Identifiability of the Simplex Volume Minimization Criterion for Blind Hyperspectral Unmixing: The No-Pure-Pixel Case

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

Research output: Contribution to journalArticlepeer-review

51 Citations (Scopus)

Abstract

In blind hyperspectral unmixing (HU), the pure-pixel assumption is well known to be powerful in enabling simple and effective blind HU solutions. However, the pure-pixel assumption is not always satisfied in an exact sense, especially for scenarios where pixels are heavily mixed. In the no-pure-pixel case, a good blind HU approach to consider is the minimum volume enclosing simplex (MVES). Empirical experience has suggested that MVES algorithms can perform well without pure pixels, although it was not totally clear why this is true from a theoretical viewpoint. This paper aims to address the latter issue. We develop an analysis framework wherein the perfect endmember identifiability of MVES is studied under the noiseless case. We prove that MVES is indeed robust against lack of pure pixels, as long as the pixels do not get too heavily mixed and too asymmetrically spread. The theoretical results are supported by numerical simulation results.

Original languageEnglish
Article number7107995
Pages (from-to)5530-5546
Number of pages17
JournalIEEE Transactions on Geoscience and Remote Sensing
Volume53
Issue number10
DOIs
Publication statusPublished - 2015 Oct 1

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering
  • Earth and Planetary Sciences(all)

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