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Blind beamforming for Non Gaussian Signals

by Jean-François Cardoso, Antoine Souloumiac - IEE Proceedings-F , 1993

"... This paper considers an application of blind identification to beamforming. The key point is to use estimates of directional vectors rather than resorting to their hypothesized value. By using estimates of the directional vectors obtained via blind identification i.e. without knowing the arrray mani ..."

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This paper considers an application of blind identification to beamforming. The key point is to use estimates of directional vectors rather than resorting to their hypothesized value. By using estimates of the directional vectors obtained via blind identification i.e. without knowing the arrray manifold, beamforming is made robust with respect to array deformations, distortion of the wave front, pointing errors, etc ... so that neither array calibration nor physical modeling are necessary. Rather surprisingly, `blind beamformers' may outperform `informed beamformers' in a plausible range of parameters, even when the array is perfectly known to the informed beamformer. The key assumption blind identification relies on is the statistical independence of the sources, which we exploit using fourth-order cumulants. A computationally efficient technique is presented for the blind estimation of directional vectors, based on joint diagonalization of 4th-order cumulant matrices

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... context, the signal emitted by a spatially coherent source may be estimated by forming the inner product between the array output and a m \Theta 1 vector acting as a spatial filter. The review paper =-=[1]-=- is a good introduction to various strategies for designing spatial filters or `beamformers. Denote f p the spatial filter designed to extract s p (t), the signal of interest. The simplest approach t...

A robust and precise method for solving the permutation problem of frequency-domain blind source separation

by Hiroshi Sawada, Ryo Mukai, Shoko Araki, Shoji Makino - IEEE Trans. on Speech and Audio Processing 12 , 2004

"... This paper presents a robust and precise method for solving the permutation problem of frequency-domain blind source separation. It is based on two previous approaches: the direction of arrival estimation and the inter-frequency correlation. We discuss the advantages and disadvantages of the two app ..."

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This paper presents a robust and precise method for solving the permutation problem of frequency-domain blind source separation. It is based on two previous approaches: the direction of arrival estimation and the inter-frequency correlation. We discuss the advantages and disadvantages of the two approaches, and integrate them to exploit their respective advantages. We also present a closed form formula to estimate the directions of source signals from a separating matrix obtained by ICA. Experimental results show that our method solved permutation problems almost perfectly for a situation that two sources were mixed in a room whose reverberation time was 300 ms. 1.

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... Yr(f,m). Let dq be the position of sensor q (we assume linearly arranged array sensors), and θ p be the direction of source sp (the direction orthogonal to the array is 90 ◦ ). In beamforming theory =-=[11]-=-, the frequency response of an impulse response hqp(t) is approximated as Hqp(f) =ej2πfc−1 dq cos θp , (3.1) where c is the propagation velocity. In this approximation, we assume a plane wavefront and...

Localization of brain electrical activity via linearly constrained minimum variance spatial filtering

by Barry D. Van Veen, Wim Van Drongelen, Moshe Yuchtman, Akifumi Suzuki - IEEE Trans. Biomed. Eng , 1997

"... Abstract—A spatial filtering method for localizing sources of brain electrical activity from surface recordings is described and analyzed. The spatial filters are implemented as a weighted sum of the data recorded at different sites. The weights are chosen to minimize the filter output power subject ..."

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Abstract—A spatial filtering method for localizing sources of brain electrical activity from surface recordings is described and analyzed. The spatial filters are implemented as a weighted sum of the data recorded at different sites. The weights are chosen to minimize the filter output power subject to a linear constraint. The linear constraint forces the filter to pass brain electrical activity from a specified location, while the power minimization attenuates activity originating at other locations. The estimated output power as a function of location is normalized by the estimated noise power as a function of location to obtain a neural activity index map. Locations of source activity correspond to maxima in the neural activity index map. The method does not require any prior assumptions about the number of active sources of their geometry because it exploits the spatial covariance of the source electrical activity. This paper presents a development and analysis of the method and explores its sensitivity to deviations between actual and assumed data models. The effect on the algorithm of covariance matrix estimation, correlation between sources, and choice of reference is discussed. Simulated and measured data is used to illustrate the efficacy of the approach. Index Terms — Dipole localization, EEG localization, linearly constrained minimum variance filter, MEG localization, reference

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