TY - CHAP
T1 - Endmember Finding in Compressively Sensed Band Domain
AU - Chang, Chein I.
AU - Bekit, Adam
N1 - Publisher Copyright:
© 2023 John Wiley & Sons, Inc.
PY - 2022/11/11
Y1 - 2022/11/11
N2 - Endmember finding is a crucial step prior to spectral unmixing for hyperspectral imagery where a well-known N-finder algorithm (N-FINDR) has been widely used for this purpose. Since N-FINDR must find all endmembers simultaneously, it requires exhausting all possible p-endmember combinations among the entire data samples where p is the total number of endmembers required to be found. Accordingly, directly implementing N-FINDR is practically infeasible. To mitigate this dilemma, two recently developed algorithms called sequential N-FINDR (SQ N-FINDR) and successive N-FINDR (SC N-FINDR) were developed to make N-FINDR numerically implementable. In addition, another remaining and challenging unsolved issue for N-FINDR is spectral dimensionality reduction. Due to the fact that a p-vertex simplex is embedded in a (p-1)-dimensional spectral data space, N-FINDR does not require full spectral dimensionality to calculate simplex volume (SV). This chapter presents a compressive sensing (CS) approach to N-FINDR that can find a p-vertex simplex with the maximal SV found by SQ/SC N-FINDR in a compressively sensed band domain (CSBD). In particular, to make this idea work, a new CS-based property, called restricted simplex volume property (RSVP), is further shown to be preserved in CSBD via a sensing matrix. It is this property to guarantee that what N-FINDR and SQ/SC N-FINDR can achieve in the original data space (ODS) can be also achieved in CSBD. To demonstrate the utility of SQ/SC N-FINDR in both ODS and CSBD preserved by RSVP, a series of experiments are conducted for performance analysis.
AB - Endmember finding is a crucial step prior to spectral unmixing for hyperspectral imagery where a well-known N-finder algorithm (N-FINDR) has been widely used for this purpose. Since N-FINDR must find all endmembers simultaneously, it requires exhausting all possible p-endmember combinations among the entire data samples where p is the total number of endmembers required to be found. Accordingly, directly implementing N-FINDR is practically infeasible. To mitigate this dilemma, two recently developed algorithms called sequential N-FINDR (SQ N-FINDR) and successive N-FINDR (SC N-FINDR) were developed to make N-FINDR numerically implementable. In addition, another remaining and challenging unsolved issue for N-FINDR is spectral dimensionality reduction. Due to the fact that a p-vertex simplex is embedded in a (p-1)-dimensional spectral data space, N-FINDR does not require full spectral dimensionality to calculate simplex volume (SV). This chapter presents a compressive sensing (CS) approach to N-FINDR that can find a p-vertex simplex with the maximal SV found by SQ/SC N-FINDR in a compressively sensed band domain (CSBD). In particular, to make this idea work, a new CS-based property, called restricted simplex volume property (RSVP), is further shown to be preserved in CSBD via a sensing matrix. It is this property to guarantee that what N-FINDR and SQ/SC N-FINDR can achieve in the original data space (ODS) can be also achieved in CSBD. To demonstrate the utility of SQ/SC N-FINDR in both ODS and CSBD preserved by RSVP, a series of experiments are conducted for performance analysis.
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U2 - 10.1002/9781119687788.ch8
DO - 10.1002/9781119687788.ch8
M3 - Chapter
AN - SCOPUS:85147784139
SN - 9781119687788
SP - 228
EP - 251
BT - Advances in Hyperspectral Image Processing Techniques
PB - Wiley-Blackwell
ER -