A NEW TECHNIQUE FOR BLIND SOURCE SEPARATION USING SUBBAND SUBSPACE ANALYSIS IN CORRELATED MULTICHANNEL SIGNAL ENVIRONMENTS Karim G. Oweiss, David J. Anderson Electrical Eng. & Computer Sc. Dept., University of Michigan, Ann Arbor 48109, USA ABSTRACT We investigate a new framework for the problem of blind source identification in multichannel signal processing. Inspired by a neurophysiological data environment, where an array of closely spaced recording electrodes is surrounded by multiple neural cell sources [1], significant spatial correlation of source signals motivated the need for an efficient technique for reliable multichannel blind source identification. In a previous work [2], we adopted a new approach for noise suppression based on thresholding an Array Discrete Wavelet Transform (ADWT) representation of the multichannel data. We extend the work in [2] to identify sources from the observation mixtures. The technique relies on separating sources with highest spatial energy distribution in each frequency subband spanned by the corresponding wavelet basis. Accordingly, the best basis selection criterion we propose benefits from the additional degree of freedom offered by the space domain. The amplitude and shift invariance properties revealed by this technique make it very efficient to track spatial source variations sometimes encountered in multichannel neural recordings. Results from multichannel multiunit neural data are presented and the overall performance is evaluated. 1. INTRODUCTION Multichannel signal processing aims at fusing data collected at several sensors in order to carry out an estimation task of signal sources. Generally speaking, the parameters to be estimated reveal important information characterizing the sources from which the data is observed. Among the numerous biomedical applications of array processing [3-4], neurophysiological recordings of neural cells in the brain using an array of closely spaced electrodes has received much attention in the last decade due to recent advances in microprobe fabrication and packaging [1]. Nevertheless, the need for efficient array processing algorithms to process the vast amount *This work was supported by NIH under grant number P41RR09754. of information obtained in the nervous system continues to emerge as more data becomes feasible to acquire. In a previous work [2], we showed that it is possible to efficiently suppress noise processes in multichannel recordings with an array denoising algorithm with the minimal number of assumptions governing the underlying signal and noise processes. In this work, the primary focus is on the source separation problem. We approach the problem from a new Multi-Resolution Subspace Analysis (MRSA) framework. In the next section, we describe the relevant DWT theory and focus on important properties revealed by applying MRSA to the transform domain. 2. MULTIRESOLUTION ANALYSIS 2.1. The Discrete Wavelet Transform The transform consists of an atomic decomposition representing the discrete signal in l 2 (Z) successively into different frequency bands in terms of shifted and dilated versions of a prototype bandpass wavelet function ) (n ψ and a low pass scaling function ) (n φ . An orthonormal basis is formed with a special choice of the wavelet and scaling functions [5].The basis functions can be obtained from the prototype wavelet and scaling functions as ) 2 ( 2 ) ( 2 / k n n j j jk - = - - ψ ψ j=1,2, … L, k=1,2, …, N (1) ) 2 ( 2 ) ( 2 / k n n j j jk - = - - φ φ j=1,2, … L, k=1,2, …, N (2) The single channel data vector denoted by ]) [ ],..., 2 [ ], 1 [ ( N x x x = x will accordingly be represented by ∑ ∑∑ = + = k L j jk k k j Lk k L n d n a 1 , , ) ( ) ( ψ φ x (3) where the approximation coefficients and the details coefficients, comprising the DWT at level j, are respectively, given by j j φ , x a = (4) j ψ , x d j = (5)