Autonomous single-pass endmember approximation using lattice auto-associative memories

We propose a novel method for the autonomous determination of endmembers that employs recent results from the theory of lattice based auto-associative memories. In contrast to several other existing methods, the endmembers determined by the proposed method are physically linked to the data set spectra. Numerical examples are provided to illustrate lattice theoretical concepts and a hyperspectral image subcube, from the Cuprite site in Nevada, is used to find all endmember candidates in a single pass.

[1]  Margaret E. Gardner,et al.  Mapping Chaparral in the Santa Monica Mountains Using Multiple Endmember Spectral Mixture Models , 1998 .

[2]  Robert D. Guenther,et al.  Encyclopedia of modern optics , 2005 .

[3]  Manuel Graña,et al.  Associative morphological memories for endmember determination in spectral unmixing , 2003, The 12th IEEE International Conference on Fuzzy Systems, 2003. FUZZ '03..

[4]  M. E. Winter Comparison of approaches for determining end-members in hyperspectral data , 2000, 2000 IEEE Aerospace Conference. Proceedings (Cat. No.00TH8484).

[5]  Joseph W. Boardman,et al.  Analysis, understanding, and visualization of hyperspectral data as convex sets in n space , 1995, Defense, Security, and Sensing.

[6]  C. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[7]  Peter Sussner,et al.  Associative memories based on lattice algebra , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[8]  Daniel S. Myers,et al.  HYPERSPECTRAL ENDMEMBER DETECTION USING MORPHOLOGICAL AUTOASSOCIATIVE MEMORIES , 2005 .

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

[10]  Nirmal Keshava,et al.  A Survey of Spectral Unmixing Algorithms , 2003 .

[11]  Gerhard X. Ritter,et al.  Reconstruction of Patterns from Noisy Inputs Using Morphological Associative Memories , 2003, Journal of Mathematical Imaging and Vision.

[12]  V. Kumar,et al.  Elements of lattice theory , 1977 .

[13]  Wallace M. Porter,et al.  The airborne visible/infrared imaging spectrometer (AVIRIS) , 1993 .

[14]  Manuel Graña,et al.  Lattice Independence, Autoassociative Morphological Memories and unsupervised segmentation of Hyperspectral Images , 2007 .

[15]  Peter Sussner,et al.  Morphological associative memories , 1998, IEEE Trans. Neural Networks.

[16]  Peter Sussner Fixed points of autoassociative morphological memories , 2000, Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium.

[17]  John F. Mustard,et al.  Spectral unmixing , 2002, IEEE Signal Process. Mag..

[18]  Manuel Graña,et al.  Hyperspectral image analysis with associative morphological memories , 2003, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429).

[19]  M. Grana,et al.  Associative morphological memories for endmember induction , 2003, IGARSS 2003. 2003 IEEE International Geoscience and Remote Sensing Symposium. Proceedings (IEEE Cat. No.03CH37477).

[20]  R. Cuninghame-Green Minimax Algebra and Applications , 1994 .

[21]  Computer-Algebra Implementation of the Least-Squares Method on the Nonnegative Orthant , 2006 .

[22]  Juan-Carlos Valdiviezo-Navarro,et al.  Hyperspectral endmember detection based on strong lattice independence , 2007, SPIE Optical Engineering + Applications.

[23]  Gonzalo Urcid-S.,et al.  Generation of lattice independent vector sets for pattern recognition applications , 2007, SPIE Optical Engineering + Applications.

[24]  Manuel Graña,et al.  Two lattice computing approaches for the unsupervised segmentation of hyperspectral images , 2009, Neurocomputing.

[25]  Jean Gallier,et al.  Geometric Methods and Applications: For Computer Science and Engineering , 2000 .

[26]  Paul D. Gader,et al.  Fixed Points of Lattice Transforms and Lattice Associative Memories , 2006 .

[27]  Ralph Selfridge,et al.  A small part of lattice theory , 2007, APLQ.

[28]  Peter Sussner,et al.  Gray-scale morphological associative memories , 2006, IEEE Transactions on Neural Networks.