Fast Blind Hyperspectral Unmixing Based on Graph Laplacian

Jing Qin; Harlin Lee; Jocelyn T. Chi; Yifei Lou; Jocelyn Chanussot; Andrea L. Bertozzi

doi:10.1109/WHISPERS.2019.8921375

Fast Blind Hyperspectral Unmixing Based on Graph Laplacian

Jing Qin, Harlin Lee, Jocelyn T. Chi, Yifei Lou, Jocelyn Chanussot, Andrea L. Bertozzi

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

6 Scopus citations

Abstract

Blind hyperspectral unmixing is a challenging problem in remote sensing, which aims to infer material spectra and abundances from the given hyperspectral data. Many traditional methods suffer from poor identification of materials and/or expensive computational costs, which can be partially eased by trading the accuracy with efficiency. In this work, we propose a fast graph-based blind unmixing approach. In particular, we apply the Nyström method to efficiently approximate eigenvalues and eigenvectors of a matrix corresponding to a normalized graph Laplacian. Then the alternating direction method of multipliers (ADMM) yields a fast numerical algorithm. Experiments on a real dataset illustrate great potential of the proposed method in terms of accuracy and efficiency.

Original language	English
Title of host publication	2019 10th Workshop on Hyperspectral Imaging and Signal Processing
Subtitle of host publication	Evolution in Remote Sensing, WHISPERS 2019
ISBN (Electronic)	9781728152943
DOIs	https://doi.org/10.1109/WHISPERS.2019.8921375
State	Published - Sep 2019
Event	10th Workshop on Hyperspectral Imaging and Signal Processing: Evolution in Remote Sensing, WHISPERS 2019 - Amsterdam, Netherlands Duration: Sep 24 2019 → Sep 26 2019

Publication series

Name	Workshop on Hyperspectral Image and Signal Processing, Evolution in Remote Sensing
Volume	2019-September
ISSN (Print)	2158-6276

Conference

Conference	10th Workshop on Hyperspectral Imaging and Signal Processing: Evolution in Remote Sensing, WHISPERS 2019
Country/Territory	Netherlands
City	Amsterdam
Period	9/24/19 → 9/26/19

Bibliographical note

Funding Information:
The initial research for this effort was conducted at the Research Collaboration Workshop for Women in Data Science and Mathematics that was held at ICERM, July 29-August 2, 2019. Funding for the workshop was provided by ICERM. In addition, Qin is supported by the NSF grant DMS- 1941197, Lou by the NSF CAREER grant DMS-1846690, Lee by the ONR grant N00014-19-1-2404, Chi by the NSF grant DMS-1760374, Chaussot by the Grant ANR-16 ASTR-0027-01, and Bertozzi by the DARPA grant FA8750-18-2-0066

Funding Information:
The initial research for this effort was conducted at the Research Collaboration Workshop for Women in Data Science and Mathematics that was held at ICERM, July 29-August 2, 2019. Funding for the workshop was provided by ICERM. In addition, Qin is supported by the NSF grant DMS-1941197, Lou by the NSF CAREER grant DMS-1846690, Lee by the ONR grant N00014-19-1-2404, Chi by the NSF grant DMS-1760374, Chaussot by the Grant ANR-16 ASTR-0027-01, and Bertozzi by the DARPA grant FA8750-18-2-0066

Publisher Copyright:
© 2019 IEEE.

Keywords

Hyperspectral imaging
Nystrom method
alternating direction method of multipliers
graph Laplacian
hyperspectral unmixing

ASJC Scopus subject areas

Computer Vision and Pattern Recognition
Signal Processing

Access to Document

10.1109/WHISPERS.2019.8921375

Cite this

Qin, J., Lee, H., Chi, J. T., Lou, Y., Chanussot, J., & Bertozzi, A. L. (2019). Fast Blind Hyperspectral Unmixing Based on Graph Laplacian. In 2019 10th Workshop on Hyperspectral Imaging and Signal Processing: Evolution in Remote Sensing, WHISPERS 2019 Article 8921375 (Workshop on Hyperspectral Image and Signal Processing, Evolution in Remote Sensing; Vol. 2019-September). https://doi.org/10.1109/WHISPERS.2019.8921375

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title = "Fast Blind Hyperspectral Unmixing Based on Graph Laplacian",

abstract = "Blind hyperspectral unmixing is a challenging problem in remote sensing, which aims to infer material spectra and abundances from the given hyperspectral data. Many traditional methods suffer from poor identification of materials and/or expensive computational costs, which can be partially eased by trading the accuracy with efficiency. In this work, we propose a fast graph-based blind unmixing approach. In particular, we apply the Nystr{\"o}m method to efficiently approximate eigenvalues and eigenvectors of a matrix corresponding to a normalized graph Laplacian. Then the alternating direction method of multipliers (ADMM) yields a fast numerical algorithm. Experiments on a real dataset illustrate great potential of the proposed method in terms of accuracy and efficiency.",

keywords = "Hyperspectral imaging, Nystrom method, alternating direction method of multipliers, graph Laplacian, hyperspectral unmixing",

author = "Jing Qin and Harlin Lee and Chi, {Jocelyn T.} and Yifei Lou and Jocelyn Chanussot and Bertozzi, {Andrea L.}",

note = "Funding Information: The initial research for this effort was conducted at the Research Collaboration Workshop for Women in Data Science and Mathematics that was held at ICERM, July 29-August 2, 2019. Funding for the workshop was provided by ICERM. In addition, Qin is supported by the NSF grant DMS- 1941197, Lou by the NSF CAREER grant DMS-1846690, Lee by the ONR grant N00014-19-1-2404, Chi by the NSF grant DMS-1760374, Chaussot by the Grant ANR-16 ASTR-0027-01, and Bertozzi by the DARPA grant FA8750-18-2-0066 Funding Information: The initial research for this effort was conducted at the Research Collaboration Workshop for Women in Data Science and Mathematics that was held at ICERM, July 29-August 2, 2019. Funding for the workshop was provided by ICERM. In addition, Qin is supported by the NSF grant DMS-1941197, Lou by the NSF CAREER grant DMS-1846690, Lee by the ONR grant N00014-19-1-2404, Chi by the NSF grant DMS-1760374, Chaussot by the Grant ANR-16 ASTR-0027-01, and Bertozzi by the DARPA grant FA8750-18-2-0066 Publisher Copyright: {\textcopyright} 2019 IEEE.; 10th Workshop on Hyperspectral Imaging and Signal Processing: Evolution in Remote Sensing, WHISPERS 2019 ; Conference date: 24-09-2019 Through 26-09-2019",

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Qin, J, Lee, H, Chi, JT, Lou, Y, Chanussot, J & Bertozzi, AL 2019, Fast Blind Hyperspectral Unmixing Based on Graph Laplacian. in 2019 10th Workshop on Hyperspectral Imaging and Signal Processing: Evolution in Remote Sensing, WHISPERS 2019., 8921375, Workshop on Hyperspectral Image and Signal Processing, Evolution in Remote Sensing, vol. 2019-September, 10th Workshop on Hyperspectral Imaging and Signal Processing: Evolution in Remote Sensing, WHISPERS 2019, Amsterdam, Netherlands, 9/24/19. https://doi.org/10.1109/WHISPERS.2019.8921375

Fast Blind Hyperspectral Unmixing Based on Graph Laplacian. / Qin, Jing; Lee, Harlin; Chi, Jocelyn T. et al.
2019 10th Workshop on Hyperspectral Imaging and Signal Processing: Evolution in Remote Sensing, WHISPERS 2019. 2019. 8921375 (Workshop on Hyperspectral Image and Signal Processing, Evolution in Remote Sensing; Vol. 2019-September).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Lou, Yifei

AU - Chanussot, Jocelyn

AU - Bertozzi, Andrea L.

N1 - Funding Information: The initial research for this effort was conducted at the Research Collaboration Workshop for Women in Data Science and Mathematics that was held at ICERM, July 29-August 2, 2019. Funding for the workshop was provided by ICERM. In addition, Qin is supported by the NSF grant DMS- 1941197, Lou by the NSF CAREER grant DMS-1846690, Lee by the ONR grant N00014-19-1-2404, Chi by the NSF grant DMS-1760374, Chaussot by the Grant ANR-16 ASTR-0027-01, and Bertozzi by the DARPA grant FA8750-18-2-0066 Funding Information: The initial research for this effort was conducted at the Research Collaboration Workshop for Women in Data Science and Mathematics that was held at ICERM, July 29-August 2, 2019. Funding for the workshop was provided by ICERM. In addition, Qin is supported by the NSF grant DMS-1941197, Lou by the NSF CAREER grant DMS-1846690, Lee by the ONR grant N00014-19-1-2404, Chi by the NSF grant DMS-1760374, Chaussot by the Grant ANR-16 ASTR-0027-01, and Bertozzi by the DARPA grant FA8750-18-2-0066 Publisher Copyright: © 2019 IEEE.

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AB - Blind hyperspectral unmixing is a challenging problem in remote sensing, which aims to infer material spectra and abundances from the given hyperspectral data. Many traditional methods suffer from poor identification of materials and/or expensive computational costs, which can be partially eased by trading the accuracy with efficiency. In this work, we propose a fast graph-based blind unmixing approach. In particular, we apply the Nyström method to efficiently approximate eigenvalues and eigenvectors of a matrix corresponding to a normalized graph Laplacian. Then the alternating direction method of multipliers (ADMM) yields a fast numerical algorithm. Experiments on a real dataset illustrate great potential of the proposed method in terms of accuracy and efficiency.

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Fast Blind Hyperspectral Unmixing Based on Graph Laplacian

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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