Least Angle Regression-Based Constrained Sparse Unmixing of Hyperspectral Remote Sensing Imagery

Sparse unmixing has been successfully applied in hyperspectral remote sensing imagery analysis based on a standard spectral library known in advance. This approach involves reformulating the traditional linear spectral unmixing problem by finding the optimal subset of signatures in this spectral library using the sparse regression technique, and has greatly improved the estimation of fractional abundances in ubiquitous mixed pixels. Since the potentially large standard spectral library can be given a priori, the most challenging task is to compute the regression coefficients, i.e., the fractional abundances, for the linear regression problem. There are many mathematical techniques that can be used to deal with the spectral unmixing problem; e.g., ordinary least squares (OLS), constrained least squares (CLS), orthogonal matching pursuit (OMP), and basis pursuit (BP). However, due to poor prediction accuracy and non-interpretability, the traditional methods often cannot obtain satisfactory estimations or achieve a reasonable interpretation. In this paper, to improve the regression accuracy of sparse unmixing, least angle regression-based constrained sparse unmixing (LARCSU) is introduced to further enhance the precision of sparse unmixing. Differing from the classical greedy algorithms and some of the cautious sparse regression-based approaches, the LARCSU algorithm has two main advantages. Firstly, it introduces an equiangular vector to seek the optimal regression steps based on the simple underlying geometry. Secondly, unlike the alternating direction method of multipliers (ADMM)-based algorithms that introduce one or more multipliers or augmented terms during their optimization procedures, no parameters are required in the computational process of the LARCSU approach. The experimental results obtained with both simulated datasets and real hyperspectral images confirm the effectiveness of LARCSU compared with the current state-of-the-art spectral unmixing algorithms. LARCSU can obtain a better fractional abundance map, as well as a higher unmixing accuracy, with the same order of magnitude of computational effort as the CLS-based methods. Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Ruyi Feng [verfasserIn] Lizhe Wang [verfasserIn] Yanfei Zhong [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Schlagwörter:	sparse unmixing least angle regression equiangular vector linear regression hyperspectral remote sensing imagery

Übergeordnetes Werk:	In: Remote Sensing - MDPI AG, 2009, 10(2018), 10, p 1546
Übergeordnetes Werk:	volume:10 ; year:2018 ; number:10, p 1546

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/rs10101546

Katalog-ID:	DOAJ017943817

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allfields	10.3390/rs10101546 doi (DE-627)DOAJ017943817 (DE-599)DOAJd83f47becf9c457a801b12d74e4805ed DE-627 ger DE-627 rakwb eng Ruyi Feng verfasserin aut Least Angle Regression-Based Constrained Sparse Unmixing of Hyperspectral Remote Sensing Imagery 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sparse unmixing has been successfully applied in hyperspectral remote sensing imagery analysis based on a standard spectral library known in advance. This approach involves reformulating the traditional linear spectral unmixing problem by finding the optimal subset of signatures in this spectral library using the sparse regression technique, and has greatly improved the estimation of fractional abundances in ubiquitous mixed pixels. Since the potentially large standard spectral library can be given a priori, the most challenging task is to compute the regression coefficients, i.e., the fractional abundances, for the linear regression problem. There are many mathematical techniques that can be used to deal with the spectral unmixing problem; e.g., ordinary least squares (OLS), constrained least squares (CLS), orthogonal matching pursuit (OMP), and basis pursuit (BP). However, due to poor prediction accuracy and non-interpretability, the traditional methods often cannot obtain satisfactory estimations or achieve a reasonable interpretation. In this paper, to improve the regression accuracy of sparse unmixing, least angle regression-based constrained sparse unmixing (LARCSU) is introduced to further enhance the precision of sparse unmixing. Differing from the classical greedy algorithms and some of the cautious sparse regression-based approaches, the LARCSU algorithm has two main advantages. Firstly, it introduces an equiangular vector to seek the optimal regression steps based on the simple underlying geometry. Secondly, unlike the alternating direction method of multipliers (ADMM)-based algorithms that introduce one or more multipliers or augmented terms during their optimization procedures, no parameters are required in the computational process of the LARCSU approach. The experimental results obtained with both simulated datasets and real hyperspectral images confirm the effectiveness of LARCSU compared with the current state-of-the-art spectral unmixing algorithms. LARCSU can obtain a better fractional abundance map, as well as a higher unmixing accuracy, with the same order of magnitude of computational effort as the CLS-based methods. sparse unmixing least angle regression equiangular vector linear regression hyperspectral remote sensing imagery Science Q Lizhe Wang verfasserin aut Yanfei Zhong verfasserin aut In Remote Sensing MDPI AG, 2009 10(2018), 10, p 1546 (DE-627)608937916 (DE-600)2513863-7 20724292 nnns volume:10 year:2018 number:10, p 1546 https://doi.org/10.3390/rs10101546 kostenfrei https://doaj.org/article/d83f47becf9c457a801b12d74e4805ed kostenfrei http://www.mdpi.com/2072-4292/10/10/1546 kostenfrei https://doaj.org/toc/2072-4292 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4700 AR 10 2018 10, p 1546
spelling	10.3390/rs10101546 doi (DE-627)DOAJ017943817 (DE-599)DOAJd83f47becf9c457a801b12d74e4805ed DE-627 ger DE-627 rakwb eng Ruyi Feng verfasserin aut Least Angle Regression-Based Constrained Sparse Unmixing of Hyperspectral Remote Sensing Imagery 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sparse unmixing has been successfully applied in hyperspectral remote sensing imagery analysis based on a standard spectral library known in advance. This approach involves reformulating the traditional linear spectral unmixing problem by finding the optimal subset of signatures in this spectral library using the sparse regression technique, and has greatly improved the estimation of fractional abundances in ubiquitous mixed pixels. Since the potentially large standard spectral library can be given a priori, the most challenging task is to compute the regression coefficients, i.e., the fractional abundances, for the linear regression problem. There are many mathematical techniques that can be used to deal with the spectral unmixing problem; e.g., ordinary least squares (OLS), constrained least squares (CLS), orthogonal matching pursuit (OMP), and basis pursuit (BP). However, due to poor prediction accuracy and non-interpretability, the traditional methods often cannot obtain satisfactory estimations or achieve a reasonable interpretation. In this paper, to improve the regression accuracy of sparse unmixing, least angle regression-based constrained sparse unmixing (LARCSU) is introduced to further enhance the precision of sparse unmixing. Differing from the classical greedy algorithms and some of the cautious sparse regression-based approaches, the LARCSU algorithm has two main advantages. Firstly, it introduces an equiangular vector to seek the optimal regression steps based on the simple underlying geometry. Secondly, unlike the alternating direction method of multipliers (ADMM)-based algorithms that introduce one or more multipliers or augmented terms during their optimization procedures, no parameters are required in the computational process of the LARCSU approach. The experimental results obtained with both simulated datasets and real hyperspectral images confirm the effectiveness of LARCSU compared with the current state-of-the-art spectral unmixing algorithms. LARCSU can obtain a better fractional abundance map, as well as a higher unmixing accuracy, with the same order of magnitude of computational effort as the CLS-based methods. sparse unmixing least angle regression equiangular vector linear regression hyperspectral remote sensing imagery Science Q Lizhe Wang verfasserin aut Yanfei Zhong verfasserin aut In Remote Sensing MDPI AG, 2009 10(2018), 10, p 1546 (DE-627)608937916 (DE-600)2513863-7 20724292 nnns volume:10 year:2018 number:10, p 1546 https://doi.org/10.3390/rs10101546 kostenfrei https://doaj.org/article/d83f47becf9c457a801b12d74e4805ed kostenfrei http://www.mdpi.com/2072-4292/10/10/1546 kostenfrei https://doaj.org/toc/2072-4292 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4700 AR 10 2018 10, p 1546
allfields_unstemmed	10.3390/rs10101546 doi (DE-627)DOAJ017943817 (DE-599)DOAJd83f47becf9c457a801b12d74e4805ed DE-627 ger DE-627 rakwb eng Ruyi Feng verfasserin aut Least Angle Regression-Based Constrained Sparse Unmixing of Hyperspectral Remote Sensing Imagery 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sparse unmixing has been successfully applied in hyperspectral remote sensing imagery analysis based on a standard spectral library known in advance. This approach involves reformulating the traditional linear spectral unmixing problem by finding the optimal subset of signatures in this spectral library using the sparse regression technique, and has greatly improved the estimation of fractional abundances in ubiquitous mixed pixels. Since the potentially large standard spectral library can be given a priori, the most challenging task is to compute the regression coefficients, i.e., the fractional abundances, for the linear regression problem. There are many mathematical techniques that can be used to deal with the spectral unmixing problem; e.g., ordinary least squares (OLS), constrained least squares (CLS), orthogonal matching pursuit (OMP), and basis pursuit (BP). However, due to poor prediction accuracy and non-interpretability, the traditional methods often cannot obtain satisfactory estimations or achieve a reasonable interpretation. In this paper, to improve the regression accuracy of sparse unmixing, least angle regression-based constrained sparse unmixing (LARCSU) is introduced to further enhance the precision of sparse unmixing. Differing from the classical greedy algorithms and some of the cautious sparse regression-based approaches, the LARCSU algorithm has two main advantages. Firstly, it introduces an equiangular vector to seek the optimal regression steps based on the simple underlying geometry. Secondly, unlike the alternating direction method of multipliers (ADMM)-based algorithms that introduce one or more multipliers or augmented terms during their optimization procedures, no parameters are required in the computational process of the LARCSU approach. The experimental results obtained with both simulated datasets and real hyperspectral images confirm the effectiveness of LARCSU compared with the current state-of-the-art spectral unmixing algorithms. LARCSU can obtain a better fractional abundance map, as well as a higher unmixing accuracy, with the same order of magnitude of computational effort as the CLS-based methods. sparse unmixing least angle regression equiangular vector linear regression hyperspectral remote sensing imagery Science Q Lizhe Wang verfasserin aut Yanfei Zhong verfasserin aut In Remote Sensing MDPI AG, 2009 10(2018), 10, p 1546 (DE-627)608937916 (DE-600)2513863-7 20724292 nnns volume:10 year:2018 number:10, p 1546 https://doi.org/10.3390/rs10101546 kostenfrei https://doaj.org/article/d83f47becf9c457a801b12d74e4805ed kostenfrei http://www.mdpi.com/2072-4292/10/10/1546 kostenfrei https://doaj.org/toc/2072-4292 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4700 AR 10 2018 10, p 1546
allfieldsGer	10.3390/rs10101546 doi (DE-627)DOAJ017943817 (DE-599)DOAJd83f47becf9c457a801b12d74e4805ed DE-627 ger DE-627 rakwb eng Ruyi Feng verfasserin aut Least Angle Regression-Based Constrained Sparse Unmixing of Hyperspectral Remote Sensing Imagery 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sparse unmixing has been successfully applied in hyperspectral remote sensing imagery analysis based on a standard spectral library known in advance. This approach involves reformulating the traditional linear spectral unmixing problem by finding the optimal subset of signatures in this spectral library using the sparse regression technique, and has greatly improved the estimation of fractional abundances in ubiquitous mixed pixels. Since the potentially large standard spectral library can be given a priori, the most challenging task is to compute the regression coefficients, i.e., the fractional abundances, for the linear regression problem. There are many mathematical techniques that can be used to deal with the spectral unmixing problem; e.g., ordinary least squares (OLS), constrained least squares (CLS), orthogonal matching pursuit (OMP), and basis pursuit (BP). However, due to poor prediction accuracy and non-interpretability, the traditional methods often cannot obtain satisfactory estimations or achieve a reasonable interpretation. In this paper, to improve the regression accuracy of sparse unmixing, least angle regression-based constrained sparse unmixing (LARCSU) is introduced to further enhance the precision of sparse unmixing. Differing from the classical greedy algorithms and some of the cautious sparse regression-based approaches, the LARCSU algorithm has two main advantages. Firstly, it introduces an equiangular vector to seek the optimal regression steps based on the simple underlying geometry. Secondly, unlike the alternating direction method of multipliers (ADMM)-based algorithms that introduce one or more multipliers or augmented terms during their optimization procedures, no parameters are required in the computational process of the LARCSU approach. The experimental results obtained with both simulated datasets and real hyperspectral images confirm the effectiveness of LARCSU compared with the current state-of-the-art spectral unmixing algorithms. LARCSU can obtain a better fractional abundance map, as well as a higher unmixing accuracy, with the same order of magnitude of computational effort as the CLS-based methods. sparse unmixing least angle regression equiangular vector linear regression hyperspectral remote sensing imagery Science Q Lizhe Wang verfasserin aut Yanfei Zhong verfasserin aut In Remote Sensing MDPI AG, 2009 10(2018), 10, p 1546 (DE-627)608937916 (DE-600)2513863-7 20724292 nnns volume:10 year:2018 number:10, p 1546 https://doi.org/10.3390/rs10101546 kostenfrei https://doaj.org/article/d83f47becf9c457a801b12d74e4805ed kostenfrei http://www.mdpi.com/2072-4292/10/10/1546 kostenfrei https://doaj.org/toc/2072-4292 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4700 AR 10 2018 10, p 1546
allfieldsSound	10.3390/rs10101546 doi (DE-627)DOAJ017943817 (DE-599)DOAJd83f47becf9c457a801b12d74e4805ed DE-627 ger DE-627 rakwb eng Ruyi Feng verfasserin aut Least Angle Regression-Based Constrained Sparse Unmixing of Hyperspectral Remote Sensing Imagery 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Sparse unmixing has been successfully applied in hyperspectral remote sensing imagery analysis based on a standard spectral library known in advance. This approach involves reformulating the traditional linear spectral unmixing problem by finding the optimal subset of signatures in this spectral library using the sparse regression technique, and has greatly improved the estimation of fractional abundances in ubiquitous mixed pixels. Since the potentially large standard spectral library can be given a priori, the most challenging task is to compute the regression coefficients, i.e., the fractional abundances, for the linear regression problem. There are many mathematical techniques that can be used to deal with the spectral unmixing problem; e.g., ordinary least squares (OLS), constrained least squares (CLS), orthogonal matching pursuit (OMP), and basis pursuit (BP). However, due to poor prediction accuracy and non-interpretability, the traditional methods often cannot obtain satisfactory estimations or achieve a reasonable interpretation. In this paper, to improve the regression accuracy of sparse unmixing, least angle regression-based constrained sparse unmixing (LARCSU) is introduced to further enhance the precision of sparse unmixing. Differing from the classical greedy algorithms and some of the cautious sparse regression-based approaches, the LARCSU algorithm has two main advantages. Firstly, it introduces an equiangular vector to seek the optimal regression steps based on the simple underlying geometry. Secondly, unlike the alternating direction method of multipliers (ADMM)-based algorithms that introduce one or more multipliers or augmented terms during their optimization procedures, no parameters are required in the computational process of the LARCSU approach. The experimental results obtained with both simulated datasets and real hyperspectral images confirm the effectiveness of LARCSU compared with the current state-of-the-art spectral unmixing algorithms. LARCSU can obtain a better fractional abundance map, as well as a higher unmixing accuracy, with the same order of magnitude of computational effort as the CLS-based methods. sparse unmixing least angle regression equiangular vector linear regression hyperspectral remote sensing imagery Science Q Lizhe Wang verfasserin aut Yanfei Zhong verfasserin aut In Remote Sensing MDPI AG, 2009 10(2018), 10, p 1546 (DE-627)608937916 (DE-600)2513863-7 20724292 nnns volume:10 year:2018 number:10, p 1546 https://doi.org/10.3390/rs10101546 kostenfrei https://doaj.org/article/d83f47becf9c457a801b12d74e4805ed kostenfrei http://www.mdpi.com/2072-4292/10/10/1546 kostenfrei https://doaj.org/toc/2072-4292 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4700 AR 10 2018 10, p 1546
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topic_title	Least Angle Regression-Based Constrained Sparse Unmixing of Hyperspectral Remote Sensing Imagery sparse unmixing least angle regression equiangular vector linear regression hyperspectral remote sensing imagery
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title	Least Angle Regression-Based Constrained Sparse Unmixing of Hyperspectral Remote Sensing Imagery
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title_full	Least Angle Regression-Based Constrained Sparse Unmixing of Hyperspectral Remote Sensing Imagery
author_sort	Ruyi Feng
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author_browse	Ruyi Feng Lizhe Wang Yanfei Zhong
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title_sort	least angle regression-based constrained sparse unmixing of hyperspectral remote sensing imagery
title_auth	Least Angle Regression-Based Constrained Sparse Unmixing of Hyperspectral Remote Sensing Imagery
abstract	Sparse unmixing has been successfully applied in hyperspectral remote sensing imagery analysis based on a standard spectral library known in advance. This approach involves reformulating the traditional linear spectral unmixing problem by finding the optimal subset of signatures in this spectral library using the sparse regression technique, and has greatly improved the estimation of fractional abundances in ubiquitous mixed pixels. Since the potentially large standard spectral library can be given a priori, the most challenging task is to compute the regression coefficients, i.e., the fractional abundances, for the linear regression problem. There are many mathematical techniques that can be used to deal with the spectral unmixing problem; e.g., ordinary least squares (OLS), constrained least squares (CLS), orthogonal matching pursuit (OMP), and basis pursuit (BP). However, due to poor prediction accuracy and non-interpretability, the traditional methods often cannot obtain satisfactory estimations or achieve a reasonable interpretation. In this paper, to improve the regression accuracy of sparse unmixing, least angle regression-based constrained sparse unmixing (LARCSU) is introduced to further enhance the precision of sparse unmixing. Differing from the classical greedy algorithms and some of the cautious sparse regression-based approaches, the LARCSU algorithm has two main advantages. Firstly, it introduces an equiangular vector to seek the optimal regression steps based on the simple underlying geometry. Secondly, unlike the alternating direction method of multipliers (ADMM)-based algorithms that introduce one or more multipliers or augmented terms during their optimization procedures, no parameters are required in the computational process of the LARCSU approach. The experimental results obtained with both simulated datasets and real hyperspectral images confirm the effectiveness of LARCSU compared with the current state-of-the-art spectral unmixing algorithms. LARCSU can obtain a better fractional abundance map, as well as a higher unmixing accuracy, with the same order of magnitude of computational effort as the CLS-based methods.
abstractGer	Sparse unmixing has been successfully applied in hyperspectral remote sensing imagery analysis based on a standard spectral library known in advance. This approach involves reformulating the traditional linear spectral unmixing problem by finding the optimal subset of signatures in this spectral library using the sparse regression technique, and has greatly improved the estimation of fractional abundances in ubiquitous mixed pixels. Since the potentially large standard spectral library can be given a priori, the most challenging task is to compute the regression coefficients, i.e., the fractional abundances, for the linear regression problem. There are many mathematical techniques that can be used to deal with the spectral unmixing problem; e.g., ordinary least squares (OLS), constrained least squares (CLS), orthogonal matching pursuit (OMP), and basis pursuit (BP). However, due to poor prediction accuracy and non-interpretability, the traditional methods often cannot obtain satisfactory estimations or achieve a reasonable interpretation. In this paper, to improve the regression accuracy of sparse unmixing, least angle regression-based constrained sparse unmixing (LARCSU) is introduced to further enhance the precision of sparse unmixing. Differing from the classical greedy algorithms and some of the cautious sparse regression-based approaches, the LARCSU algorithm has two main advantages. Firstly, it introduces an equiangular vector to seek the optimal regression steps based on the simple underlying geometry. Secondly, unlike the alternating direction method of multipliers (ADMM)-based algorithms that introduce one or more multipliers or augmented terms during their optimization procedures, no parameters are required in the computational process of the LARCSU approach. The experimental results obtained with both simulated datasets and real hyperspectral images confirm the effectiveness of LARCSU compared with the current state-of-the-art spectral unmixing algorithms. LARCSU can obtain a better fractional abundance map, as well as a higher unmixing accuracy, with the same order of magnitude of computational effort as the CLS-based methods.
abstract_unstemmed	Sparse unmixing has been successfully applied in hyperspectral remote sensing imagery analysis based on a standard spectral library known in advance. This approach involves reformulating the traditional linear spectral unmixing problem by finding the optimal subset of signatures in this spectral library using the sparse regression technique, and has greatly improved the estimation of fractional abundances in ubiquitous mixed pixels. Since the potentially large standard spectral library can be given a priori, the most challenging task is to compute the regression coefficients, i.e., the fractional abundances, for the linear regression problem. There are many mathematical techniques that can be used to deal with the spectral unmixing problem; e.g., ordinary least squares (OLS), constrained least squares (CLS), orthogonal matching pursuit (OMP), and basis pursuit (BP). However, due to poor prediction accuracy and non-interpretability, the traditional methods often cannot obtain satisfactory estimations or achieve a reasonable interpretation. In this paper, to improve the regression accuracy of sparse unmixing, least angle regression-based constrained sparse unmixing (LARCSU) is introduced to further enhance the precision of sparse unmixing. Differing from the classical greedy algorithms and some of the cautious sparse regression-based approaches, the LARCSU algorithm has two main advantages. Firstly, it introduces an equiangular vector to seek the optimal regression steps based on the simple underlying geometry. Secondly, unlike the alternating direction method of multipliers (ADMM)-based algorithms that introduce one or more multipliers or augmented terms during their optimization procedures, no parameters are required in the computational process of the LARCSU approach. The experimental results obtained with both simulated datasets and real hyperspectral images confirm the effectiveness of LARCSU compared with the current state-of-the-art spectral unmixing algorithms. LARCSU can obtain a better fractional abundance map, as well as a higher unmixing accuracy, with the same order of magnitude of computational effort as the CLS-based methods.
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title_short	Least Angle Regression-Based Constrained Sparse Unmixing of Hyperspectral Remote Sensing Imagery
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