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    GROWING SIMPLEX VOLUME ANALYSIS FOR FINDING ENDMEMBERS IN HYPERSPECTRAL IMAGERY

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    Li_umbc_0434D_11452.pdf (2.560Mb)
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    http://hdl.handle.net/11603/15482
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    • UMBC Theses and Dissertations
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    Author/Creator
    Unknown author
    Date
    2016-01-01
    Type of Work
    Text
    dissertation
    Department
    Computer Science and Electrical Engineering
    Program
    Engineering, Electrical
    Rights
    This item may be protected under Title 17 of the U.S. Copyright Law. It is made available by UMBC for non-commercial research and education. For permission to publish or reproduce, please see http://aok.lib.umbc.edu/specoll/repro.php or contact Special Collections at speccoll(at)umbc.edu
    Distribution Rights granted to UMBC by the author.
    Subjects
    Convex Cone
    Endmember Finding Algorithm
    Hyperspectral Imagery
    Simplex
    Abstract
    Finding endmembers is a fundamental task in hyperspectral data exploitation. Many Endmember Finding Algorithms (EFAs) have been proposed over the past years. Among all the algorithms, using maximal Simplex Volume (SV) as an optimal criterion for finding endmembers has been a major approach, which results in a well-known algorithm, N-finder algorithm (N-FINDR). As an alternative to N-FINDR, Simplex Growing Algorithm (SGA) was further proposed to reduce computational complexity to avoid an exhaustive search for endmembers required by N-FINDR. Nevertheless, both N-FINDR and SGA still suffer from an issue of numerical instability when it comes to SV calculation via matrix determinant. The research conducted in this dissertation converts Determinant-based SV calculation to Geometric SV (GSV) calculation by taking advantage of geometric structures of simplexes. As a result, there is no longer a need of using matrix determinant to calculate SV. Instead, GSV calculates the volume of a simplex by multiplying its base and height of a simplex. Many benefits can be gained from GSV, such as (1) no need of dimensionality reduction; (2) avoidance of numerical instability incurred by finding determinants of a non-square matrices; (3) no matrix inverses required; (4) significantly reduced computational complexity and computing cost; (5) easy implementation in hardware design. By virtue of GSV calculation several GSV-based EFAs can be re-derived to replace original Determinant SGA (DSGA), which include Orthogonal Projection-based SGA (OP-SGA), Geometric SGA (GSGA), and Geometric Convex Cone Volume Analysis (GCCVA). In order to facilitate real-time processing capability, these algorithms are further extended to their respective recursive counterparts which also result in Kalman filter-like EFAs.


    Albin O. Kuhn Library & Gallery
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    Albin O. Kuhn Library & Gallery
    University of Maryland, Baltimore County
    1000 Hilltop Circle
    Baltimore, MD 21250
    www.umbc.edu/scholarworks

    Contact information:
    Email: scholarworks-group@umbc.edu
    Phone: 410-455-3544


    If you wish to submit a copyright complaint or withdrawal request, please email mdsoar-help@umd.edu.