Matrix-Vector Nonnegative Tensor Factorization for Blind Unmixing of Hyperspectral Imagery

Many spectral unmixing approaches ranging from geometry, algebra to statistics have been proposed, in which nonnegative matrix factorization (NMF)-based ones form an important family. The original NMF-based unmixing algorithm loses the spectral and spatial information between mixed pixels when stack...

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Veröffentlicht in:	IEEE transactions on geoscience and remote sensing Jg. 55; H. 3; S. 1776 - 1792
Hauptverfasser:	Qian, Yuntao, Xiong, Fengchao, Zeng, Shan, Zhou, Jun, Tang, Yuan Yan
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York IEEE 01.03.2017 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Data processing Decomposition Distance measurement Factorization Feature extraction Hyperspectral imagery (HSI) Hyperspectral imaging Imagery Mathematical analysis Mathematical models Matrix algebra Matrix decomposition Matrix methods Mixture models Pixels Spatial data Spectra spectral unmixing spectral-spatial structure State of the art Statistical methods Tensile stress tensor factorization Tensors
ISSN:	0196-2892, 1558-0644
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Abstract	Many spectral unmixing approaches ranging from geometry, algebra to statistics have been proposed, in which nonnegative matrix factorization (NMF)-based ones form an important family. The original NMF-based unmixing algorithm loses the spectral and spatial information between mixed pixels when stacking the spectral responses of the pixels into an observed matrix. Therefore, various constrained NMF methods are developed to impose spectral structure, spatial structure, and spectral-spatial joint structure into NMF to enforce the estimated endmembers and abundances preserve these structures. Compared with matrix format, the third-order tensor is more natural to represent a hyperspectral data cube as a whole, by which the intrinsic structure of hyperspectral imagery can be losslessly retained. Extended from NMF-based methods, a matrix-vector nonnegative tensor factorization (NTF) model is proposed in this paper for spectral unmixing. Different from widely used tensor factorization models, such as canonical polyadic decomposition CPD) and Tucker decomposition, the proposed method is derived from block term decomposition, which is a combination of CPD and Tucker decomposition. This leads to a more flexible frame to model various application-dependent problems. The matrix-vector NTF decomposes a third-order tensor into the sum of several component tensors, with each component tensor being the outer product of a vector (endmember) and a matrix (corresponding abundances). From a formal perspective, this tensor decomposition is consistent with linear spectral mixture model. From an informative perspective, the structures within spatial domain, within spectral domain, and cross spectral-spatial domain are retreated interdependently. Experiments demonstrate that the proposed method has outperformed several state-of-the-art NMF-based unmixing methods.
AbstractList	Many spectral unmixing approaches ranging from geometry, algebra to statistics have been proposed, in which nonnegative matrix factorization (NMF)-based ones form an important family. The original NMF-based unmixing algorithm loses the spectral and spatial information between mixed pixels when stacking the spectral responses of the pixels into an observed matrix. Therefore, various constrained NMF methods are developed to impose spectral structure, spatial structure, and spectral-spatial joint structure into NMF to enforce the estimated endmembers and abundances preserve these structures. Compared with matrix format, the third-order tensor is more natural to represent a hyperspectral data cube as a whole, by which the intrinsic structure of hyperspectral imagery can be losslessly retained. Extended from NMF-based methods, a matrix-vector nonnegative tensor factorization (NTF) model is proposed in this paper for spectral unmixing. Different from widely used tensor factorization models, such as canonical polyadic decomposition CPD) and Tucker decomposition, the proposed method is derived from block term decomposition, which is a combination of CPD and Tucker decomposition. This leads to a more flexible frame to model various application-dependent problems. The matrix-vector NTF decomposes a third-order tensor into the sum of several component tensors, with each component tensor being the outer product of a vector (endmember) and a matrix (corresponding abundances). From a formal perspective, this tensor decomposition is consistent with linear spectral mixture model. From an informative perspective, the structures within spatial domain, within spectral domain, and cross spectral-spatial domain are retreated interdependently. Experiments demonstrate that the proposed method has outperformed several state-of-the-art NMF-based unmixing methods.
Author	Yuan Yan Tang Jun Zhou Shan Zeng Yuntao Qian Fengchao Xiong
Author_xml	– sequence: 1 givenname: Yuntao orcidid: 0000-0002-7418-5891 surname: Qian fullname: Qian, Yuntao – sequence: 2 givenname: Fengchao surname: Xiong fullname: Xiong, Fengchao – sequence: 3 givenname: Shan surname: Zeng fullname: Zeng, Shan – sequence: 4 givenname: Jun orcidid: 0000-0001-5822-8233 surname: Zhou fullname: Zhou, Jun – sequence: 5 givenname: Yuan Yan surname: Tang fullname: Tang, Yuan Yan
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SubjectTerms	Data processing Decomposition Distance measurement Factorization Feature extraction Hyperspectral imagery (HSI) Hyperspectral imaging Imagery Mathematical analysis Mathematical models Matrix algebra Matrix decomposition Matrix methods Mixture models Pixels Spatial data Spectra spectral unmixing spectral-spatial structure State of the art Statistical methods Tensile stress tensor factorization Tensors
Title	Matrix-Vector Nonnegative Tensor Factorization for Blind Unmixing of Hyperspectral Imagery
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