Sparse and low rank hyperspectral unmixing

In this paper, hyperspectral data is modeled as a combination of a sparse component, a low rank component and noise. The low rank component is a product of the endmembers and the abundances in an image, and the sparse component is composed of outliers and structured noise. Outliers and structured noise in this context are, e.g. band specific noise, vertical or horizontal artifacts or saturated pixels. Sparse and low rank matrix decomposition (SLR) is a method that has recently been developed for estimating those components. Here, an algorithm based on l1 SLR is developed using sparse blind hyperspectral unmixing and soft thresholding. The number of endmembers and the sparsity parameters are selected using the extended Bayesian information criterion (EBIC). The proposed algorithm is evaluated using a real remote sensing hyperspectral image.

[1]  Bin Wang,et al.  Hyperspectral Anomaly Detection Based on Low-Rank Representation and Learned Dictionary , 2016, Remote. Sens..

[2]  D. Field,et al.  Natural image statistics and efficient coding. , 1996, Network.

[3]  Xiaodong Li,et al.  Stable Principal Component Pursuit , 2010, 2010 IEEE International Symposium on Information Theory.

[4]  Liangpei Zhang,et al.  Hyperspectral Image Restoration Using Low-Rank Matrix Recovery , 2014, IEEE Transactions on Geoscience and Remote Sensing.

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

[6]  A. Willsky,et al.  Sparse and low-rank matrix decompositions , 2009 .

[7]  Goran Marjanovic,et al.  Sparse and low rank decomposition using l0 penalty , 2015, 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[8]  Yi Ma,et al.  Robust principal component analysis? , 2009, JACM.

[9]  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.

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

[11]  A. Cichocki,et al.  Flexible HALS algorithms for sparse non-negative matrix/tensor factorization , 2008, 2008 IEEE Workshop on Machine Learning for Signal Processing.

[12]  Jiahua Chen,et al.  Extended Bayesian information criteria for model selection with large model spaces , 2008 .

[13]  Xiaoming Yuan,et al.  Recovering Low-Rank and Sparse Components of Matrices from Incomplete and Noisy Observations , 2011, SIAM J. Optim..

[14]  Angshul Majumdar,et al.  Hyperspectral Unmixing in the Presence of Mixed Noise Using Joint-Sparsity and Total Variation , 2016, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[15]  Ian T. Jolliffe,et al.  Principal Component Analysis , 2002, International Encyclopedia of Statistical Science.