We derive a new self-organizing learning algorithm that maximizes the information transferred in a network of nonlinear units. The algorithm does not assume any knowledge of the input distributions, and is defined here for the zero-noise limit. Under these conditions, information maximization has extra properties not found in the linear case (Linsker 1989). The nonlinearities in the transfer function are able to pick up higher-order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation. This enables the network to separate statistically independent components in the inputs: a higher-order generalization of principal components analysis. We apply the network to the source separation (or cocktail party) problem, successfully separating unknown mixtures of up to 10 speakers. We also show that a variant on the network architecture is able to perform blind deconvolution (cancellation of unknown echoes and reverberation in a speech signal). Finally, we derive dependencies of information transfer on time delays. We suggest that information maximization provides a unifying framework for problems in "blind" signal processing.

/pdf/an-information-maximization-approach-to-blind-separation-and-1cnlj7ibol.pdf

An information-maximization approach to blind separation and blind deconvolution

Find the secret to improve the quality of life by reading this adaptive blind signal and image processing. This is a kind of book that you need now. Besides, it can be your favorite book to read after having this book. Do you ask why? Well, this is a book that has different characteristic with others. You may not need to know who the author is, how well-known the work is. As wise word, never judge the words from who speaks, but make the words as your good value to your life.

Adaptive blind signal and image processing

A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the original data. Well-known linear transformation methods include, for example, principal component analysis, factor analysis, and projection pursuit. A recently developed linear transformation method is independent component analysis (ICA), in which the desired representation is the one that minimizes the statistical dependence of the components of the representation. Such a representation seems to capture the essential structure of the data in many applications. In this paper, we survey the existing theory and methods for ICA.

Survey on Independent Component Analysis

. Preface. Acknowledgments. List of Figures. List of Tables. Abbreviations and Symbols. Introduction. Part I: Independent Component Analysis: Theory. 1. Basics. 2. Independent Component Analysis. 3. A Unifying Information-Theoretic Framework for ICA. 4. Blind Separation of Time-Delayed and Convolved Sources. 5. ICA Using Overcomplete Representations. 6. First Steps towards Nonlinear ICA. Part II: Independent Component Analysis: Applications. 7. Biomedical Applications of ICA. 8. ICA for Feature Extraction. 9. Unsupervised Classification with ICA Mixture Models. 10. Conclusions and Future Research. Bibliography. About the Author. Index.

Independent Component Analysis: Theory and Applications

We consider a sensor array located in an enclosure, where arbitrary transfer functions (TFs) relate the source signal and the sensors. The array is used for enhancing a signal contaminated by interference. Constrained minimum power adaptive beamforming, which has been suggested by Frost (1972) and, in particular, the generalized sidelobe canceler (GSC) version, which has been developed by Griffiths and Jim (1982), are the most widely used beamforming techniques. These methods rely on the assumption that the received signals are simple delayed versions of the source signal. The good interference suppression attained under this assumption is severely impaired in complicated acoustic environments, where arbitrary TFs may be encountered. In this paper, we consider the arbitrary TF case. We propose a GSC solution, which is adapted to the general TF case. We derive a suboptimal algorithm that can be implemented by estimating the TFs ratios, instead of estimating the TFs. The TF ratios are estimated by exploiting the nonstationarity characteristics of the desired signal. The algorithm is applied to the problem of speech enhancement in a reverberating room. The discussion is supported by an experimental study using speech and noise signals recorded in an actual room acoustics environment.

Signal enhancement using beamforming and nonstationarity with applications to speech

We consider the problem in which we want to separate two (or more) signals that are coupled to each other through an unknown multiple-input-multiple-output linear system (channel). We prove that the signals can be decoupled, or separated, using only the condition that they are statistically independent, and find even weaker sufficient conditions involving their cross-polyspectra. By imposing these conditions on the reconstructed signals, we obtain a class of criteria for signal separation. These criteria are universal in the sense that they do not require any prior knowledge or information concerning The nature of the source signals. They may be communication signals, or speech signals, or any other 1-D or multidimensional signals (e.g., images). Computationally efficient algorithms for implementing the proposed criteria, that only involve the iterative solution to a linear least squares problem, are presented. >

Criteria for multichannel signal separation

The conventional method for identifying the transfer function of an unknown linear system consists of a least squares fit of its input to its output. It is equivalent to identifying the frequency response of the system by calculating the empirical cross-spectrum between the system's input and output, divided by the empirical auto-spectrum of the input process. However, if the additive noise at the system's output is correlated with the input process, e.g., in case of environmental noise that affects both system's input and output, the method may suffer from a severe bias effect. We present a modification of the cross-spectral method that exploits nonstationary features in the data in order to circumvent bias effects caused by correlated stationary noise. The proposed method is particularly attractive to problems of multichannel signal enhancement and noise cancellation, when the desired signal is nonstationary in nature, e.g., speech or image.

System identification using nonstationary signals

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Criteria for multichannel signal separation

System identification using nonstationary signals