When can the minimum volume enclosing simplex identify the endmembers correctly when there is no pure pixel?

Wing Kin Ma, Chia Hsiang Lin, Wei Chiang Li, Chong Yung Chi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In blind hyperspectral unmixing, it has been commonly believed that the minimum volume enclosing simplex (MVES) criterion is robust against lack of pure pixels. Specifically, such a belief has been based on empirical experience, where extensive numerical results showed that MVES-based algorithms may identify the underlying endmembers quite accurately under high signal-to-noise ratios and without pure pixels. In this paper, we report some theoretical results on the endmember identifiability of the MVES criterion in the noiseless case. We employ an assumption that is a two-mixture generalization of the pure-pixel assumption; particularly, we require a set of pixels, each being constituted by only two endmembers (rather than one as in the pure-pixel assumption), to exist in the data set. Under this assumption and some rather mild condition, we show that the MVES solution perfectly identifies the true endmembers. Numerical simulation results are provided to verify our theoretical results.

Original languageEnglish
Title of host publication2015 7th Workshop on Hyperspectral Image and Signal Processing
Subtitle of host publicationEvolution in Remote Sensing, WHISPERS 2015
PublisherIEEE Computer Society
ISBN (Electronic)9781467390156
DOIs
Publication statusPublished - 2015 Jul 2
Event7th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, WHISPERS 2015 - Tokyo, Japan
Duration: 2015 Jun 22015 Jun 5

Publication series

NameWorkshop on Hyperspectral Image and Signal Processing, Evolution in Remote Sensing
Volume2015-June
ISSN (Print)2158-6276

Conference

Conference7th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, WHISPERS 2015
CountryJapan
CityTokyo
Period15-06-0215-06-05

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All Science Journal Classification (ASJC) codes

  • Computer Vision and Pattern Recognition
  • Signal Processing

Cite this

Ma, W. K., Lin, C. H., Li, W. C., & Chi, C. Y. (2015). When can the minimum volume enclosing simplex identify the endmembers correctly when there is no pure pixel? In 2015 7th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, WHISPERS 2015 [8075410] (Workshop on Hyperspectral Image and Signal Processing, Evolution in Remote Sensing; Vol. 2015-June). IEEE Computer Society. https://doi.org/10.1109/WHISPERS.2015.8075410