An Automatic Sparse Pruning Endmember Extraction Algorithm with a Combined Minimum Volume and Deviation Constraint

In this paper, an automatic sparse pruning endmember extraction algorithm with a combined minimum volume and deviation constraint (SPEEVD) is proposed. The proposed algorithm can adaptively determine the number of endmembers through a sparse pruning method and, at the same time, can weaken the noise interference by a minimum volume and deviation constraint. A non-negative matrix factorization solution based on the projection gradient is mathematically applied to solve the combined constrained optimization problem, which makes sure that the convergence is steady and robust. Experiments were carried out on both simulated data sets and real AVIRIS data sets. The experimental results indicate that the proposed method does not require a predetermined endmember number, but it still manifests an improvement in both the root-mean-square error (RMSE) and the endmember spectra, compared to the other state-of-the-art methods, most of which need an accurate pre-estimation of endmember number.

[1]  Salah Bourennane,et al.  Dimensionality Reduction Based on Tensor Modeling for Classification Methods , 2009, IEEE Transactions on Geoscience and Remote Sensing.

[2]  Lizhe Wang,et al.  Rolling Guidance Based Scaled-Aware Spatial Sparse Unmixing for Hyperspectral Remote Sensing Imagery , 2017, IGARSS 2018 - 2018 IEEE International Geoscience and Remote Sensing Symposium.

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

[4]  Andreas T. Ernst,et al.  ICE: a statistical approach to identifying endmembers in hyperspectral images , 2004, IEEE Transactions on Geoscience and Remote Sensing.

[5]  Qian Du,et al.  Anomaly-Based JPEG2000 Compression of Hyperspectral Imagery , 2008, IEEE Geoscience and Remote Sensing Letters.

[6]  ZhongPing Lee,et al.  Hyperspectral Shallow-Water Remote Sensing with an Enhanced Benthic Classifier , 2018, Remote. Sens..

[7]  John B. Greer,et al.  Sparse Demixing of Hyperspectral Images , 2012, IEEE Transactions on Image Processing.

[8]  Mário A. T. Figueiredo.  Adaptive Sparseness for Supervised Learning , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  Antonio J. Plaza,et al.  Spatial/spectral endmember extraction by multidimensional morphological operations , 2002, IEEE Trans. Geosci. Remote. Sens..

[10]  Chein-I Chang,et al.  Estimation of number of spectrally distinct signal sources in hyperspectral imagery , 2004, IEEE Transactions on Geoscience and Remote Sensing.

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

[12]  Konrad Schindler,et al.  Hyperspectral Super-Resolution with Spectral Unmixing Constraints , 2017, Remote. Sens..

[13]  Chein-I Chang,et al.  A New Growing Method for Simplex-Based Endmember Extraction Algorithm , 2006, IEEE Transactions on Geoscience and Remote Sensing.

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

[15]  Bo Du,et al.  PLTD: Patch-Based Low-Rank Tensor Decomposition for Hyperspectral Images , 2017, IEEE Transactions on Multimedia.

[16]  Marco Diani,et al.  Hyperspectral Signal Subspace Identification in the Presence of Rare Signal Components , 2010, IEEE Transactions on Geoscience and Remote Sensing.

[17]  Maurice D. Craig,et al.  Minimum-volume transforms for remotely sensed data , 1994, IEEE Trans. Geosci. Remote. Sens..

[18]  José M. Bioucas-Dias,et al.  Hyperspectral Subspace Identification , 2008, IEEE Transactions on Geoscience and Remote Sensing.

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

[20]  Fubiao Feng,et al.  Dimensionality Reduction of Hyperspectral Image with Graph-Based Discriminant Analysis Considering Spectral Similarity , 2017, Remote. Sens..

[21]  Bo Du,et al.  Target detection based on a dynamic subspace , 2014, Pattern Recognit..

[22]  Bo Du,et al.  Beyond the Sparsity-Based Target Detector: A Hybrid Sparsity and Statistics-Based Detector for Hyperspectral Images , 2016, IEEE Transactions on Image Processing.

[23]  Chein-I Chang,et al.  Multispectral and hyperspectral image analysis with convex cones , 1999, IEEE Trans. Geosci. Remote. Sens..

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

[25]  Masahiro Okuda,et al.  Joint Local Abundance Sparse Unmixing for Hyperspectral Images , 2017, Remote. Sens..

[26]  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.

[27]  Liangpei Zhang,et al.  A Hybrid Automatic Endmember Extraction Algorithm Based on a Local Window , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[28]  Paul D. Gader,et al.  Sparsity Promoting Iterated Constrained Endmember Detection in Hyperspectral Imagery , 2007, IEEE Geoscience and Remote Sensing Letters.

[29]  Antonio J. Plaza,et al.  A New Minimum-Volume Enclosing Algorithm for Endmember Identification and Abundance Estimation in Hyperspectral Data , 2012, IEEE Transactions on Geoscience and Remote Sensing.

[30]  David Malah,et al.  Rank Estimation and Redundancy Reduction of High-Dimensional Noisy Signals With Preservation of Rare Vectors , 2007, IEEE Transactions on Signal Processing.

[31]  Chong-Yung Chi,et al.  A convex analysis-based minimum-volume enclosing simplex algorithm for hyperspectral unmixing , 2009, IEEE Trans. Signal Process..

[32]  Bo Du,et al.  A Discriminative Metric Learning Based Anomaly Detection Method , 2014, IEEE Transactions on Geoscience and Remote Sensing.

[33]  Wei Xia,et al.  An approach based on constrained nonnegative matrix factorization to unmix hyperspectral data , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[34]  Peter M. Williams,et al.  Bayesian Regularization and Pruning Using a Laplace Prior , 1995, Neural Computation.

[35]  Bo Du,et al.  Random-Selection-Based Anomaly Detector for Hyperspectral Imagery , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[36]  Konstantinos Koutroumbas,et al.  A Novel Hierarchical Bayesian Approach for Sparse Semisupervised Hyperspectral Unmixing , 2012, IEEE Transactions on Signal Processing.

[37]  Chein-I Chang,et al.  Improved Process for Use of a Simplex Growing Algorithm for Endmember Extraction , 2009, IEEE Geoscience and Remote Sensing Letters.

[38]  Peter G. Casazza,et al.  Optimally Sparse Frames , 2010, IEEE Transactions on Information Theory.

[39]  Jun Huang,et al.  Sparse Unmixing of Hyperspectral Data with Noise Level Estimation , 2017, Remote. Sens..

[40]  Jin Chen,et al.  A Quantitative Analysis of Virtual Endmembers' Increased Impact on the Collinearity Effect in Spectral Unmixing , 2011, IEEE Transactions on Geoscience and Remote Sensing.

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

[42]  Peter Bajorski,et al.  Second Moment Linear Dimensionality as an Alternative to Virtual Dimensionality , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[43]  Paul D. Gader,et al.  Hyperspectral Band Selection and Endmember Detection Using Sparsity Promoting Priors , 2008, IEEE Geoscience and Remote Sensing Letters.

[44]  Qian Du,et al.  Hyperspectral Dimensionality Reduction by Tensor Sparse and Low-Rank Graph-Based Discriminant Analysis , 2017, Remote. Sens..

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

[46]  Shen-En Qian,et al.  Hyperspectral data compression using a fast vector quantization algorithm , 2004, IEEE Transactions on Geoscience and Remote Sensing.

[47]  Wei Xiong,et al.  Stacked Convolutional Denoising Auto-Encoders for Feature Representation , 2017, IEEE Transactions on Cybernetics.

[48]  Shengli Xie,et al.  Blind Spectral Unmixing Based on Sparse Nonnegative Matrix Factorization , 2011, IEEE Transactions on Image Processing.