基于数据场的端元提取算法研究

传统端元提取算法一般需要人工指定端元数目,易导致多选或漏选端元。利用数据场自然拓扑聚类、可视化的特性,提出了基于数据场的端元提取方法。首先对图像进行分区处理,然后应用数据场思想计算各区域数据点的势能,并分别选择一定数量的特征点,将所有特征点集合成特征图像,再计算特征图像的数据场;最后根据数据场形成的拓扑聚类结构,可视化地提取端元,获得最佳端元的数目和位置。利用Cuprite矿区的AVIRIS数据进行端元提取实验,结果表明:该方法是合理有效的,能够应用于高光谱图像的端元提取中。     

Analysis and acceleration strategy of endmember extraction algorithms based on convex geometry

Under a linear mixture model with non-negativity and sum-to-one constraints, the spectral unmixing problem can be seen as a convex geometry problem. This article first analyses three commonly used endmember extraction criteria including the extreme projection criterion, the maximum simplex volume criterion and the minimum volume enclosing simplex criterion, which are derived from the geometrical explanation of the linear mixture model. And then an acceleration strategy is introduced to shorten the computing time of endmember extraction algorithms. The acceleration strategy exploits two facts: (1) the endmembers corresponding to the vertices of a simplex composed of the mixed pixels can be determined only by the boundary points, with little or no affect by the interior points; (2) the boundary points can be found in a series of two-dimensional subspace. Experiments using simulated data on eight popular endmember extraction algorithms show that the proposed acceleration strategy can reduce the computing time and then improve the speed of endmember extraction, while maintaining the same results or little sacrifice of computing precision.     

基于拉格朗日的高光谱解混算法研究*

针对混合像元分解误差问题,提出一种基于拉格朗日算法的高光谱解混算法。通过变分增广拉格朗日算法提取出部分端元,由于端元组中存在相似端元影响解混精度,利用基于梯度的光谱信息散度算法进行光谱区分,除去相似端元。通过对得到的端元进行排序,依次增加端元进行光谱解混,将满足条件的端元增加进端元组,最终得到优选端元。该方法不仅有效去除了相似端元的干扰,而且不需要不断搜索端元的组合,根据每个端元对于混合像元的重要性做出相应次数的非限制性最小二乘法计算,得到更精确高光谱端元的子集,该方法对高光谱混合像元解混的效率以及可靠性均有所提高。     

非监督正交子空间投影的高光谱混合像元自动分解

利用混合像元线性分解技术处理高光谱影像，以获取研究区域中同一像元的不同组份是遥感应用的主要目的之一。近年来，研究者们发展了一种正交子空间投影技术(0SP)，用来探测感兴趣目标，进一步可以用来分解混合像元，然而应用这种方法分解混合像元的缺陷是需要有研究区域的先验信息，这就制约了它在这方面的应用。为此针对这种不足，提出一种非监督的正交子空间投影(UOSP)技术，用来自动获取影像端元光谱，同时进行混合像元分解。并用成像光谱数据(PHI)实例测试了这个方法，结果表明该方法自动获取的端元比较合理，且分解混合像元精度较高。     

基于线性混合模型的高光谱图像端元提取

近年来,基于线性混合模型的光谱解混合技术正在越来越广泛地用在光谱数据分析和遥感地物量化中,这项技术的关键就在于确定端元(Endmember)光谱。通常,端元的荻取有两种方式：来源于光谱库以及来源于图像数据,相比之下后者得到的结果更能体现真实的地面信息。为此,从线性混合模型的特点出发,归纳了目前几种比较成熟的端元提取算法,分析了它们的主要思想和存在的优缺点,并总结了评估算法结果的依据,最后介绍了端元提取技术的发展趋势。     

A new volume formula for a simplex and its application to endmember extraction for hyperspectral image analysis

Based on the geometric properties of a simplex, endmembers can be extracted automatically from a hyperspectral image. To avoid the shortcomings of the N-FINDR algorithm, which requires the dimensions of the data to be one less than the number of endmembers needed, a new volume formula for the simplex without the requirement of dimension reduction is presented here. We demonstrate that the N-FINDR algorithm is a special case of the new method. Moreover, whether the null vector is included as an endmember has an important effect on the final result of the endmember extraction. Finally, we compare the new method with previous methods for endmember extraction of hyperspectral data collected by the Advanced Visible and Infrared Imaging Spectrometer (AVIRIS) over Cuprite, Nevada.     

基于粒子群优化的高光谱影像端元提取算法

回顾了粒子群算法的基本原理,分析了端元提取算法的两种技术途径。利用粒子群优化的原理,结合凸面几何学理论和线性光谱混合模型,设计了一种粒子群优化端元提取算法,并设计了算法的快速实现方法。该算法不需要假设影像中存在纯像元,同时保持了端元光谱的形状。利用模拟数据和AVIRIS影像对该算法、SGA算法和NMF算法进行实验对比分析,实验结果证明该算法的端元提取精度优于其他二者。     

基于光谱信息散度与光谱角匹配的高光谱解混算法

针对采用线性逆卷积(LD)算法进行端元初选过程中,端元子集中存在相似端元光谱,影响解混精度的问题,提出了一种基于光谱信息散度(SID)与光谱角匹配(SAM)算法的端元子集优选光谱解混算法。通过在端元进行二次选择时,采用以光谱信息散度和光谱角(SID-SA)混合法准则作为最相似端元选择的判据,去除相似端元,降低相似端元对解混精度的影响。实验结果表明,基于SID与SAM的高光谱解混算法将重构影像的均方根误差(RMSE)降低到0.0104,该方法比传统方法提高了端元的选择精度,减少了丰度估计误差,误差分布更加均匀。     

粒子群空间优化的端元提取算法

粒子群优化算法（Particle Swarm Optimization,PSO）应用于高光谱影像端元提取时,由于影像中存在端元的像元数所占比例极小且分布零散,导致粒子群的搜索空间破碎,存在收敛性能低、容易陷入局部最优解等缺陷。对粒子群的搜索空间进行优化,选择影像中纯净像元指数（Pixel Purity Index,PPI）较大的像元作为预选像元,然后对预选像元进行光谱聚类排序,将排序后的集合作为粒子群的搜索空间,优化了粒子的搜索空间。并在迭代过程中,充分利用粒子群的信息自适应地调整其系数,在缩小原始图像与反演图像的误差同时,增加体积约束,在提取端元时更好地保持其原有的形状。通过模拟数据和AVIRIS影像的实验表明该算法具有较好端元提取效果。     

基于RM S 误差分析的高光谱图像自动端元提取算法

提出了一种基于RM S ( root mean square) 误差分析的自动端元提取算法。对图像每做一次线性解混合, 就得到一幅以均方根RMS误差表示的残余误差图像, 从中选出误差较大的像素作为新的端元开始下一次解混合, 通过多次迭代, 直到得到了要求数目的端元。该算法克服了以往端元提取方法监督特性的局限, 减少了对先验信息的依赖, 同时保留了图像中的异常。利用仿真和实验数据验证了该算法的有效性。     

Integration of spatial-spectral information for the improved extraction of endmembers

Spectral-based image endmember extraction methods hinge on the ability to discriminate between pixels based on spectral characteristics alone. Endmembers with distinct spectral features (high spectral contrast) are easy to select, whereas those with minimal unique spectral information (low spectral contrast) are more problematic. Spectral contrast, however, is dependent on the endmember assemblage, such that as the assemblage changes so does the “relative” spectral contrast of each endmember to all other endmembers. It is then possible for an endmember to have low spectral contrast with respect to the full image, but have high spectral contrast within a subset of the image. The spatial-spectral endmember extraction tool (SSEE) works by analyzing a scene in parts (subsets), such that we increase the spectral contrast of low contrast endmembers, thus improving the potential for these endmembers to be selected. The SSEE method comprises three main steps: 1) application of singular value decomposition (SVD) to determine a set of basis vectors that describe most of the spectral variance for subsets of the image; 2) projection of the full image data set onto the locally defined basis vectors to determine a set of candidate endmember pixels; and, 3) imposing spatial constraints for averaging spectrally similar endmembers, allowing for separation of endmembers that are spectrally similar, but spatially independent. The SSEE method is applied to two real hyperspectral data sets to demonstrate the effects of imposing spatial constraints on the selection of endmembers. The results show that the SSEE method is an effective approach to extracting image endmembers. Specific improvements include the extraction of physically meaningful, low contrast endmembers that occupy unique image regions.     

On Endmember Identification in Hyperspectral Images Without Pure Pixels: A Comparison of Algorithms

Hyperspectral imaging is an active area of research in Earth and planetary observation. One of the most important techniques for analyzing hyperspectral images is spectral unmixing, in which mixed pixels (resulting from insufficient spatial resolution of the imaging sensor) are decomposed into a collection of spectrally pure constituent spectra, called endmembers weighted by their correspondent fractions, or abundances. Over the last years, several algorithms have been developed for automatic endmember extraction. Many of them assume that the images contain at least one pure spectral signature for each distinct material. However, this assumption is usually not valid due to spatial resolution, mixing phenomena, and other considerations. A?recent trend in the hyperspectral imaging community is to design endmember identification algorithms which do not assume the presence of pure pixels. Despite the proliferation of this kind of algorithms, many of which are based on minimum enclosing simplex concepts, a rigorous quantitative and comparative assessment is not yet available. In this paper, we provide a comparative analysis of endmember extraction algorithms without the pure pixel assumption. In our experiments we use synthetic hyperspectral data sets (constructed using fractals) and real hyperspectral scenes collected by NASA’s Jet Propulsion Laboratory.     

Implementation and evaluation distributed mixed pixels analysis algorithm for hyperspectral image based on constraint non-negative matrix factorization

As an effective blind source separation method, non-negative matrix factorization has been widely adopted to analyze mixed data in hyperspectral images. To avoid trapping in local optimum, appropriate constraints are added to the objective function of NMF, whose reflections of image essential attribute determine the performance finally. In this paper, a new NMF-based mixed data analysis algorithm is presented, with maximum overall coverage constraint introduced in traditional NMF. The new constraint was proposed using data geometrical properties in the feature space to maximizes the number of pixels contained in the simplex constructed by endmembers compulsorily and introduced in objective function of NMF, named maximum overall coverage constraint NMF (MOCC-NMF), to analyze mixed data in highly mixed hyperspectral data without pure pixels. For implementing easily, multiplicative update rules are applied to avoid step size selection problem occurred in traditional gradient-based optimization algorithm frequently. Furthermore, in order to handle huge computation involved, parallelism implementation of the proposed algorithm using MapReduce is described and the new partitioning strategy to obtain matrix multiplication and determinant value is discussed in detail. In the numerical experiments conducted on real hyperspectral and synthetic datasets of different sizes, the efficiency and scalability of the proposed algorithm are confirmed.     

一种端元可变的混合像元分解方法

混合像元线性分解是高光谱影像处理的常用方法，它使用相同的端元矩阵对像元进行分解，其结果是分解精度不高。为此提出了一种端元可变的混合像元分解方法，在确定端元矩阵时，首先考察混合像元与端元的光谱相似性，结合地物空间分布特点，实现了可变端元的混合像元分解。试验结果表明，该分解方法分解精度优于传统线性模型，符合实际情况。     

基于异常探测的高光谱端元提取方法研究

端元提取是高光谱影像分析重要且具有挑战性的任务,是解决高光谱图像混合像元分解关键的步骤。现行的高光谱端元提取算法在端元提取过程中,异常像元同时加入到端元数组中,如何有效区分异常与端元,成为高光谱遥感端元提取的瓶颈,也是提高高光谱图像混合像元分解精度的关键因素。提出一种基于异常探测的高光谱端元提取方法,首先利用RX算法对原始影像进行异常探测,根据异常探测的结果剔除一定数量的像元,将剔除的像元用原始图像均值向量替代,再对影像进行正交子空间投影(OSP)提取端元。实验表明,该方法能够有效区分异常与端元,抑制异常像元参与端元提取,同时处理后的图像端元提取的结果受异常处理的影响很小,证明了去除异常信息后提取端元的可行性。     

A new non-negative matrix factorization method based on barycentric coordinates for endmember extraction in hyperspectral remote sensing

In this study, we present a new non-negative matrix factorization (NMF) method using the pixel's barycentric coordinates for endmember extraction, named BC-NMF. Our method applies the geometrical property of simplex in the calculation of abundance fraction. That is, for any pixel in an image, its abundance fractions are its barycentric coordinates within the endmember coordinate system. Experiments using both simulated and real hyperspectral images show that BC-NMF can generate endmembers with higher accuracy and lower computational complexity than NMF.     

基于改进SAM的高光谱影像混合像元分解算法研究

将传统遥感图像分类方法中的光谱角度制图法(Spectral Angle Mapping-SAM)加以变换,改进为一种符合全约束条件下的高光谱遥感图像的混合像元分解模型.新算法在端元丰度比例满足全约束的条件下,通过逼近的方法寻找一种端元丰度的比例组合,使测试光谱与目标光谱的广义夹角最小,从而认为该比例组合就是混合像元分解...     

利用稳健非负矩阵分解实现无监督高光谱解混

目的 基于非负矩阵分解的高光谱图像无监督解混算法普遍存在着目标函数对噪声敏感、在低信噪比条件下端元提取和丰度估计性能不佳的缺点。因此,提出一种基于稳健非负矩阵分解的高光谱图像混合像元分解算法。方法 首先在传统基于非负矩阵分解的解混算法基础上,对目标函数加以改进,用更加稳健的L₁范数作为重建误差项,提高算法对噪声的适应能力,得到新的无监督解混目标函数。针对新目标函数的非凸特性,利用梯度下降法对端元矩阵和丰度矩阵交替迭代求解,进而完成优化求解,得到端元和丰度估计值。结果 分别利用模拟和真实高光谱数据,对算法性能进行定性和定量分析。在模拟数据集中,将本文算法与具有代表性的5种无监督解混算法进行比较,相比于对比算法中最优者,本文算法在典型信噪比20 dB下,光谱角距离（spectral angle distance,SAD）增大了10.5%,信号重构误差（signal to reconstruction error,SRE）减小了9.3%;在真实数据集中,利用光谱库中的地物光谱特征验证本文算法端元提取质量,并利用真实地物分布定性分析丰度估计结果。结论 提出的基于稳健非负矩阵分解的高光谱无监督解混算法,在低信噪比条件下,能够获得较好的端元提取和丰度估计精度,解混效果更好。     

基于自组织映射和模糊隶属度的混合像元分解

遥感图像中普遍存在着混合像元,将混合像元分解为端元和它们之间混合的丰度,对于高精度的地物识别和定量遥感具有重要意义.结合自组织映射神经网络和模糊理论中的模糊隶属度,提出一种新的多光谱和高光谱遥感图像混合像元分解的方法.首先对自组织映射神经网络进行有监督的训练,然后基于模糊模型对混合像元进行分解.其分解结果自动满足混合像元分解问题所要求的2个约束:丰度值非负约束及丰度值和为1约束.实验结果表明,该方法不仅适用于线性光谱混合的情况,也适用于非线性光谱混合的情况,能够获得较好的混合像元分解结果,同时具有较强的抗噪声能力.     

Modified N-FINDR endmember extraction algorithm for remote-sensing imagery

The N-FINDR, developed by Winter, is one of the most widely used algorithms for endmember extraction for hyperspectral images. N-FINDR usually needs an outer loop to control the stopping rule and two inner loops for pixel replacement, so it suffers from computational inefficiency, particularly when the size of the remote-sensing image is large. Recently, geometric unmixing using a barycentric coordinate has become a popular research field in hyperspectral remote sensing. According to Cramer’s rule, a barycentric coordinate estimated by the ratios of simplex volumes is equivalent to a least-squares solution of a linear mixture model. This property implies a brand new strategy for endmember extraction. In other words, we can deduce endmembers by comparison only of abundances derived from a least-squares approach rather than a complicated volume comparison in N-FINDR. Theoretical analysis shows that the proposed method has the same performance as N-FINDR but with much lower computational complexity. In the experiment using real hyperspectral data, our method outperforms several other N-FINDR-based methods in terms of computing times.