SPTM-9.1

Separation of a class of convolutive mixtures: a contrast function approach
Carine Simon, Philippe Loubaton, Christophe Vignat (Laboratoire systèmes de communication - UMLV - Champs sur Marne - 5, bvd Descartes - 77454 Marne la Vallée Cedex - FRANCE), Christian Jutten (LIS/TIRF - 44,avenue Félix Viallet - 38031 Grenoble Cedex - FRANCE), Guy d'Urso (EDF/DER - 6, quai Watier - 78401 Chatou Cedex - FRANCE)

In this paper, we address the problem of the separation of convolutive mixtures in the case where the non Gaussian source signals are not necessarily filtered versions of i.i.d. sequences. In this context, we show that the contrast functions, used in the linear process source case, still allow to separate the sources by a deflation approach. Some particular properties of higher order cumulants based contrast functions are also given.

SPTM-9.2

A New Time-Domain Deconvolution Algorithm And Its Applications
T.Engin Tuncer (Middle East Technical Unv., EE. Dept., Ankara, Turkey)

Recently a new time-domain method has been presented for deconvolution [1]. This multidimensional method completely eliminates the problems of the previous methods in one dimension and covers a reasonable part of the solutions in multidimensions. In this paper, we present some of the properties of this method. We will especially focus on the frequency domain behaviour of the algorithm as well as the performance under numerical errors and errors due to noise. In addition we will present examples of the applications including deconvolution with a modified NAS-RIF algorithm.

SPTM-9.3

Blind Signal Separation for Convolutive Mixing Environments Using Spatial-Temporal Processing
James P Reilly (Communications Research Laboratory, McMaster University, 1280 Main St. W., Hamilton Ontario, CANADA L8S 4K1), Lino E Coria Mendoza (Communications Research Laboratory, McMaster University, 1280 Main St. W, Hamilton, Ontario, CANADA L8S 4K1)

In this paper we extend the \emph{infomax} technique [1] for blind signal separation from the instantaneous mixing case to the convolutive mixing case. Separation in the convolutive case requires an unmixing system which uses present and past values of the observation vector, when the mixing system is causal. Thus, in developing an infomax process, both temporal and spatial dependence of the observations must be considered. We propose a stochastic gradient based structure which accomplishes this task. Performance of the proposed method is verified by subjective listening tests and quantitative measurements.

SPTM-9.4

Dynamic Signal Mixtures and Blind Source Separation
Dragan Obradovic (Siemens, ZT IK 4)

Methods for blind source separation (BSS) from linear instantaneous signal mixtures have drawn a significant attention due to their ability to recover original independent non-Gaussian sources without analyzing their temporal statistics. Hence, original voices or images (modulo permutation and linear scaling) are extracted from their mixtures without modeling the dynamics of the signals. The typical methods for performing blind source separation are Linear Independent Component Analysis (ICA) and the InfoMax method. Linear ICA directly penalizes a suitably chosen measure of the statistical dependence between the extracted signals. These measures are either obtained from the Information theoretic postulates such as the mutual information or from the cumulant expansion of the associated probability density functions. The InfoMax method is based on the entropy maximization of the non-linear transformation of the separated signals. This paper analyzes extensions of the instantaneous blind source separation techniques to the case of linear dynamic signal mixtures. Furthermore, the paper introduces a novel method based on combining Time Delayed Decorrelation (TDD) with the minimization of the cumulant cost function. TDD is used to obtain an acceptable initial condition for the cumulant based cost function optimization in order to reduce the numerical complexity of the latter method. This combined approach is illustrated on two examples including a real life cocktail party example. Keywords: higher order statistics, signal reconstruction

SPTM-9.5

On Underdetermined Source Separation
Anisse TALEB, Christian JUTTEN (LIS)

This paper discusses some theoritical results on underdetermined source separation i.e. when the mixing matrix is degenerate, espcially when there is more sources than observations. In this case, we show that the sources can be restored up to an arbitrary additive random vector. In the particular case of discrete sources, very relevant for digital communications, we show that this vector is certain.

SPTM-9.6

Single Channel Signal Separation using Linear Time Varying Filters: Separability of Non-Stationary Stochastic Signals
James R Hopgood, Peter J.W Rayner (Signal Processing Laboratory, Department of Engineering, University of Cambridge)

Separability of signal mixtures given only one mixture observation is defined as the identification of the accuracy to which the signals can be separated. The paper shows that when signals are separated using the generalised Wiener filter, the degree of separability can be deduced from the filter structure. To identify this structure, the processes are represented on an arbitrary spectral domain, and a sufficient solution to the Wiener filter is obtained. The filter is composed of a term independent of the signal values, corresponding to regions in the spectral domain where the desired signal components are not distorted by interfering noise components, and a term dependent on the signal correlations, corresponding to the region where components overlap. An example of determining perfect separability of modulated random signals is given.

SPTM-9.7

Blind Source Separation without Optimization Criteria?
Vicente Zarzoso, Asoke K Nandi (Signal Processing Division, Department of Electronic and Electrical Engineering, University of Strathclyde)

Blind source separation aims to extract a set of independent signals from a set of observed linear mixtures. After whitening the sensor output, the separation is achieved by estimating an orthogonal transformation, which in the real-mixture two-source two-sensor case is entirely characterized by a single rotation angle. This contribution studies an estimator of such an angle. Even though it is derived from geometric notions based on the scatter-plots of the signals involved, it is found, empirically, to exhibit a performance clearly up to the mark of other methods based on optimality criteria and, theoretically, to improve and generalize one of such procedures. The simplicity of the suggested estimator results in a straightforward adaptive version, which converges regardless of the source distribution, for quite mild conditions, and whose asymptotic analysis is easy to carry out. The applicability of the estimator in a full separation system is also illustrated.

SPTM-9.8

Deconvolution of Ultrasonic Nondestructive Evaluation Signals Using Higher-Order Statistics
Lahouari Ghouti (King Fahd University of Petroleum and Minerals), Chi Hau Chen (University of Massachusetts Darmouth)

In ultrasonic nondestructive evaluation (NDE) of materials, pulse echo measurements are masked by the characteristics of the measuring instruments, the propagation paths taken by the ultrasonic pulses, and are corrupted by addictive noise. Deconvolution operation seeks to undo these masking effects and extract the defect impulse response which is essential for identification. In this contribution, we show that the use of higher-order statistics (HOS)-based deconvolution methods is more suitable to unravel the aforementioned effects. Synthetic and real ultrasonic data obtained from artificial defects is used to show the improved performance of the proposed technique over conventional ones, based on second-order statistics (SOS), commonly used in ultrasonic NDE.

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Last Update: February 4, 1999 Ingo Höntsch