Nonnegative-Matrix-Factorization-Based Hyperspectral Unmixing With Partially Known Endmembers

Hyperspectral unmixing is an important technique for estimating fractions of various materials from remote sensing imagery. Most unmixing methods make the assumption that no prior knowledge of endmembers is available before the estimation. This is, however, not true for some unmixing tasks for which part of the endmember signatures may be known in advance. In this paper, we address the hyperspectral unmixing problem with partially known endmembers. We extend nonnegative-matrix-factorization-based unmixing algorithms to incorporate prior information into their models. The proposed approach uses the spectral signature of known endmembers as a constraint, among others, in the unmixing model, and propagates the knowledge by an optimization process which minimizes the difference between the image data and the prior knowledge. Results on both synthetic and real data have validated the effectiveness of the proposed method and have shown that it has outperformed several state-of-the-art methods that use or do not use prior knowledge of endmembers.

[1]  Johannes R. Sveinsson,et al.  Spectral and spatial classification of hyperspectral data using SVMs and morphological profiles , 2008, 2007 IEEE International Geoscience and Remote Sensing Symposium.

[2]  Zhenwei Shi,et al.  Nonnegative matrix factorization for hyperspectral unmixing using prior knowledge of spectral signatures , 2012 .

[3]  Antonio J. Plaza,et al.  Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches , 2012, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[4]  V. P. Pauca,et al.  Nonnegative matrix factorization for spectral data analysis , 2006 .

[5]  José M. Bioucas-Dias,et al.  A variable splitting augmented Lagrangian approach to linear spectral unmixing , 2009, 2009 First Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing.

[6]  Zhenwei Shi,et al.  Sparse Unmixing of Hyperspectral Data Using Spectral A Priori Information , 2015, IEEE Transactions on Geoscience and Remote Sensing.

[7]  José M. Bioucas-Dias,et al.  Vertex component analysis: a fast algorithm to unmix hyperspectral data , 2005, IEEE Transactions on Geoscience and Remote Sensing.

[8]  S. J. Sutley,et al.  USGS Digital Spectral Library splib06a , 2007 .

[9]  Patrik O. Hoyer,et al.  Non-negative Matrix Factorization with Sparseness Constraints , 2004, J. Mach. Learn. Res..

[10]  Antonio J. Plaza,et al.  Collaborative Sparse Regression for Hyperspectral Unmixing , 2014, IEEE Transactions on Geoscience and Remote Sensing.

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

[12]  Yin Zhang,et al.  Accelerating the Lee-Seung Algorithm for Nonnegative Matrix Factorization , 2005 .

[13]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[14]  H. Poilvé,et al.  Hyperspectral Imaging and Stress Mapping in Agriculture , 1998 .

[15]  A F Goetz,et al.  Imaging Spectrometry for Earth Remote Sensing , 1985, Science.

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

[17]  Sen Jia,et al.  Constrained Nonnegative Matrix Factorization for Hyperspectral Unmixing , 2009, IEEE Transactions on Geoscience and Remote Sensing.

[18]  W. Marsden.  I and J , 2012 .

[19]  Sen Jia,et al.  Spectral and Spatial Complexity-Based Hyperspectral Unmixing , 2007, IEEE Transactions on Geoscience and Remote Sensing.

[20]  Ajmal S. Mian,et al.  Repeated constrained sparse coding with partial dictionaries for hyperspectral unmixing , 2014, IEEE Winter Conference on Applications of Computer Vision.

[21]  Johannes R. Sveinsson,et al.  Endmember constrained semi-supervised hyperspectral unmixing , 2014, 2014 6th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS).

[22]  R. K. Shyamasundar,et al.  Introduction to algorithms , 1996 .

[23]  Antonio J. Plaza,et al.  Total Variation Spatial Regularization for Sparse Hyperspectral Unmixing , 2012, IEEE Transactions on Geoscience and Remote Sensing.

[24]  J. Boardman.  Automating spectral unmixing of AVIRIS data using convex geometry concepts , 1993 .

[25]  Chein-I Chang,et al.  Fully constrained least squares linear spectral mixture analysis method for material quantification in hyperspectral imagery , 2001, IEEE Trans. Geosci. Remote. Sens..

[26]  Antonio J. Plaza,et al.  MUSIC-CSR: Hyperspectral Unmixing via Multiple Signal Classification and Collaborative Sparse Regression , 2014, IEEE Transactions on Geoscience and Remote Sensing.

[27]  José M. Bioucas-Dias,et al.  A robust subspace method for semiblind dictionary-aided hyperspectral unmixing , 2014, 2014 6th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS).

[28]  Hairong Qi,et al.  Endmember Extraction From Highly Mixed Data Using Minimum Volume Constrained Nonnegative Matrix Factorization , 2007, IEEE Transactions on Geoscience and Remote Sensing.

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

[30]  Ying Wang,et al.  Structured Sparse Method for Hyperspectral Unmixing , 2014, ArXiv.

[31]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[32]  Ronald G. Resmini,et al.  Mineral mapping with HYperspectral Digital Imagery Collection Experiment (HYDICE) sensor data at Cuprite, Nevada, U.S.A. , 1997 .

[33]  H. Sebastian Seung,et al.  Learning the parts of objects by non-negative matrix factorization , 1999, Nature.

[34]  Antonio J. Plaza,et al.  Sparse Unmixing of Hyperspectral Data , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[35]  Chunxia Zhang,et al.  Enhancing Spectral Unmixing by Local Neighborhood Weights , 2012, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[36]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[37]  José M. Bioucas-Dias,et al.  Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing , 2010, 2010 2nd Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing.

[38]  Fernando Pereira,et al.  Aggregate and mixed-order Markov models for statistical language processing , 1997, EMNLP.

[39]  Bo Du,et al.  An Endmember Dissimilarity Constrained Non-Negative Matrix Factorization Method for Hyperspectral Unmixing , 2013, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[40]  Mario Winter,et al.  N-FINDR: an algorithm for fast autonomous spectral end-member determination in hyperspectral data , 1999, Optics & Photonics.

[41]  Xuelong Li,et al.  Manifold Regularized Sparse NMF for Hyperspectral Unmixing , 2013, IEEE Transactions on Geoscience and Remote Sensing.

[42]  H. Sebastian Seung,et al.  Algorithms for Non-negative Matrix Factorization , 2000, NIPS.

[43]  Jun Zhou,et al.  Hyperspectral Unmixing via $L_{1/2}$ Sparsity-Constrained Nonnegative Matrix Factorization , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[44]  Chih-Jen Lin,et al.  On the Convergence of Multiplicative Update Algorithms for Nonnegative Matrix Factorization , 2007, IEEE Transactions on Neural Networks.