Blind Separation of Noisy Multivariate Data Using Second-Order Statistics: Remote-Sensing Applications

In this paper a second-order method for blind source separation of noisy instantaneous linear mixtures is presented for the case where the signal order k is unknown. Its performance advantages are illustrated by simulations and by application to Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) multichannel visible/infrared data. The model assumes that m mixtures x of dimension n are observed, where x = Ap + Gw, and the underlying signal vector p has k < n/3 independent unit-variance elements. A is the mixing matrix, G is diagonal, and w is a normalized white-noise vector. The algorithm estimates the Second-Order separation matrix A, signal Order k, and Noise and is therefore designated as SOON. SOON first iteratively estimates k and G using a scree metric, singular-value decomposition, and the expectation-maximization algorithm, and then determines the values of AP and W. The final step estimates A and the set of m signal vectors p using a variant of the joint-diagonalization method used in the Second-Order Blind Identification (SOBI) and Second-Order NonStationary (SONS) source-separation algorithms. The SOON extension of SOBI and SONS significantly improves their separation of simulated sources hidden in noise. SOON also reveals interesting thermal dynamics within AVIRIS multichannel visible/infrared imaging data not found by noise-adjusted principal-component analysis.

[1]  S. Macenka,et al.  Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) , 1988 .

[2]  José M. Bioucas-Dias,et al.  Hyperspectral Subspace Identification , 2008, IEEE Transactions on Geoscience and Remote Sensing.

[3]  D. Rowe.  A Bayesian approach to blind source separation , 2002 .

[4]  Eric Moulines,et al.  A blind source separation technique using second-order statistics , 1997, IEEE Trans. Signal Process..

[5]  Andrzej Cichocki,et al.  Adaptive blind signal and image processing , 2002 .

[6]  Jean-François Cardoso,et al.  Dependence, Correlation and Gaussianity in Independent Component Analysis , 2003, J. Mach. Learn. Res..

[7]  J. Cardoso,et al.  Maximum Likelihood Source SeparationBy the Expectation-Maximization Technique : Deterministic and Stochastic Implementation , 1995 .

[8]  H. Akaike.  A new look at the statistical model identification , 1974 .

[9]  Junehee Lee.  Blind noise estimation and compensation for improved characterization of multivariable processes , 2000 .

[10]  Dinh-Tuan Pham,et al.  Blind separation of instantaneous mixture of sources based on order statistics , 2000, IEEE Trans. Signal Process..

[11]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[12]  E. Oja,et al.  Independent Component Analysis , 2001 .

[13]  Amy Mueller,et al.  Iterative blind separation of Gaussian data of unknown order , 2003 .

[14]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[15]  Jean-Francois Cardoso,et al.  Blind signal separation: statistical principles , 1998, Proc. IEEE.

[16]  P. Switzer,et al.  A transformation for ordering multispectral data in terms of image quality with implications for noise removal , 1988 .

[17]  Thomas Kailath,et al.  Detection of signals by information theoretic criteria , 1985, IEEE Trans. Acoust. Speech Signal Process..

[18]  Hagai Attias,et al.  Independent Factor Analysis , 1999, Neural Computation.

[19]  Carlos R. Cabrera-Mercader.  Robust compression of multispectrtal remote sensing data , 1999 .

[20]  L. A. Nunes Amaral,et al.  Heuristic segmentation of a nonstationary time series. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Gregg Vane.  Airborne Visible/Infrared Imaging Spectrometer (AVIRIS). A description of the sensor, ground data processing facility, laboratory calibration, and first results , 1987 .

[22]  J. B. Lee,et al.  Enhancement of high spectral resolution remote-sensing data by a noise-adjusted principal components transform , 1990 .

[23]  D. H. Staelin,et al.  Iterative signal-order and noise estimation for multivariate data , 2001 .

[24]  Z. Bai,et al.  On detection of the number of signals in presence of white noise , 1985 .

[25]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[26]  Lucas C. Parra,et al.  A SURVEY OF CONVOLUTIVE BLIND SOURCE SEPARATION METHODS , 2007 .

[27]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.

[28]  J. Cardoso,et al.  On optimal source separation based on second and fourth order cumulants , 1996, Proceedings of 8th Workshop on Statistical Signal and Array Processing.

[29]  R. Okafor.  Maximum likelihood estimation from incomplete data , 1987 .

[30]  Lang Tong,et al.  A finite-step global convergence algorithm for the parameter estimation of multichannel MA processes , 1992, IEEE Trans. Signal Process..

[31]  J. Cardoso.  Infomax and maximum likelihood for blind source separation , 1997, IEEE Signal Processing Letters.

[32]  H. Hartley.  Maximum Likelihood Estimation from Incomplete Data , 1958 .