A Convex Analysis-Based Minimum-Volume Enclosing Simplex Algorithm for Hyperspectral Unmixing

Hyperspectral unmixing aims at identifying the hidden spectral signatures (or endmembers) and their corresponding proportions (or abundances) from an observed hyperspectral scene. Many existing hyperspectral unmixing algorithms were developed under a commonly used assumption that pure pixels exist. However, the pure-pixel assumption may be seriously violated for highly mixed data. Based on intuitive grounds, Craig reported an unmixing criterion without requiring the pure-pixel assumption, which estimates the endmembers by vertices of a minimum-volume simplex enclosing all the observed pixels. In this paper, we incorporate convex analysis and Craig's criterion to develop a minimum-volume enclosing simplex (MVES) formulation for hyperspectral unmixing. A cyclic minimization algorithm for approximating the MVES problem is developed using linear programs (LPs), which can be practically implemented by readily available LP solvers. We also provide a non-heuristic guarantee of our MVES problem formulation, where the existence of pure pixels is proved to be a sufficient condition for MVES to perfectly identify the true endmembers. Some Monte Carlo simulations and real data experiments are presented to demonstrate the efficacy of the proposed MVES algorithm over several existing hyperspectral unmixing methods.     

基于像元纯净指数的多端元提取算法

针对传统单端元提取方法不能描述端元变异、限制混合像元分解精度的缺点,提出一种基于像元纯净指数的多端元提取算法(Multiple Endmember Extraction Algorithm Based on Pixel Purity Index,PPI-MEE)。首先将图像划分为不重叠的图像块,并分别利用改进的PPI算法提取候选端元集,然后利用候选端元的邻域像元光谱信息对候选端元进行优化和精选。最后,对优化精选后的端元集分类得到每类地物的多端元光谱集。仿真数据和真实高光谱数据的实验结果表明,提出的多端元提取策略具有表征遥感图像中端元光谱变异的能力,能够提高端元提取精度和混合像元分解精度。     

高光谱图像混合像元分解算法

传统的高光谱图像混合像元分解技术包括端元提取和估计每个端元的混合比例.虽然很多模型都能得到可以接受的解混结果,但是一些未知端元的存在使得结果在包含未知端元的像素点处出现偏差.因此,提出了一种基于支持向量数据描述的高光谱图像混合像元分解算法.首先高光谱图像数据被分成类内和类外两部分,类内是完全由已知端元数据混合的像素点,而类外数据是包含未知端元的像素点.两类数据交界处被认为是已知端元和未知端元混合的数据.然后再对这些像素点进行混合像元分解,分别对仿真数据和真实高光谱图像进行实验.结果表明该算法可以有效地解决因存在未知端元对解混精度的影响,而且能给出未知端元的解混分量.该方法的解混结果几乎不受未知端元的影响,优于直接解混结果     

基于代数余子式的N-FINDR快速端元提取算法

基于高光谱图像特征空间几何分布的端元提取方法通常可分为投影类算法和单形体体积最大类算法,通常前者精度不好,后者计算复杂度较高。该文提出一种基于代数余子式的快速N-FINDR端元提取算法(FCA),该算法融合了投影类算法速度快和单形体体积最大类算法精度高的优势,利用像元投影到端元矩阵元素的代数余子式构成的向量上的方法,寻找最大体积的单形体。此外,该算法在端元搜索方面较为灵活,每次迭代都可用纯度更高的像元代替已有端元,因此能保证用该端元确定的单形体,可以将特征空间中全部像元包含在内。仿真和实际高光谱数据实验结果表明,该文算法在精准提取出端元的同时,收敛速度非常快。     

基于测地线距离和正交投影的端元提取算法

端元提取是高光谱遥感图像混合像元分解的关键步骤。传统线性端元提取方法忽略了像元内地物的非线性混合因素,制约了混合像元分解精度的提升。针对高光谱图像数据的非线性结构,提出一种基于测地线距离的正交投影端元提取算法,将测地线距离引入端元单体提取过程,利用正交投影方法逐个提取端元。为了降低测地线距离计算量,在端元提取前先利用自动目标生成方法和无约束最小二乘法对原始高光谱数据进行数据约减。模拟和真实高光谱图像实验表明,该方法能够表征光谱数据中非线性因素,端元提取结果优于传统自动目标生成端元提取方法。     

基于同质区分割的非线性端元提取算法

端元提取是高光谱遥感图像混合像元分解的关键步骤。传统端元提取算法忽略了高光谱图像中地物空间分布相关性与非线性结构,制约了端元提取算法的精度。针对高光谱图像的空间关系与非线性结构,提出一种基于同质区分割的非线性端元提取算法。使用超像素分割方法将图像分割为若干同质区,利用流形学习构造高光谱图像数据的非线性结构,最后在同质区内提取端元并利用聚类方法优选端元。模拟和真实图像数据实验表明,该算法能够保证高光谱数据的非线性结构,端元提取结果优于其他传统线性端元提取方法,在低信噪比的情况下,可以保持较好的端元提取结果。     

基于高光谱解混的伪装目标识别技术研究

高光谱遥感图像识别技术在伪装目标识别方面具有很大的应用前景。针对高光谱遥感图像中的混合像元和光谱变异问题,提出基于高光谱解混技术的伪装目标识别方法。该方法采用扩展线性混合模型表征高光谱图像中的光谱变异问题,利用超像元分割技术将原始高光谱图像转换为粗细多尺度特征图,对超像元丰度矩阵附加8-邻域空间加权与行约束,以降低噪声和奇异点像元的影响。针对伪装目标空间分布稀疏的特点,在模型中增加丰度矩阵的截断加权核范数作为正则化项,以提高算法精度。实验结果表明提出的方法具有良好的抗噪性和较高的解混精度,可以有效提高伪装目标识别精度。     

A quantitative and comparative analysis of endmember extraction algorithms from hyperspectral data

Linear spectral unmixing is a commonly accepted approach to mixed-pixel classification in hyperspectral imagery. This approach involves two steps. First, to find spectrally unique signatures of pure ground components, usually known as endmembers, and, second, to express mixed pixels as linear combinations of endmember materials. Over the past years, several algorithms have been developed for autonomous and supervised endmember extraction from hyperspectral data. Due to a lack of commonly accepted data and quantitative approaches to substantiate new algorithms, available methods have not been rigorously compared by using a unified scheme. In this paper, we present a comparative study of standard endmember extraction algorithms using a custom-designed quantitative and comparative framework that involves both the spectral and spatial information. The algorithms considered in this study represent substantially different design choices. A database formed by simulated and real hyperspectral data collected by the Airborne Visible and Infrared Imaging Spectrometer (AVIRIS) is used to investigate the impact of noise, mixture complexity, and use of radiance/reflectance data on algorithm performance. The results obtained indicate that endmember selection and subsequent mixed-pixel interpretation by a linear mixture model are more successful when methods combining spatial and spectral information are applied.     

一种改进的基于自动形态学的端元提取算法

自动形态学端元提取（AMEE）算法中的形态学算子在纯像元集中分布的区域无法得到正确的结果。现有膨胀操作在每个结构元素内只能提取一个候选端元,会造成重要像元丢失。为了解决这些问题,采用改进的形态学算子和结构元素对AMEE算法进行了改进。首先引入参考光谱向量的概念构建了改进的形态学算子,并给出了形态学离心率指数新的计算方法,然后利用偶数大小、改进的结构元素,从每个结构元素内选出4个候选端元,最后对改进的基于自动形态学的端元提取算法进行了分析和实验验证。结果表明,改进的方法能从纯像元集中分布的区域获得正确的候选端元,并在一定程度上避免膨胀过程中的信息遗失,从而能够有效地提升端元提取的精度和像元解混的效果。     

一种改进的N-FINDR高光谱端元提取算法

光谱端元提取是对高光谱数据进一步分析的重要前提。在各种端元提取算法中,N-FINDR算法因其全自动和选择效果较好等优点受到了广泛的关注。然而样本的排序对该算法的端元提取会造成一定影响,并且传统N-FINDR算法需要根据端元的个数进行降维处理,从而限制了该算法的应用。实际高光谱数据中存在的同一地物在高维空间中非紧密团聚现象也对端元提取增加了难度。为此该文提出改进的算法停机准则和数据特征预处理方法,并使用支持向量机对提取到的端元进行二次提取。实验结果表明,改进的停机准则进一步增加了由端元向量组组成的凸体体积。数据特征预处理和基于支持向量机的二次端元提取分别提升了数据的可分性和提取到端元的精度。     

A maximum entropy approach to unsupervised mixed-pixel decomposition.

Due to the wide existence of mixed pixels, the derivation of constituent components (endmembers) and their fractional proportions (abundances) at the subpixel scale has been given a lot of attention. The entire process is often referred to as mixed-pixel decomposition or spectral unmixing. Although various algorithms have been proposed to solve this problem, two potential issues still need to be further investigated. First, assuming the endmembers are known, the abundance estimation is commonly performed by employing a least-squares error criterion, which, however, makes the estimation sensitive to noise and outliers. Second, the mathematical intractability of the abundance non-negative constraint results in computationally expensive numerical approaches. In this paper, we propose an unsupervised decomposition method based on the classic maximum entropy principle, termed the gradient descent maximum entropy (GDME), aiming at robust and effective estimates. We address the importance of the maximum entropy principle for mixed-pixel decomposition from a geometric point of view and demonstrate that when the given data present strong noise or when the endmember signatures are close to each other, the proposed method has the potential of providing more accurate estimates than the popular least-squares methods (e.g., fully constrained least squares). We apply the proposed GDME to the subject of unmixing multispectral and hyperspectral data. The experimental results obtained from both simulated and real images show the effectiveness of the proposed method.     

基于分层的多端元光谱解混算法

高光谱图像中,单一端元光谱很难准确刻画一个类别,导致解混结果不准确。针对经典多端元光谱解混(MESMA)算法存在计算量大、端元预选繁琐等缺点,提出基于分层的MESMA(HMESMA)算法,第1层确定像元包含地物类别,第2层在第1层的基础上再分层确定像元包含最优端元个数。采用模拟数据和真实高光谱数据进行实验,证明了本文算法比固定端元解混效果好,平均丰度误差最高降低了2.65%,与经典的MESMA算法精度相当,但大大降低了计算量,提高了计算效率。     

高光谱遥感图像端元提取的零空间光谱投影算法

端元提取技术是高光谱遥感图像光谱解混的关键.在线性光谱混合分析中,首先引入了高光谱遥感图像经过零空间光谱投影后具有单形体的凸不变性.在此基础上,提出了零空间光谱投影算法,通过设计各种度量和准则,制定不同的单次端元提取策略,灵活地实现算法.经过证明,零空间光谱投影算法是对基于子空间投影距离算法(包括零空间投影距离算法与经典正交子空间投影算法)的进一步延伸,提供了更多的端元提取策略.实验结果表明,零空间光谱投影算法在模拟图像以及真实高光谱遥感图像中都能够有效地提取出图像中的各种端元.     

Spatial/spectral endmember extraction by multidimensional morphological operations

Spectral mixture analysis provides an efficient mechanism for the interpretation and classification of remotely sensed multidimensional imagery. It aims to identify a set of reference signatures (also known as endmembers) that can be used to model the reflectance spectrum at each pixel of the original image. Thus, the modeling is carried out as a linear combination of a finite number of ground components. Although spectral mixture models have proved to be appropriate for the purpose of large hyperspectral dataset subpixel analysis, few methods are available in the literature for the extraction of appropriate endmembers in spectral unmixing. Most approaches have been designed from a spectroscopic viewpoint and, thus, tend to neglect the existing spatial correlation between pixels. This paper presents a new automated method that performs unsupervised pixel purity determination and endmember extraction from multidimensional datasets; this is achieved by using both spatial and spectral information in a combined manner. The method is based on mathematical morphology, a classic image processing technique that can be applied to the spectral domain while being able to keep its spatial characteristics. The proposed methodology is evaluated through a specifically designed framework that uses both simulated and real hyperspectral data.     

基于Fisher判别零空间的高光谱图像混合像元分解

传统的光谱混合分析方法假设每个端元必须具有完全稳定的光谱特性,而在实际问题中同类地物的端元光谱往 往存在着差异。为了有效地抑制同物异谱对混合像元分解的影响,本文提出一种基于Fisher判别零空间的高光谱遥感图像混合像元分 解算法。Fisher判别零空间方法通过对高光谱图像数据进行线性变换,使得变换后的数据中同一端元内的光谱差异减小为零,而不同 端元间的光谱差异尽可能地增大。利用变换后的光谱数据对混合像元进行分解就可以较大程度地减少同物异谱现象对分解结果的影响。 对模拟高光谱图像数据以及Indiana地区和Cuprite地区的实际AVIRIS数据的解混结果表明,用Fisher判别零空间方法处理混合像元分 解问题,可以得到较高的分解精度。     

Iterative Spectral Unmixing for Optimizing Per-Pixel Endmember Sets

Fractional abundances predicted for a given pixel using spectral mixture analysis (SMA) are most accurate when only the endmembers that comprise it are used, with larger errors occurring if inappropriate endmembers are included in the unmixing process. This paper presents an iterative implementation of SMA (ISMA) to determine optimal per-pixel endmember sets from the image endmember set using two steps: 1) an iterative unconstrained unmixing, which removes one endmember per iteration based on minimum abundance and 2) analysis of the root-mean-square error as a function of iteration to locate the critical iteration defining the optimal endmember set. The ISMA was tested using simulated data at various signal-to-noise ratios (SNRs), and the results were compared with those of published unmixing methods. The ISMA method correctly selected the optimal endmember set 96% of the time for SNR of 100 : 1. As a result, per-pixel errors in fractional abundances were lower than for unmixing each pixel using the full endmember set. ISMA was also applied to Airborne Visible/Infrared Imaging Spectrometer hyperspectral data of Cuprite, NV. Results show that the ISMA is effective in obtaining abundance fractions that are physically realistic (sum close to one and nonnegative) and is more effective at selecting endmembers that occur within a pixel as opposed to those that are simply used to improve the goodness of fit of the model but not part of the mixture     

高光谱解混方法研究

高光谱图像的空间分辨率较低,导致大量混合像元存在于高光谱图像中。混合像元的存在是使高光谱图像目标分类准确率降低的主要原因之一。高光谱像元解混在高光谱遥感图像处理中具有非常重要的意义。高光谱像元解混主要分为线性和非线性光谱解混两种方法,研究最广泛的是线性光谱解混。归纳了线性光谱解混的两个步骤:（1）提取纯净像元中地物的光谱信号,即提取端元,这是关键步骤;（2）利用端元的加权线性组合对混合像元进行光谱解混,即丰度反演。简述了端元提取及丰度反演研究的主要进展,介绍了端元提取的几种典型算法。通过归纳、对比和分析,总结了不同端元提取方法的特点,并对高光谱解混的研究前景进行了展望。     

Spectral linear mixing model in low spatial resolution image data

Different ways to estimate the spectral reflectance for the component classes in a mixture problem have been proposed in the literature (pure pixels, spectral library, field measurements). One of the most common approaches consists in the use of pure pixels, i.e., pixels that are covered by a single component class. This approach presents the advantage of allowing the extraction of the components' reflectance directly from the image data. This approach, however, is generally not feasible in the case of low spatial resolution image data, due to the large ground area covered by a single pixel. In this paper, a methodology aiming to overcome this limitation is proposed. The proposed approach makes use of the spectral linear mixing model. In the proposed methodology, the components' proportions in image data are estimated using a medium spatial resolution image as auxiliary data. The linear mixing model is then solved for the unknown spectral reflectances. Experiments are presented, using Terra Moderate Resolution Imaging Spectroradiometer (MODIS) and Landsat Enhanced Thematic Mapper Plus, as low and medium spatial resolution image data, respectively, acquired on the same date over the Tapajos study site, Brazilian Amazon. Three component classes or endmembers are present in the scene covered by the experiment, namely vegetation, exposed soil, and shade. The components' spectral reflectance for the Terra MODIS spectral bands were then estimated by applying the proposed methodology. The reliability of these estimates is appraised by analyzing scatter diagrams produced by the Terra MODIS spectral bands and also by comparing the fraction images produced using both image datasets. This methodology appears appropriate for up-scaling information for regional and global studies.     

基于端元优化的非线性高光谱分解算法

针对高光谱图像中端元的可变性和光谱的非线性混合特性,提出一种基于端元优化的非线性光谱解混算法,通过加入阴影端元对混合像元的端元集进行优化,对优化的端元子集采用基于分层贝叶斯模型的双线性光谱分解算法进行光谱分解。模拟数据和真实数据实验表明,提出的算法能很好地解决高光谱图像中存在的阴影效应,分解效果优于FCLS和GBM算法。     

Vertex component analysis: a fast algorithm to unmix hyperspectral data

Given a set of mixed spectral (multispectral or hyperspectral) vectors, linear spectral mixture analysis, or linear unmixing, aims at estimating the number of reference substances, also called endmembers, their spectral signatures, and their abundance fractions. This paper presents a new method for unsupervised endmember extraction from hyperspectral data, termed vertex component analysis (VCA). The algorithm exploits two facts: (1) the endmembers are the vertices of a simplex and (2) the affine transformation of a simplex is also a simplex. In a series of experiments using simulated and real data, the VCA algorithm competes with state-of-the-art methods, with a computational complexity between one and two orders of magnitude lower than the best available method.