-world mixtures. BSS and ICA have strong relations also, apart from signal processing, with other fields such as statistics and artificial neural networks. As long as we can find a system that emits signals propagated through a mean, andthosesignalsarereceivedbyasetofsensorsandthereisaninterestinrecovering the original sources, we have a potential field of application for BSS and ICA. Inside that wide range of applications we can find, for instance: noise reduction applications, biomedical applications, audio systems, telecommunications, and many others. This volume comes out just 20 years after the first contributions in ICA and BSS 1 appeared . Therein after, the number of research groups working in ICA and BSS has been constantly growing, so that nowadays we can estimate that far more than 100 groups are researching in these fields. As proof of the recognition among the scientific community of ICA and BSS developments there have been numerous special sessions and special issues in several well- 1 J. Herault, B. Ans, "Circuits neuronaux à synapses modi?ables: décodage de messages composites para apprentissage non supervise", C.R. de l'Académie des Sciences, vol. 299, no. III-13,pp.525-528,1984
Blind identification consists of estimating a multi-dimensional system only through the use of its output, and source separation, the blind estimation of the inverse of the system. Estimation is generally carried out using different statistics of the output. The authors of this book consider the blind identification and source separation problem in the complex-domain, where the available statistical properties are richer and include non-circularity of the sources – underlying components. They define identifiability conditions and present state-of-the-art algorithms that are based on algebraic methods as well as iterative algorithms based on maximum likelihood theory. Contents 1. Mathematical Preliminaries. 2. Estimation by Joint Diagonalization. 3. Maximum Likelihood ICA. About the Authors Eric Moreau is Professor of Electrical Engineering at the University of Toulon, France. His research interests concern statistical signal processing, high order statistics and matrix/tensor decompositions with applications to data analysis, telecommunications and radar. Tülay Adali is Professor of Electrical Engineering and Director of the Machine Learning for Signal Processing Laboratory at the University of Maryland, Baltimore County, USA. Her research interests concern statistical and adaptive signal processing, with an emphasis on nonlinear and complex-valued signal processing, and applications in biomedical data analysis and communications. Blind identification consists of estimating a multidimensional system through the use of only its output. Source separation is concerned with the blind estimation of the inverse of the system. The estimation is generally performed by using different statistics of the outputs. The authors consider the blind estimation of a multiple input/multiple output (MIMO) system that mixes a number of underlying signals of interest called sources. They also consider the case of direct estimation of the inverse system for the purpose of source separation. They then describe the estimation theory associated with the identifiability conditions and dedicated algebraic algorithms. The algorithms depend critically on (statistical and/or time frequency) properties of complex sources that will be precisely described.