2015 , Vol. 17 >Issue 8: 979 - 985

• 杨可明 , * ,
• 魏华锋 ,
• 刘飞 ,
• 史钢强 ,
• 孙阳阳

• 中国矿业大学（北京）地球科学与测绘工程学院,北京 100083

要求修回日期: 2015-02-13

网络出版日期: 2015-08-05

Improved N-FINDR Algorithm on Hyperspectral Endmember Extraction Based on Spectral Shannon Entropy

• YANG Keming , * ,
• WEI Huafeng ,
• LIU Fei ,
• SHI Gangqiang ,
• SUN Yangyang
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• College of Geosciences and Survey Engineering, China University of Mining & Technology (Beijing), Beijing 100083, China
*Corresponding author: YANG Keming, E-mail:

Request revised date: 2015-02-13

Online published: 2015-08-05

《地球信息科学学报》编辑部 所有

### Abstract

Endmember extraction is a key step for unmixing hyperspectral mixed pixels and an important prerequisite in the further analysis of hyperspectral imagery. The traditional N-FINDR algorithm is a classical and effective algorithm among various endmember extraction methods. However, the N-FINDR algorithm need to compute all the possible pixel combinations, thus it is time consuming. In order to improve the time efficiency of the N-FINDR algorithm, this paper proposed an improved N-FINDR algorithm on hyperspectral endmember extraction based on spectral Shannon entropy theory and the convex geometry, meanwhile we utilize the characteristic that in spectral feature space, all pixels of the hyperspectral imagery could compose a single shape body, in which the pure pixels are located at the apex and the mixed pixels in the interior or at the surface. The spectral Shannon entropies of all pixels are calculated according to the pixel gray probability, and are used to determine the purity of pixels. The pixel is removed if its spectral Shannon entropy is greater than the threshold value of the spectral Shannon entropy, otherwise it is preserved. Next, the N-FINDR was used to search the largest volume from the single shape body composed by the preserved pixels, and the pixels at the apex of the body with the largest volume would be the endmembers. Finally, we use the Hyperion data of a copper mine in Dexing city from Jiangxi province to testify the improved N-FINDR algorithm. By analyzing the experimental results, the improved algorithm ensured a high accuracy as well as improved the data processing efficiency very greatly in the course of extracting hyperspectral endmembers.

### 2 理论与算法

#### 2.1 光谱信息熵

$H ( X ) = E ( I ( X ) )$ （1）

$H ( j , k ) = - ∑ i = 1 n p ( x i ) lo g 2 p ( x i )$ （2）

#### 2.2 传统N-FINDR算法

$V ( e 1 , e 2 , ⋯ , e m ) = 1 ( m - 1 ) ! abs det 1 1 ⋯ e 1 e 2 ⋯ 1 e m$ （3）

#### 2.3 结合光谱信息熵改进后的N-FINDR算法

（1）根据统计学原理计算每个像元所有波段的概率,然后根据式（2）计算每个像元的光谱信息熵;
（2）依据计算出的光谱信息熵大小,通过设定阈值的方式获得小于阈值的像元,这些像元即为影像中相对纯净的像元;
（3）把这些纯净像元在高维空间组成凸面体,结合凸面几何学理论,运用传统N-FINDR算法,计算凸面体的最大体积,此最大单形体顶点处的像元即为本文需要提取的端元。

### 3 实验分析与算法比较

#### 3.2 改进N-FINDR算法提取端元

##### Fig. 5 Inversion maps of the extracted endmember abundance

###### Tab. 1 Analysis of similarity between the extracted endmembers and USGS-library

1 Staurol 十字石 0.849 0.758
2 Galena 方铅矿 0.781 0.836
3 Juniper 刺柏 0.908 0.756
4 Stilbite 辉沸石 0.866 0.794
5 Epsomite 泻利盐 0.838 0.748
6 Augite 斜辉石 0.859 0.805
7 Hematita 赤铁矿 0.836 0.766
8 Mascagnin 硫铵石 0.769 0.728
9 Cookeite 锂绿泥石 0.868 0.795

#### 3.3 算法的时效对比分析

###### Tab. 2 Comparison of calculation time for 100×100 pixel image

N-FINDR 改进的N-FINDR N-FINDR 改进的N-FINDR
1 315.8 19.3 535.7 23.7
2 338.1 18.1 520.6 25.4
3 319.3 18.4 529.4 23.3
4 304.6 19.7 537.9 23.9
5 310.4 19.0 531.6 24.2
###### Tab. 3 Comparison of calculation time for 400×250 pixel image

N-FINDR 改进的N-FINDR N-FINDR 改进的N-FINDR
1 952.8 43.3 1558.4 69.4
2 979.3 47.9 1498.4 61.7
3 971.8 50.3 1532.7 73.3
4 980.6 55.7 1626.3 66.7
5 968.7 49.6 1573.6 75.8

##### Fig. 6 Endmember spectra extracted by improved N-FINDR, traditional N-FINDR and SMACC algorithms

###### Tab. 4 Comparison of accuracy between traditional N-FINDR, improved N-FINDR and SMACC algorithms for endmember extraction

N-FINDR 十字石0.744 赤铁矿0.791 锂绿泥石0.832 刺柏0.793 斜辉石0.795 泻利盐0.770 辉沸石0.845 硫铵石0.837 未知

SMACC 十字石0.753 赤铁矿0.741 锂绿泥石0.615 刺柏0.674 斜辉石0.579 海绿石0.586 方铅石
0.683

### 4 结语

The authors have declared that no competing interests exist.

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