Weighted Blind ℓq Hyperspectral Unmixing

Blind hyperspectral unmixing is the process of decomposing hyperspectral images (HSIs) into pure material spectra (endmembers) and abundances. In this paper, we examine scaling the pixels of the HSI inversely proportional to their ℓ2 norm, controlled with a tuning parameter. We promote sparse abundances using an ℓq penalty and softly enforce the abundance sum constraint using matrix augmentation. The minimization problem is solved using a variant of sparse nonnegative matrix factorization (NMF) and all tuning parameters are selected using Bayesian optimization. The proposed method is evaluated using two real hyperspectral images.

[1]  Jasper Snoek,et al.  Practical Bayesian Optimization of Machine Learning Algorithms , 2012, NIPS.

[2]  Zhijing Yang,et al.  Does Normalization Methods Play a Role for Hyperspectral Image Classification? , 2017, ArXiv.

[3]  Johannes R. Sveinsson,et al.  Sparse Distributed Multitemporal Hyperspectral Unmixing , 2017, IEEE Transactions on Geoscience and Remote Sensing.

[4]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

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

[6]  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.

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

[8]  David R. Thompson,et al.  Sparse superpixel unmixing for exploratory analysis of CRISM hyperspectral images , 2009, 2009 First Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing.

[9]  Paul Van Dooren,et al.  Weighted Nonnegative Matrix Factorization and Face Feature Extraction , 2007 .

[10]  Jocelyn Chanussot,et al.  Blind hyperspectral unmixing using an extended linear mixing model to address spectral variability , 2015, WHISPERS.

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

[12]  Feiyun Zhu,et al.  Spectral Unmixing Datasets with Ground Truths , 2017, ArXiv.

[13]  Alfred O. Hero,et al.  Nonlinear Unmixing of Hyperspectral Images: Models and Algorithms , 2013, IEEE Signal Processing Magazine.

[14]  Seungjin Choi,et al.  Weighted nonnegative matrix factorization , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

[15]  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.

[16]  Johannes R. Sveinsson,et al.  Blind Hyperspectral Unmixing Using Total Variation and $\ell_q$ Sparse Regularization , 2016, IEEE Transactions on Geoscience and Remote Sensing.

[17]  Antonio J. Plaza,et al.  Robust Collaborative Nonnegative Matrix Factorization for Hyperspectral Unmixing , 2015, IEEE Transactions on Geoscience and Remote Sensing.

[18]  Patrik O. Hoyer,et al.  Non-negative sparse coding , 2002, Proceedings of the 12th IEEE Workshop on Neural Networks for Signal Processing.

[19]  Johannes R. Sveinsson,et al.  Parameter Estimation For Blind lq Hyperspectral Unmixing Using Bayesian Optimization , 2018, 2018 9th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS).

[20]  Johannes R. Sveinsson,et al.  Hyperspectral Unmixing With $l_{q}$ Regularization , 2014, IEEE Transactions on Geoscience and Remote Sensing.