A Convex Analysis-Based Minimum-Volume Enclosing Simplex Algorithm for Hyperspectral Unmixing
Hyperspectral unmixing aims at identifying the hidden spectral signatures (or endmembers) and their corresponding proportions (or abundances) from an observed hyperspectral scene. Many existing hyperspectral unmixing algorithms were developed under a commonly used assumption that pure pixels exist....
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| Veröffentlicht in: | IEEE transactions on signal processing 2009-11, Vol.57 (11), p.4418-4432 |
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| container_title | IEEE transactions on signal processing |
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| creator | CHAN, Tsung-Han CHI, Chong-Yung HUANG, Yu-Min MA, Wing-Kin |
| description | Hyperspectral unmixing aims at identifying the hidden spectral signatures (or endmembers) and their corresponding proportions (or abundances) from an observed hyperspectral scene. Many existing hyperspectral unmixing algorithms were developed under a commonly used assumption that pure pixels exist. However, the pure-pixel assumption may be seriously violated for highly mixed data. Based on intuitive grounds, Craig reported an unmixing criterion without requiring the pure-pixel assumption, which estimates the endmembers by vertices of a minimum-volume simplex enclosing all the observed pixels. In this paper, we incorporate convex analysis and Craig's criterion to develop a minimum-volume enclosing simplex (MVES) formulation for hyperspectral unmixing. A cyclic minimization algorithm for approximating the MVES problem is developed using linear programs (LPs), which can be practically implemented by readily available LP solvers. We also provide a non-heuristic guarantee of our MVES problem formulation, where the existence of pure pixels is proved to be a sufficient condition for MVES to perfectly identify the true endmembers. Some Monte Carlo simulations and real data experiments are presented to demonstrate the efficacy of the proposed MVES algorithm over several existing hyperspectral unmixing methods. |
| doi_str_mv | 10.1109/TSP.2009.2025802 |
| format | Article |
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Some Monte Carlo simulations and real data experiments are presented to demonstrate the efficacy of the proposed MVES algorithm over several existing hyperspectral unmixing methods.</description><subject>Algorithm design and analysis</subject><subject>Algorithms</subject><subject>Applied sciences</subject><subject>Approximation</subject><subject>Computer simulation</subject><subject>Convex analysis</subject><subject>convex optimization</subject><subject>Councils</subject><subject>Criteria</subject><subject>Data mining</subject><subject>Exact sciences and technology</subject><subject>Formulations</subject><subject>Hyperspectral imaging</subject><subject>Hyperspectral sensors</subject><subject>hyperspectral unmixing</subject><subject>Information, signal and communications theory</subject><subject>Layout</subject><subject>linear programming</subject><subject>Minimization methods</subject><subject>minimum-volume enclosing simplex</subject><subject>Miscellaneous</subject><subject>Monitoring</subject><subject>Monte Carlo methods</subject><subject>Pixels</subject><subject>Principal component analysis</subject><subject>Signal processing</subject><subject>Signal processing algorithms</subject><subject>Solvers</subject><subject>Studies</subject><subject>Telecommunications and information theory</subject><issn>1053-587X</issn><issn>1941-0476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kctLxDAQxoso-LwLXoqgnqqTR5PmuC6-QFHwgRcp2TTRSNrUZCvuf2_WXTx48DIzML_5GL4vy3YRHCME4uTh_u4YA4hUcFkBXsk2kKCoAMrZapqhJEVZ8ef1bDPGdwBEqWAb2csoH_vuU3_lo066WbSxOJVRN_mN7Ww7tMWTd0Or87NOOR9t95rf27Z3c969-mCnb21ufMgvZ70OsddqGqTLH7vWfiV4O1sz0kW9s-xb2eP52cP4sri-vbgaj64Llb6YFhTjCceNMabEgnGKgCtFMGFy_v1ES6GFMFiWFUGaN1I1ShkGVBrUAEwI2cqOFrp98B-DjtO6tVFp52Sn_RDripdAgQNP5OG_JEmuVIigBO7_Ad_9EJJHSY0lx7n4UYMFpIKPMWhT98G2MsxqBPU8ljrFUs9jqZexpJODpa6MSjoTZKds_L3DiQPGIHF7C85qrX_XJVSCMky-AXBNlbU</recordid><startdate>20091101</startdate><enddate>20091101</enddate><creator>CHAN, Tsung-Han</creator><creator>CHI, Chong-Yung</creator><creator>HUANG, Yu-Min</creator><creator>MA, Wing-Kin</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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Many existing hyperspectral unmixing algorithms were developed under a commonly used assumption that pure pixels exist. However, the pure-pixel assumption may be seriously violated for highly mixed data. Based on intuitive grounds, Craig reported an unmixing criterion without requiring the pure-pixel assumption, which estimates the endmembers by vertices of a minimum-volume simplex enclosing all the observed pixels. In this paper, we incorporate convex analysis and Craig's criterion to develop a minimum-volume enclosing simplex (MVES) formulation for hyperspectral unmixing. A cyclic minimization algorithm for approximating the MVES problem is developed using linear programs (LPs), which can be practically implemented by readily available LP solvers. We also provide a non-heuristic guarantee of our MVES problem formulation, where the existence of pure pixels is proved to be a sufficient condition for MVES to perfectly identify the true endmembers. Some Monte Carlo simulations and real data experiments are presented to demonstrate the efficacy of the proposed MVES algorithm over several existing hyperspectral unmixing methods.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TSP.2009.2025802</doi><tpages>15</tpages></addata></record> |
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| subjects | Algorithm design and analysis Algorithms Applied sciences Approximation Computer simulation Convex analysis convex optimization Councils Criteria Data mining Exact sciences and technology Formulations Hyperspectral imaging Hyperspectral sensors hyperspectral unmixing Information, signal and communications theory Layout linear programming Minimization methods minimum-volume enclosing simplex Miscellaneous Monitoring Monte Carlo methods Pixels Principal component analysis Signal processing Signal processing algorithms Solvers Studies Telecommunications and information theory |
| title | A Convex Analysis-Based Minimum-Volume Enclosing Simplex Algorithm for Hyperspectral Unmixing |
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