### 摘要

Hyperspectral unmixing (HU) is a crucial signal processing procedure to identify the underlying materials (or endmembers) and their corresponding proportions (or abundances) from an observed hyperspectral scene. A well-known blind HU criterion, advocated by Craig during the early 1990s, considers the vertices of the minimum-volume enclosing simplex of the data cloud as good endmember estimates, and it has been empirically and theoretically found effective even in the scenario of no pure pixels. However, such kinds of algorithms may suffer from heavy simplex volume computations in numerical optimization, etc. In this paper, without involving any simplex volume computations, by exploiting a convex geometry fact that a simplest simplex of N vertices can be defined by N associated hyperplanes, we propose a fast blind HU algorithm, for which each of the N hyperplanes associated with the Craig's simplex of N vertices is constructed from N-1 affinely independent data pixels, together with an endmember identifiability analysis for its performance support. Without resorting to numerical optimization, the devised algorithm searches for the N(N-1) active data pixels via simple linear algebraic computations, accounting for its computational efficiency. Monte Carlo simulations and real data experiments are provided to demonstrate its superior efficacy over some benchmark Craig-criterion-based algorithms in both computational efficiency and estimation accuracy.

原文 | English |
---|---|

文章編號 | 7355384 |

頁（從 - 到） | 1946-1961 |

頁數 | 16 |

期刊 | IEEE Transactions on Signal Processing |

卷 | 64 |

發行號 | 8 |

DOIs | |

出版狀態 | Published - 2016 四月 15 |

### 指紋

### All Science Journal Classification (ASJC) codes

- Signal Processing
- Electrical and Electronic Engineering

### 引用此文

*IEEE Transactions on Signal Processing*,

*64*(8), 1946-1961. [7355384]. https://doi.org/10.1109/TSP.2015.2508778

}

*IEEE Transactions on Signal Processing*, 卷 64, 編號 8, 7355384, 頁 1946-1961. https://doi.org/10.1109/TSP.2015.2508778

**A Fast Hyperplane-Based Minimum-Volume Enclosing Simplex Algorithm for Blind Hyperspectral Unmixing.** / Lin, Chia Hsiang; Chi, Chong Yung; Wang, Yu Hsiang; Chan, Tsung Han.

研究成果: Article

TY - JOUR

T1 - A Fast Hyperplane-Based Minimum-Volume Enclosing Simplex Algorithm for Blind Hyperspectral Unmixing

AU - Lin, Chia Hsiang

AU - Chi, Chong Yung

AU - Wang, Yu Hsiang

AU - Chan, Tsung Han

PY - 2016/4/15

Y1 - 2016/4/15

N2 - Hyperspectral unmixing (HU) is a crucial signal processing procedure to identify the underlying materials (or endmembers) and their corresponding proportions (or abundances) from an observed hyperspectral scene. A well-known blind HU criterion, advocated by Craig during the early 1990s, considers the vertices of the minimum-volume enclosing simplex of the data cloud as good endmember estimates, and it has been empirically and theoretically found effective even in the scenario of no pure pixels. However, such kinds of algorithms may suffer from heavy simplex volume computations in numerical optimization, etc. In this paper, without involving any simplex volume computations, by exploiting a convex geometry fact that a simplest simplex of N vertices can be defined by N associated hyperplanes, we propose a fast blind HU algorithm, for which each of the N hyperplanes associated with the Craig's simplex of N vertices is constructed from N-1 affinely independent data pixels, together with an endmember identifiability analysis for its performance support. Without resorting to numerical optimization, the devised algorithm searches for the N(N-1) active data pixels via simple linear algebraic computations, accounting for its computational efficiency. Monte Carlo simulations and real data experiments are provided to demonstrate its superior efficacy over some benchmark Craig-criterion-based algorithms in both computational efficiency and estimation accuracy.

AB - Hyperspectral unmixing (HU) is a crucial signal processing procedure to identify the underlying materials (or endmembers) and their corresponding proportions (or abundances) from an observed hyperspectral scene. A well-known blind HU criterion, advocated by Craig during the early 1990s, considers the vertices of the minimum-volume enclosing simplex of the data cloud as good endmember estimates, and it has been empirically and theoretically found effective even in the scenario of no pure pixels. However, such kinds of algorithms may suffer from heavy simplex volume computations in numerical optimization, etc. In this paper, without involving any simplex volume computations, by exploiting a convex geometry fact that a simplest simplex of N vertices can be defined by N associated hyperplanes, we propose a fast blind HU algorithm, for which each of the N hyperplanes associated with the Craig's simplex of N vertices is constructed from N-1 affinely independent data pixels, together with an endmember identifiability analysis for its performance support. Without resorting to numerical optimization, the devised algorithm searches for the N(N-1) active data pixels via simple linear algebraic computations, accounting for its computational efficiency. Monte Carlo simulations and real data experiments are provided to demonstrate its superior efficacy over some benchmark Craig-criterion-based algorithms in both computational efficiency and estimation accuracy.

UR - http://www.scopus.com/inward/record.url?scp=84963757025&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84963757025&partnerID=8YFLogxK

U2 - 10.1109/TSP.2015.2508778

DO - 10.1109/TSP.2015.2508778

M3 - Article

AN - SCOPUS:84963757025

VL - 64

SP - 1946

EP - 1961

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 8

M1 - 7355384

ER -