Blind Hyperspectral Unmixing Based on Graph Total Variation Regularization

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

doi:10.1109/TGRS.2020.3020810

Blind Hyperspectral Unmixing Based on Graph Total Variation Regularization

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

Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

Remote sensing data from hyperspectral cameras suffer from limited spatial resolution, in which a single pixel of a hyperspectral image may contain information from several materials in the field of view. Blind hyperspectral image unmixing is the process of identifying the pure spectra of individual materials (i.e., endmembers) and their proportions (i.e., abundances) at each pixel. In this article, we propose a novel blind hyperspectral unmixing model based on the graph total variation (gTV) regularization, which can be solved efficiently by the alternating direction method of multipliers (ADMM). To further alleviate the computational cost, we apply the Nyström method to approximate a fully connected graph by a small subset of sampled points. Furthermore, we adopt the Merriman-Bence-Osher (MBO) scheme to solve the gTV-involved subproblem in ADMM by decomposing a gray-scale image into a bitwise form. A variety of numerical experiments on synthetic and real hyperspectral images are conducted, showcasing the potential of the proposed method in terms of identification accuracy and computational efficiency.

Original language	English
Article number	9200736
Pages (from-to)	3338-3351
Number of pages	14
Journal	IEEE Transactions on Geoscience and Remote Sensing
Volume	59
Issue number	4
DOIs	https://doi.org/10.1109/TGRS.2020.3020810
State	Published - Apr 2021

Bibliographical note

Funding Information:
Manuscript received February 24, 2020; revised July 2, 2020 and August 19, 2020; accepted August 28, 2020. Date of publication September 18, 2020; date of current version March 25, 2021. The work of Jing Qin was supported by NSF under Grant DMS #1941197. The work of Harlin Lee was supported in part by the Office of Naval Research (ONR) under Grant N00014-19-1-2404, and in part by the Army Research Office (ARO) under Grant W911NF-18-1-0303. The work of Jocelyn T. Chi was supported by NSF under Grant DMS-1760374. The work of Lucas Drumetz was supported by the Programme National de Teledétection Spatiale (PNTS) under Grant PNTS-2019-4. The work of Jocelyn Chanussot was supported by the Grant ANR-16 ASTR-0027-01. The work of Yifei Lou was supported by the NSF CAREER under Grant DMS-1846690. The work of Andrea L. Bertozzi was supported in part by the Defense Advanced Research Projects Agency (DARPA) under Grant FA8750-18-2-0066, and in part by NSF under Grant DMS-1737770. (Corresponding author: Yifei Lou.) Jing Qin is with the Department of Mathematics, University of Kentucky, Lexington, KY 40506 USA (e-mail: jing.qin@uky.edu).

Funding Information:
The initial research for this effort was conducted at the Research Collaboration Workshop for Women in Data Science and Mathematics, July 29–August 2, 2019, held at Institute for Computational and Experimental Research in Mathematics (ICERM). Funding for the workshop was provided by ICERM. The authors would like to thank Linda Ness for her helpful suggestions and discussions.

Publisher Copyright:
© 1980-2012 IEEE.

Keywords

Alternating direction method of multipliers (ADMM)
Nyström method
blind hyperspectral unmixing
graph Laplacian
graph total variation (gTV)

ASJC Scopus subject areas

Electrical and Electronic Engineering
Earth and Planetary Sciences (all)

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10.1109/TGRS.2020.3020810

Cite this

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title = "Blind Hyperspectral Unmixing Based on Graph Total Variation Regularization",

abstract = "Remote sensing data from hyperspectral cameras suffer from limited spatial resolution, in which a single pixel of a hyperspectral image may contain information from several materials in the field of view. Blind hyperspectral image unmixing is the process of identifying the pure spectra of individual materials (i.e., endmembers) and their proportions (i.e., abundances) at each pixel. In this article, we propose a novel blind hyperspectral unmixing model based on the graph total variation (gTV) regularization, which can be solved efficiently by the alternating direction method of multipliers (ADMM). To further alleviate the computational cost, we apply the Nystr{\"o}m method to approximate a fully connected graph by a small subset of sampled points. Furthermore, we adopt the Merriman-Bence-Osher (MBO) scheme to solve the gTV-involved subproblem in ADMM by decomposing a gray-scale image into a bitwise form. A variety of numerical experiments on synthetic and real hyperspectral images are conducted, showcasing the potential of the proposed method in terms of identification accuracy and computational efficiency.",

keywords = "Alternating direction method of multipliers (ADMM), Nystr{\"o}m method, blind hyperspectral unmixing, graph Laplacian, graph total variation (gTV)",

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

note = "Funding Information: Manuscript received February 24, 2020; revised July 2, 2020 and August 19, 2020; accepted August 28, 2020. Date of publication September 18, 2020; date of current version March 25, 2021. The work of Jing Qin was supported by NSF under Grant DMS #1941197. The work of Harlin Lee was supported in part by the Office of Naval Research (ONR) under Grant N00014-19-1-2404, and in part by the Army Research Office (ARO) under Grant W911NF-18-1-0303. The work of Jocelyn T. Chi was supported by NSF under Grant DMS-1760374. The work of Lucas Drumetz was supported by the Programme National de Teled{\'e}tection Spatiale (PNTS) under Grant PNTS-2019-4. The work of Jocelyn Chanussot was supported by the Grant ANR-16 ASTR-0027-01. The work of Yifei Lou was supported by the NSF CAREER under Grant DMS-1846690. The work of Andrea L. Bertozzi was supported in part by the Defense Advanced Research Projects Agency (DARPA) under Grant FA8750-18-2-0066, and in part by NSF under Grant DMS-1737770. (Corresponding author: Yifei Lou.) Jing Qin is with the Department of Mathematics, University of Kentucky, Lexington, KY 40506 USA (e-mail: jing.qin@uky.edu). Funding Information: The initial research for this effort was conducted at the Research Collaboration Workshop for Women in Data Science and Mathematics, July 29–August 2, 2019, held at Institute for Computational and Experimental Research in Mathematics (ICERM). Funding for the workshop was provided by ICERM. The authors would like to thank Linda Ness for her helpful suggestions and discussions. Publisher Copyright: {\textcopyright} 1980-2012 IEEE.",

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AU - Lou, Yifei

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N2 - Remote sensing data from hyperspectral cameras suffer from limited spatial resolution, in which a single pixel of a hyperspectral image may contain information from several materials in the field of view. Blind hyperspectral image unmixing is the process of identifying the pure spectra of individual materials (i.e., endmembers) and their proportions (i.e., abundances) at each pixel. In this article, we propose a novel blind hyperspectral unmixing model based on the graph total variation (gTV) regularization, which can be solved efficiently by the alternating direction method of multipliers (ADMM). To further alleviate the computational cost, we apply the Nyström method to approximate a fully connected graph by a small subset of sampled points. Furthermore, we adopt the Merriman-Bence-Osher (MBO) scheme to solve the gTV-involved subproblem in ADMM by decomposing a gray-scale image into a bitwise form. A variety of numerical experiments on synthetic and real hyperspectral images are conducted, showcasing the potential of the proposed method in terms of identification accuracy and computational efficiency.

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Blind Hyperspectral Unmixing Based on Graph Total Variation Regularization

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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