Blind spectral unmixing by local maximization of non-Gaussianity

We approach the estimation of material percentages per pixel (endmember fractional abundances) in hyperspectral remote-sensed images as a blind source separation problem. This task is commonly known as spectral unmixing. Classical techniques require the knowledge of the existing materials and their spectra, which is an unrealistic situation in most cases. In contrast to recently presented blind techniques based on independent component analysis, we implement here a dependent component analysis strategy, namely the MaxNG (maximum non-Gaussianity) algorithm, which is capable to separate even strongly dependent signals. We prove that, when the abundances verify a separability condition, they can be extracted by searching the local maxima of non-Gaussianity. We also provide enough theoretical as well as experimental facts that indicate that this condition holds true for endmember abundances. In addition, we discuss the implementation of MaxNG in a noisy scenario, we introduce a new technique for the removal of scale ambiguities of estimated sources, and a new fast algorithm for the calculation of a Parzen windows-based NG measure. We compare MaxNG to commonly used independent component analysis algorithms, such as FastICA and JADE. We analyze the efficiency of MaxNG in terms of the number of sensor channels, the number of available samples and other factors, by testing it on synthetically generated as well as real data. Finally, we present some examples of application of our technique to real images captured by the MIVIS airborne imaging spectrometer. Our results show that MaxNG is a good tool for spectral unmixing in a blind scenario.

[1]  Vwani P. Roychowdhury,et al.  Independent component analysis based on nonparametric density estimation , 2004, IEEE Transactions on Neural Networks.

[2]  Erkki Oja,et al.  Independent Component Analysis , 2001 .

[3]  C. Caiafa,et al.  Separation of statistically dependent sources using an L 2 -distance non-Gaussianity measure , 2006 .

[4]  M. Girolami,et al.  Advances in Independent Component Analysis , 2000, Perspectives in Neural Computing.

[5]  Yukio Kosugi,et al.  ICA-aided mixed-pixel analysis of hyperspectral data in agricultural land , 2005, IEEE Geoscience and Remote Sensing Letters.

[6]  Fred A. Kruse,et al.  The Spectral Image Processing System (SIPS) - Interactive visualization and analysis of imaging spectrometer data , 1993 .

[7]  Ben Gorte.  Supervised image classification , 1999 .

[8]  E. Parzen.  On Estimation of a Probability Density Function and Mode , 1962 .

[9]  Michael S. Lewicki,et al.  Unsupervised image classification, segmentation, and enhancement using ICA mixture models , 2002, IEEE Trans. Image Process..

[10]  José M. Bioucas-Dias,et al.  Does independent component analysis play a role in unmixing hyperspectral data? , 2003, IEEE Transactions on Geoscience and Remote Sensing.

[11]  Pramod K. Varshney,et al.  ICA mixture model based unsupervised classification of hyperspectral imagery , 2002, Applied Imagery Pattern Recognition Workshop, 2002. Proceedings..

[12]  Shigeo Abe DrEng.  Pattern Classification , 2001, Springer London.

[13]  Danielle Nuzillard,et al.  BSS, Classification and Pixel Demixing , 2004, ICA.

[14]  Emanuele Salerno,et al.  Dependent component analysis as a tool for blind spectral unmixing of remote sensed images , 2006, 2006 14th European Signal Processing Conference.

[15]  Antoine Souloumiac,et al.  Jacobi Angles for Simultaneous Diagonalization , 1996, SIAM J. Matrix Anal. Appl..

[16]  M. Lennon,et al.  Spectral unmixing of hyperspectral images with the independent component analysis and wavelet packets , 2001, IGARSS 2001. Scanning the Present and Resolving the Future. Proceedings. IEEE 2001 International Geoscience and Remote Sensing Symposium (Cat. No.01CH37217).

[17]  Allan Kardec Barros,et al.  The Independence Assumption: Dependent Component Analysis , 2000 .

[18]  Paul E. Johnson,et al.  Spectral mixture modeling: A new analysis of rock and soil types at the Viking Lander 1 Site , 1986 .

[19]  Anna Tonazzini,et al.  Separation of Correlated Astrophysical Sources Using Multiple-Lag Data Covariance Matrices , 2005, EURASIP J. Adv. Signal Process..

[20]  David G. Stork,et al.  Pattern Classification , 1973 .

[21]  P. Mather,et al.  Classification Methods for Remotely Sensed Data , 2001 .

[22]  I. Ginsberg,et al.  Unsupervised hyperspectral image analysis using independent component analysis , 2000, IGARSS 2000. IEEE 2000 International Geoscience and Remote Sensing Symposium. Taking the Pulse of the Planet: The Role of Remote Sensing in Managing the Environment. Proceedings (Cat. No.00CH37120).

[23]  Andrzej Cichocki,et al.  Adaptive Blind Signal and Image Processing - Learning Algorithms and Applications , 2002 .

[24]  Aapo Hyvärinen,et al.  A Fast Fixed-Point Algorithm for Independent Component Analysis , 1997, Neural Computation.

[25]  S. Klinke,et al.  Exploratory Projection Pursuit , 1995 .

[26]  P. Laguna,et al.  Signal Processing , 2002, Yearbook of Medical Informatics.

[27]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[28]  Cesar F. Caiafa,et al.  Separation of statistically dependent sources using an L2-distance non-Gaussianity measure , 2006, Signal Process..

[29]  D. Chakrabarti,et al.  A fast fixed - point algorithm for independent component analysis , 1997 .