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地球信息科学学报 >

2016 , Vol. 18 >Issue 2: 263 - 271

DOI: https://doi.org/10.3724/SP.J.1047.2016.00263

光谱与空间维双重稀疏表达的高光谱影像分类

  • 朱勇 ,
  • 吴波 , *
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  • 福州大学 空间数据挖掘与信息共享教育部重点实验室,福建省空间信息工程研究中心,福州 350002
*通讯作者：吴 波(1975-),男,博士后,教授,研究方向为图像处理与时空数据挖掘。E-mail:

作者简介：朱 勇(1989-),男,硕士,研究方向为遥感图像处理。E-mail:

收稿日期: 2015-05-11

  要求修回日期: 2015-10-27

  网络出版日期: 2016-02-04

基金资助

基金项目：福建省自然科学基金项目“基于结构化稀疏表达模型的遥感影像时空融合方法研究”(2015J01163)

国家自然科学基金项目“基于稀疏转换学习的遥感影像时空融合模型与方法研究”(41571330)

国家科技支撑计划项目(2013BAC08B01)

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Classification of Hyperspectral Images with Spectral-Spatial Sparse Representation

  • ZHU Yong ,
  • WU Bo , *
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  • Key Laboratory of Spatial Data Mining and Information Sharing of Ministry of Education, Spatial Information Research Center of Fujian Province, Fuzhou University, Fuzhou 350002, China
*Corresponding author: WU Bo, E-mail:

Received date: 2015-05-11

  Request revised date: 2015-10-27

  Online published: 2016-02-04

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摘要

高光谱遥感影像的稀疏分类是当前遥感信息处理的研究热点。本文提出一种光谱与空间双重稀疏表达的高光谱遥感影像分类方法（WSSRC）。首先利用小波字典对光谱维进行稀疏表示,将光谱维稀疏分类转化到小波域稀疏分类;其次,考虑空间邻域地物光谱的统一性和差异性,对邻域内像元分别进行稀疏编码,并对编码进行累加聚合;然后,利用聚合后的稀疏编码构造线性分类器对高光谱影像进行分类;最后,通过2幅标准的高光谱影像数据验证了本文所提出的方法。实验结果表明,该方法能有效地提高影像的分类精度。

关键词： 小波; 双重稀疏分类; 稀疏编码; 高光谱影像

本文引用格式

朱勇 , 吴波 . 光谱与空间维双重稀疏表达的高光谱影像分类[J]. 地球信息科学学报, 2016 , 18(2) : 263 -271 . DOI: 10.3724/SP.J.1047.2016.00263

Abstract

A novel sparse representation classification model with spectral-spatial sparsity properties is presented to improve the classification accuracy of hyperspectral images. Firstly, this method uses the wavelet dictionary as the core dictionary to extract spectral domain sparse information, and then the spectral dimension sparse representation classification is transformed into the wavelet domain (WSRC) by inverse wavelet transformation. After that, we actually extract the sparse spectral features of the hyperspectral images and increase the recognition of the original dictionary. Secondly, considering the unity and diversity of the spatial adjacent object, we realize the sparse coding of the neighborhood pixels, and then accumulate the sparse codes. At the same time, we classify the hyperspectral images using a linear classifier that is based on the accumulated sparse codes. This method ensures that we extract the main sparse signal of the neighborhood pixels on the basis of the personality features of sparse encoding, and it performs better than the joint sparse representation model (JSRC) which is directly based on the neighborhood pixels. Finally, two commonly used hyperspectral images are utilized to validate the proposed model. The experimental results demonstrate that the proposed algorithm outperforms other models in terms of overall accuracy and kappa coefficient measurements.

Key words： wavelet transform; double sparse representation; sparse code; hyperspectral image

1 引言

近年来,稀疏表示理论的发展为图像处理领域带来了一场革命性的变革。稀疏表示主要利用冗余的数据表达模型,把图像信号表示为“过完备字典”中少数原子线性组合。由于稀疏表达符合人类视觉系统感知特性,并具有重建误差小,自适应性强和易于结合先验知识等优点,成为迄今为止最有效的图像表达模式之一,被广泛应用于图像去噪、恢复、超分重建和分类等诸多方面[1-4]。
Wright[5]等最早研究稀疏表达分类问题,并提出人脸识别的稀疏分类模型（SRC）,随后该模型被广泛应用于不同领域。Chen[6]等首先将稀疏分类模型（SRC）,引入到高光谱遥感影像分类领域,并结合空间邻域像元稀疏一致性的先验知识,提出了空间联合的稀疏分类模型（JSRC）。在此基础上,Zhang[7]等认为邻域像元对中心像元的贡献值存在差异性,进而提出了非局部加权联合稀疏分类模型（NLW-JSRC）,提高了影像的分类精度。此外,由于地面物体的多样性和复杂性,能导致光谱信号间的非线性组合,Chen[8]等利用核扩展技术,把字典和样本投影到更高维核特征空间,使得原始的光谱可在核特征空间中线性表示,进而提出了内核的稀疏分类模型（KSRC）。Liu[9]等则考虑到空间邻域信息,提出了光谱与空间相结合的内核稀疏分类模型。宋相法[10]等通过对像元进行稀疏表示,利用稀疏系数与光谱信息分别构造随机森林,并通过投票机制得到最终分类结果。孙伟伟[11]等利用随机矩阵对光谱和字典进行投影,并限定稀疏系数的非负性,得出在较大投影维数时能提高影像的分类精度。刘建军[12]等在SRC模型下,引入空间相关性约束项和训练数据的空间信息以提高稀疏模型分类的准确性。
上述研究可看出,自Chen[6]等将稀疏分类模型（SRC）引入到高光谱遥感影像分类领域以来,陆续出现了许多改进的稀疏分类模型。本文则主要从2个角度出发：（1）可否通过改善原始字典的结构或质量提高影像的分类精度?（2）能否在提取邻域像元主导信号的同时,顾及地物间的差异表达?鉴此,本文从改善原始字典的结构和空间邻域像元的同步稀疏表达出发,提出光谱与空间的双重稀疏分类模型。
稀疏分类模型字典 D 的结构或质量是决定稀疏分类精度的一个关键因素,我们总期望同类地物在光谱空间中表现为聚集性,不同地物之间则表现为相互分离的特性。由于字典 D 的各列元素（即训练样本）由相同类别或不同类别的光谱矢量组成,如果所选取的样本能满足相同类别的光谱距离差距较小,而不同类别的光谱距离差距较大,就意味着字典 D 具有较好的结构。在实际应用中,如果样本已经确定,那么通过对字典 D 的各列元素进行光谱维的变换或表达,使得能减少相同地物间的光谱差异,或者增加不同类别样本的光谱差距,则也能改善字典 D 的结构。尽管Chen等提出的联合稀疏分类模型（JSRC）,利用同步稀疏编码用于提取局部邻域中的主导信号模式,较大程度地提高了影像的分类精度[6],但该方法以忽略空间地物的差异性为代价,这是由于像元的空间邻域内可能包含同类地物,也可能包含不同的地物（或光谱差异较大的同类地物）,因而,稀疏一致性的强制约束不符合实际情况,从而可能导致错误的分类。此外,从JSRC模型本身来看,强制的稀疏一致算法,不能充分地利用字典的过完备特性。
本文提出一种光谱与空间维双重稀疏的高光谱遥感影像分类方法,以提高影像的分类精度。首先,利用小波字典 W s 对字典 D 中的原子在光谱维上进行稀疏表达,以达到优化字典的结构或质量的目的;其次,综合考虑空间邻域内地物的统一性和差异性,在小波域内对邻域像元分别进行稀疏编码,并对编码进行累加聚合,提取主导信号,进而构造线性分类器对影像进行逐像元分类。

2 光谱与空间维双重稀疏分类模型

2.1 稀疏分类模型

假设获取了高光谱影像 M 种不同地物的训练样本,其中,第 m 种类别有 N m 样本,记为 D m = { d i m } i = 1,2 , … , N m ,其中, d i m 表示第m类中第 i 类训练样本的光谱矢量。则由这 M 种地物类别样本可构成一个过完备字典 D = D 1 D 2 … D M ∈ R B × N B < N ， 其中 B 为高光谱影像的波段数, N = N 1 + N 2 + … + N M 为 M 种地物类别样本总数。根据稀疏表达理论,对于任意一个待分类像元 y ,可由字典 D 中少数几个原子线性表示,其数学模型如式（1）：
α ^ = arg min α α 0 s.t y = Dα （1）
式中： α ^ 为稀疏表示系数; α 0 表示稀疏系数中非零原子个数。式(1)等价于如下数学模型：
α ^ = arg min α y - Dα 2 2 s.t α 0 ≤ K 0 （2）
式中： K 0 称为稀疏度。由于寻求式（1）、（2）的最优解是一个NP-hard的组合优化问题,故通常采用贪婪或凸松弛的搜寻策略来寻求模型的次优解。主要算法包括正交匹配追踪（OMP）[13]和基追踪（BP）[14]。
获得待分类样本 y 的稀疏系数 α ^ 之后,构造如式（3）的线性分类器,确定待分像元的类别归属。
class y = arg min i y - D i α ^ i 2 2 , i = 1,2 , … , M （3）
式中： D i 为第 i 类字典; α ^ i 为计算出的第 i 类字典原子对应位置的稀疏系数; D i α ^ i 表示第 i 类重构信号,因此,分类器式(3)的意义为待分像元矢量 y 与各类重构信号的距离平方最小,确定待分像元的类别归属。一般地,高光谱影像稀疏分类模型（SRC）可概括为算法1：
算法1 SRC模型
输入：样本构造的过完备字典 D ,待分类别像元 y ,以及稀疏度 K 0
处理：
(1)利用OMP算法,计算待分像元 y 的稀疏系数 α ^
(2)根据式（3）的分类器确定待分像元 y 的类别归属
输出：像元 y 的类别 i （ i 为类别代号）

2.2 光谱维稀疏表达模型

算法1表明,稀疏分类模型（SRC）是通过对待分像元 y 在原始样本空间中的稀疏表达来实现像元的分类。由于高光谱影像相邻波段间存在较强的相关性,光谱信息冗余大,直接由原始样本构造的字典往往导致类别间较差的区分性,本文考虑利用少量的“特征光谱”逼近原始光谱信息,通过对字典原子在光谱维上进行稀疏表达,以达到减少光谱信息的冗余性、优化字典结构或质量的目的。基本思路首先是对字典 D 中的原子在光谱维上进行稀疏表达,然后将待分像元 y 在变换后的字典空间中进行稀疏表达和分类。
假设字典 D 中的每个原子可由一个核心字典 Φ 表示,即式（4）。
D = ΦA （4）
式中： A 为原子表示矩阵。核心字典 Φ 可以选择冗余的DCT[15]、小波字典[16-17]或其它线性变换方法。考虑到小波的多尺度、可逆变换的特性,及其在高光谱影像光谱信息特征提取中的广泛应用[18-19],本文选择小波字典 W s （小波逆变换）作为核心字典 Φ ,则稀疏表达模型（式（2））可表示为：
α ^ = arg min α y - WAα 2 2 s.t α 0 ≤ K 0 （5）
由于选择的小波变换满足完全重构条件,即 W s 可逆,则式（5）等价于式（6）。
α ^ = arg min α W a y - Aα 2 2 s.t α 0 ≤ K 0 （6）
式中： W a 代表小波分解（小波变换）;此时, A 为选定小波基后字典 D 中各原子的小波系数。
由式（6）可知,光谱维的稀疏表达可转化为小波域的稀疏表达模型,因而也可以理解为对光谱特征提取操作后对光谱特征的稀疏表达。综上所述,光谱维稀疏分类模型（WSRC）可表示为算法2。
算法2 WSRC模型
输入：样本构造的过完备字典 D ,待分类别像元 y ,小波字典 W s 以及稀疏度 K 0
处理：
（1）由 W s 获得 W a ,其中 W a = W s - 1
（2）根据选择的小波字典 W s 和原始字典 D ,得到表示小波系数 A
（3）将待分类别像元转换到小波域 W a y
（4）利用OMP算法优化式（6）,计算得到稀疏系数 α ^
（15）由以下稀疏分类器计算类别归属 i ：
class y = arg min i y - A i α ^ i 2 2 , i = 1,2 , … , M
输出：像元 y 的类别i

2.3 光谱与空间维双重稀疏表达模型

在同质区的空间邻域内,相邻的像元一般为同类地物,具有相似的光谱曲线,表现为邻域地物的统一性,因此,邻域稀疏一致性的JSRC模型能较大提高影像的分类精度。但在异质区,像元在邻域内不但具有相同的地物,还有不同的地物,而且影像中广泛存在同物异谱现象,这必然导致空间邻域像元表达的差异性。本文综合考虑空间邻域地物的统一性和差异性,先对邻域内像元进行个性化的稀疏编码,再进行累加聚合的分类策略。由于空间维的稀疏表达是基于光谱维稀疏表达（光谱小波变换）后的再次稀疏表示,因此,认为其是光谱与空间的双重稀疏分类模型（WSSRC）,模型表述如式(7)：
S ^ = arg min S Y - W s AS 2 2 s.t S row , 0 ≤ K 0 （7）
式中： Y = y 1 y 2 … y n 是以 y 1 为中心像元的像元集合, W s 小波字典(小波逆变换), S ^ 是邻域内每个像元的个性化稀疏编码系数。考虑到本文选择小波字典的可逆特性,式（7）等价于式（8）。
S ^ = arg min S W a Y - AS 2 2 s.t S row , 0 ≤ K 0 （8）
式中： W a 为小波变换。
由式（8）计算出的 S ^ 是邻域像元分别在过完备字典中的稀疏编码,因此不同邻域像元具有不同的稀疏编码位置。充分利用字典的过完备特性,体现了邻域像元间稀疏表达的差异性。为表现空间邻域像元同类地物光谱的统一性,本文综合考虑整个邻域空间,将计算出的稀疏编码 S ^ 进行累加聚合（Sum pooling）,如式（9）所示。
Poolin g sum S = Poolin g sum s 11 … s 1 n ⋮ … ⋮ s N 1 … s Nn = ∑ s 1 ∙ ⋮ ∑ s N ∙ （9）
式中： ∑ s i ∙ = ∑ j = 1 n s ij , i = 1,2 , … , N ,表示空间邻域内像元的稀疏编码按行累加操作。
由于稀疏表达是一种线性模型,某个变量（变量在归一化的前提下）系数的大小代表了该变量对表达原始信号的重要性程度。这表明稀疏编码可理解为所选择的字典原子对原始信号线性重构的权值（贡献）。因此,定义如式（10）所示的分类器,表示为将像元归属到对原始信号线性重构具有最大贡献的类别。
class y 1 = max N i ∑ Poolin g sum S ^ ∑ Poolin g sum S ^ （10）
式中： N i 表示字典中所有属于第 i 类训练样本所在位置的索引。WSSRC模型的流程如算法3：
算法3 WSSRC模型
输入：字典 D ;待分类像元 y 1 及集合 Y ;小波字典 W s ;稀疏度 K 0 ;邻域窗口 T
初始化： D 归一化处理;获得 W a
处理：
（1）根据选择的小波字典 W s 和原始字典 D ,得到表示小波系数 A
（2）将待分类别像元转换到小波域 W a y
（3）利用OMP算法优化式（8）,计算获得领域像元的稀疏编码 S ^
（4）稀疏编码 S ^ 进行累加聚合
（5）利用（10）式表达的分类器,计算获得待分像元 y 1 的类别归属 i
输出：待分像元 y 1 的类别 i

3 实验结果与分析

为了验证所提出模型的有效性,本文利用2幅标准的高光谱影像数据,将所提出的光谱与空间双重稀疏分类模型（WSRC、WSSRC）与稀疏分类模型（SRC）和联合的稀疏分类模型（JSRC）进行比较。所有的算法均在MATLAB R2012b平台上实现,并利用常用的指标总体精度OA值和kappa值[6-12]作为分类精度评价标准。

3.1 AVIRIS数据

实验1所采用的AVIRIS影像数据获取于1992年,覆盖区域为美国加利福尼亚州一处农业用实验区。该影像大小为145像元×145像元,空间分辨率为20 m,具有224个波段,包含16种典型地物。剔除水吸收波段和噪声较大的波段后,本文利用剩余的200个波段数据作为实验数据[20]。每种类别随机选择10%的样本构成字典,其余已知类别的像元数据作为测试样本,用于分类和最后的精度评定,详情见表1。测试像元和样本字典的分布如图1（a）和（b）所示。
Tab. 1 16 Ground-truth classes in AVIRIS Indian Pines and the training and test sets for each class

表1 16种真实类别地物及每类训练和测试样本数

序号 类别 训练 测试
1 苜蓿 5 41
2 玉米I 143 1285
3 玉米II 83 747
4 玉米III 24 213
5 草I 49 343
6 草II 73 657
7 草III 3 25
8 干草梗 48 430
9 燕麦 2 18
10 大豆I 98 874
11 大豆II 246 2209
12 大豆III 60 533
13 小麦 21 184
14 树丛 127 1138
15 建筑物-草-树-路 39 347
16 石-钢顶棚 10 83
总计 1031 9218
Fig. 1 Indian Pine image

图1 Indian Pine影像

3.2 字典结构评价

本实验首先证实光谱维稀疏表达能改进传统模型中字典的质量或结构。为此,选取了db4,sym2,coif2和dmey等常用小波基[21],从而确定相应的小波字典 W s ,并分别基于这些变换基,对原始的字典进行了多个层次的分解。为定量评价字典变换前后的结构,本文依据Fisher判别准则思想[22-23],选择类间距离 E d 与类内距离 E c 的差值 St ,作为衡量字典 D 结构或质量的指标。
St = E d - E c （11）
如果 St 值越大,表示类间与类内的差值越大,不同类别的像元更容易分离,表明字典的结构或质量越好。其中类内距离与类间距离分别定义为式（12）、（13）：
E c = 1 N × trace D - D ̅ T D - D ̅ （12）
E d = E - E c （13）
式中： N 为字典 D 中样本个数; D ̅ = d 1 , d 1 , … , d 1 ︷ N 1 , … , d M , d M , … d M ︷ N M , d i 为第 i 种类别的样本均值, N i 为第 i 种类别的样本个数。记 D ̿ = d , d , … , d ︷ N , 其中, d = ∑ i = 1 M d i M 为所有样本的平均值,则 E = 1 N × trace D - D ̿ T D - D ̿ 。
表2列出了不同小波基不同分解层次时光谱维稀疏分类模型（WSRC）的总体精度,以及表征字典结构或质量的指标离差指标 St 。
Tab. 2 WSRC classification accuracy and the dictionary structure index under different wave basis and decomposition levels

表2 不同小波基,不同分解层次下WSRC字典结构指标和分类精度 /(%)

小波基层次 DB4 Sym2 Coif 2 Dmey
OA St OA St OA St OA St
原始层 70.10 0.98 70.10 0.98 70.10 0.98 70.10 0.98
第1层 72.70 1.01 73.29 1.02 72.77 1.01 73.60 1.01
第2层 74.00 1.03 73.71 1.03 74.32 1.03 75.40 1.03
第3层 65.94 1.04 62.95 1.03 67.78 1.03 69.28 1.02
由表2可知,对所有的小波变换,WSRC模型在第1层和第2层分解上能有效地提高分类精度。然而,随着小波分解层次的增加,无论是字典结构,还是分类精度都有不同程度的下降。这是由于随着小波分解层次增加,光谱细节信息损失严重,并且字典的结构质量有所下降,从而综合导致分类精度逐渐降低。为此,本文选择dmey小波基作进一步分析,表3计算出光谱字典在4个分解层次上类内距离、类间距离、信息损失量和结构指标 St 指标值。从表3可看出,光谱在第3层分解后,细节信息损失严重,但字典结构指标 St 变化不甚明显。这说明第3层分解后结构指标 St 的增益将不能弥补光谱信息的损失。由表2、表3分析可知,利用小波字典 W s 对字典 D 中原子在光谱维上进行稀疏表达,只能在低层次小波分解上利用重构低频分量替代原始光谱信息,并构造新的表达字典,以增加不同类别间与相同类别间的距离,从而优化字典结构,提高分类精度。
Tab. 3 Different related indexes of the Dmey wavelet decomposition

表3 Dmey小波基不同分解层次相关指标值

Dmey 类内距离 类间距离 信息损失量 结构指标St
原始层 0.0031 0.0129 0.0000 0.0098
第1层 0.0027 0.0128 0.0022 0.0101
第2层 0.0024 0.0127 0.0039 0.0103
第3层 0.0022 0.0123 0.0102 0.0102
第4层 0.0019 0.0109 0.0305 0.0090
由于dmey小波基二层分解效果最好,其整体精度为75.40%。本文因而选择dmey小波基二层分解的低频分量系数构成小波字典进行其余的实验。为优化稀疏度参数,本文把稀疏度 K 0 从5到30进行变化,并计算不同参数下的分类效果。为了对比不同的分类精度方法,本文也在相同的条件下计算了SRC模型的分类情况。
图2是不同稀疏度下WSRC与SRC分类精度。结果表明,在较小的稀疏度下WSRC具有较高的分类精度,并且在任意的稀疏度下分类精度都显著高于SRC模型。这表明如果在模型中引入光谱维的稀疏表达,能改善字典的结构,从而显著提高影像的分类精度。图2还表明稀疏模型的分类精度与稀疏度 K 0 相关,随着稀疏度的增加,WSRC和SRC的分类精度先增加后减少。
Fig. 2 WSRC and SRC classification results under different sparsity

图2 不同稀疏度下WSRC与SRC分类结果比较

为比较本文方法（WSSRC）与JSRC模型[6]的分类效果,本文先固定窗口尺寸 sz × sz = 7 × 7 ,从5到50变化稀疏度 K 0 ,并计算WSSRC和JSRC模型分类结果（图3）。同样地,为了研究窗口大小对模型分类精度的影响,固定稀疏度 K 0 = 40 ,窗口大小T从 3 × 3 至 11 × 11 变化,分别计算出WSSRC和JSRC模型的分类结果（图4）。
图3、图4的结果表明,本文提出的WSSRC模型,在不同稀疏度或不同窗口大小的条件下,其分类结果都要好于JSRC模型,并且最后的分类精度对参数的敏感性较低,大大地提高了模型的实用性。这表明本文从光谱和空间2个角度提出的WSSRC稀疏分类模型具有明显的有效性。
Fig. 3 WSSRC and JSRC classification results under different sparsity

图3 不同稀疏度下WSSRC与JSRC分类结果比较

Fig. 4 WSSRC and JSRC classification results diffident window sizes

图4 不同窗口下WSSRC与JSRC分类结果比较

为比较本文提出的模型（WSRC、WSSRC）与SRC、JSRC模型在各个地物类别分类情况,综上分析,选择稀疏度 K 0 = 20 ,窗口大小 T = 7 × 7 ,各类别分类结果见表4,以及相应的分类图见图1(c)-(f)。
表4结果表明,双重稀疏分类模型,其大部分地物类别精度都要好于SRC/JSRC稀疏分类模型,并且分类的总体精度有了一定的提高。WSRC较SRC模型的总体精度由69.53%提高到74.46%,对应的kappa系数由0.651提高到0.708;而WSSRC较JSRC模型的总体精度由92.98%提高到96.46%,kappa系数也由0.920提高到0.960。
Tab. 4 Different models of classification accuracy / (%)

表4 不同模型各类别分类精度比较 / (%)

类别 SRC WSRC JSRC WSSRC
苜蓿 39.02 75.61 21.95 92.68
玉米I 60.31 65.45 94.09 96.11
玉米II 52.61 59.30 84.20 91.83
玉米III 32.39 42.25 85.92 95.31
草I 86.64 89.63 94.24 94.70
草II 95.74 95.89 99.70 99.70
草III 64.00 84.00 80.00 96.00
干草梗 95.81 97.44 100.00 100.00
燕麦 55.56 61.11 0.00 0.00
大豆I 56.86 69.11 85.47 91.42
大豆II 69.58 73.38 94.43 98.37
大豆III 49.91 60.41 95.87 97.94
小麦 98.37 98.37 100.00 99.46
树丛 89.89 89.10 98.51 98.86
建筑物-草-树-路 41.21 51.87 85.59 93.95
石-钢顶棚 79.52 80.72 97.59 98.80
OA 69.53 74.46 92.98 96.46
kappa系数 0.651 0.708 0.920 0.960

3.3 ROSIS数据

为进一步验证本文提出模型的有效性,实验2选择了意大利帕维亚大学ROSIS高光谱数据。ROSIS数据有115个波段,波长范围为0.43到0.86 μm,空间分辨率1.3 m,影像大小为 610 像元 × 340像元。剔除了12个水吸收的波段后,本文选取剩余103个波段的数据,其中包含了9种地物类 型[24]。同样随机选择10%的像元作为训练样本,其余像元用于分类精度测试,详见表5和图5(a)、(b)。
Tab. 5 9 Ground-truth classes of the ROSIS Pavia University data set, and the training and test sets for each class

表5 9类真实地物及每类训练和测试样本数

序号 类别 训练 测试
1 柏油 664 5967
2 草甸 1865 16 784
3 碎石 210 1889
4 树 307 2757
5 金属板 135 1210
6 裸土 503 4526
7 沥青 133 1197
8 砖 369 3313
9 阴影 95 852
总计 4281 38 495
同样,选择dmey小波基,并以2层分解的低频分量构成字典,计算出光谱稀疏表示前后字典 S 的结构指标。结果显示, S 值由0.0691提高到0.0696,表明光谱稀疏表示前后字典的结构有所提高。
相对于实验1数据,实验2影像中含有大量的树木、房屋及阴影等小尺寸地物目标,因而实验2的分类在小窗口下即可取得更好的结果。因此通过实验选择参数如下,稀疏度 K 0 = 10 和窗口 T = 9 。各种方法的总体分类结果如表6所示,相应分类图如图5(c)-(f)所示。
Fig. 5 Pavia University image

图5 PaviaU影像

从表6可看出,WSSRC模型同样优于稀疏表达模型。WSRC较SRC模型的总体精度由83.42%提高到84.54%,对应的kappa系数由0.779提高到0.794;而WSSRC较JSRC模型的总体精度由92.12%提高到94.57%,kappa系数也由0.894提高到0.927。实验表明,本文提出的光谱与空间的双重稀疏表达分类模型具有一定的普适性,更适合高光谱的影像分类。
Tab. 6 Different models of classification accuracy / (%)

表6 不同模型各类别分类精度比较 / (%)

类别 SRC WSRC JSRC WSSRC
柏油 79.97 82.62 90.16 96.75
草甸 92.75 93.11 99.41 99.21
碎石 66.65 68.29 82.69 80.36
树 89.01 88.68 94.41 95.43
金属板 99.83 99.67 99.92 99.92
裸土 66.06 66.02 74.04 79.89
沥青 68.17 76.44 89.31 88.22
砖 68.52 70.57 84.79 94.11
阴影 90.96 94.25 93.08 97.77
OA 83.42 84.54 92.12 94.57
kappa系数 0.779 0.794 0.894 0.927

4 结论

针对高光谱影像光谱信息存在冗余性,以及空间邻域像元的统一性和差异性特点,提出光谱与空间的双重稀疏分类模型（WSSRC）。该方法在光谱维对原始字典进行稀疏表达以优化字典的结构或质量,并且能兼顾空间邻域像元光谱的统一性和差异性表达,显著提高了高光谱影像的分类精度。实验表明,本文提出的WSSRC模型对参数的敏感度较低,具有更好的普适性。但本文的不足是光谱与空间的稀疏表达是独立的,难以有效刻画光谱与空间的相互关系。更好的方式是采用基于质量的稀疏理论,用统一的模型对光谱与空间进行更有效的表达,将是进一步的研究方向。

The authors have declared that no competing interests exist.

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[ Liang R H, Cheng L Z.Double sparse image representation via learning dictionaries in wavelet domain[J]. Journal of National University of Defense Technology, 2012,34(4):126-131. ]

[18]
吴波,熊助国.基于光谱最佳尺度分割特征的高光谱混合像元分解[J].测绘学报,2012,41(2):205-212.提高混合像元线性分解精度的一个关键点在于改善端元光谱矩阵的构成。本文提出一种基于光谱多尺度分割特征的混合像元分解方法。首先在分割段内离差平方和最小准则下，对高光谱影像的光谱进行多尺度分割，并以各分割段中对应像元的光谱平均值为光谱特征，最后以限制性的最小二乘方法估计出混合像元的组分。模拟与真实数据的实验结果表明，本文方法能够较大的提高遥感影像混合像元的分解精度，并且优于光谱维小波特征的分解。

[ Wu B, Xiong Z G.Unmixing of hyperspectral mixture pixels based on spectral multi-scale segmented features[J]. Acta Geodaetics et Cartographica Sinica, 2012,41(2):205-212. ]

[19]
吴波,张良培,李平湘.基于光谱维小波特征的混合像元投影迭代分解[J].电子与信息学报,2005,33(11):1933-1936.混合像元线性分解是高光谱遥感应用的关键技术之一.本文利用小波 变换多分辨率分析的特点,提出了一种以小波低频系数为特征的混合像元投影迭代分解的方法.首先利用离散二进小波提取了高光谱影像特征,再基于影像特征,用 投影迭代方法自动确定出端元光谱,并以限制性的最小二乘方法估计出混合像元的组分.实验结果表明,本文方法能够较大的提高遥感影像混合像元的分解精度.

DOI

[ Wu B, Zhang L P, Li P X.Projective iterative unmixing of hyperspectral image based on spectral domain wavelet feature[J]. Journal of Electronics & Information Technology, 2005,33(11):1933-1936. ]

[20]
Yuan H L, Tang Y Y.A novel sparsity-based framework using max pooling operation for hyperspectral image classification[J]. IEEE Journal of Selected Topics in Signal Processing, 2014,7(8):3570-2576.Various sparsity-based methods have been widely used in hyperspectral image (HSI) classification. To determine the class label of a test sample, traditional sparsity-based frameworks mainly use the sparse vectors to compute the residual error for classification. In this paper, a novel sparsity-based framework is proposed, which adopts the max pooling operation for HSI classification. Compared with the traditional sparsity-based frameworks using residual error, sparse vectors in our proposed framework are utilized to generate the feature vectors using max pooling operation. Experimental results demonstrate that our proposed framework can achieve the state-of-the-art classification performance.

DOI

[21]
Gualtieri J A, Cromp R F.Support vector machines for hyperspectral remote sensing classification[C]. The 27th AIPR Workshop: Advances in Computer-Assisted Recognition. International Society for Optics and Photonics, Springer Netherlands, 1999:221-232.

[22]
辛芳芳,焦李成,王桂婷.非局部均值加权的动态模糊Fisher分类器的遥感图像变化检测[J].测绘学报,2012,41(4):584-590.提出一种新的变化检测算法,利 用改进的动态模糊Fisher分类器,通过对多时相图像的联合直方图进行分类得到变化区域。在此基础上,根据图像空间关系对待检测点进行非局部均值加权, 并以一定比例选取可靠性高的数据先进行标类,增加数据的可分性和算法的可靠性。根据更新后的样本动态调整待检测点权重及分类器参数,直到所有点判别完毕为 止。本算法不受参数模型限制,不受差异算子影响并充分利用图像的空间与时间信息。真实遥感数据试验表明本算法提高了检测精度。

[ Xin F F,Jiao L C,Wang G T.Change detection in multitemporal remote sensing image based on dynamic fuzzy fisher classifier and non local mean weighted method[J]. Acta Geodaetica et Cartographica Sinica, 2012,41(4):584-590. ]

[23]
Yang M, Zhang D, Feng X.Fisher discrimination dictionary learning for sparse representation[C]. IEEE International Conference on Computer Vision (ICCV), 2011:543-550.

[24]
Plaza A, Benediktsson J A, Boardman J W, et al.Recent advances in techniques for hyperspectral image processing[J]. Remote Sensing of Environment, 2009,113:S110-S122.Imaging spectroscopy, also known as hyperspectral imaging, has been transformed in less than 30&nbsp;years from being a sparse research tool into a commodity product available to a broad user community. Currently, there is a need for standardized data processing techniques able to take into account the special properties of hyperspectral data. In this paper, we provide a seminal view on recent advances in techniques for hyperspectral image processing. Our main focus is on the design of techniques able to deal with the high-dimensional nature of the data, and to integrate the spatial and spectral information. Performance of the discussed techniques is evaluated in different analysis scenarios. To satisfy time-critical constraints in specific applications, we also develop efficient parallel implementations of some of the discussed algorithms. Combined, these parts provide an excellent snapshot of the state-of-the-art in those areas, and offer a thoughtful perspective on future potentials and emerging challenges in the design of robust hyperspectral imaging algorithms.

DOI

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