一种基于协同稀疏和全变差的高光谱线性解混方法

稀疏分解是高光谱图像（Hyperspectral image,HSI）解混中的常用方法,为了克服传统稀疏解混方法只重视挖掘空间相关性而忽视稀疏性精确刻画的缺点,本文提出一种新的基于协同稀疏和全变差（Total variation,TV）相结合的高光谱空谱联合线性解混方法,从而进一步提高解混的精度.该方法基于已知光谱库的高光谱稀疏线性回归模型,利用TV正则项对高光谱邻域像元间的相关性进行约束;同时,协同稀疏性被用来刻画丰度系数的行稀疏性,从而表明协同稀疏先验对空谱联合解混精度的提高至关重要;最后采用交替方向乘子法求解模型.模拟高光谱数据实验结果定量地验证本文方法能够比现有同类方法获得更精确的解混结果,同时真实高光谱数据实验结果定性地验证了本文方法的有效性.     

单形体体积最小化的差分进化光谱解混算法

目的 光谱解混是高光谱遥感图像处理的核心技术。当图像不满足纯像元假设条件时,传统算法难以适用,基于(单形体)体积最小化方法提供了一种有效的解决途径。然而这是一个复杂的约束最优化问题,更由于图像噪声等不确定性因素的存在,导致算法容易陷入局部解。方法 引入一种群智能优化技术-差分进化算法(DE),借助其较强的全局搜索能力以及优越的处理高维度问题的能力,并通过对问题编码,提出了一种体积最小化的差分进化(VolMin-DE)光谱解混算法。结果 模拟数据和真实数据实验的结果表明,与现有算法相比,该算法在15端元时精度(光谱角距离)可提高7.8%,当端元数目少于15个时,其精度普遍可以提高15%以上,特别是10端元时精度可以提高41.3%;在20~50 dB的噪声范围内,精度变化在1.9~3.2(单位:角度)之间,传统算法在2.2~3.5之间,表明该算法具有相对较好的噪声鲁棒性。结论 本文算法适用于具有纯像元以及不存在纯像元(建议最大纯度不低于0.8)这两种情况的高光谱遥感图像,并可在原始光谱维度进行光谱解混,从而避免降维所带来的累计误差,因此具有更好的适应范围和应用前景。     

Efficient sparse unmixing analysis for hyperspectral imagery based on random projection

Hyperspectral imagery including rich spectral information could be applied to detect and identify objects at a distance. In this paper, we concentrate on the surface material identification of interested objects within the domain of space object identification (SOI) and geological survey. One of the approaches is the unmixing analysis that identifies the components (called endmembers) in each pixel and estimates their corresponding fractional abundances, and then, we could obtain the space distributions of substances. To solve this problem, we present an approach in a semi-supervised fashion, by assuming that the measured spectrum is expressed in the form of linear combination of a number of pure spectral signatures in a spectral library and the fractional abundances are their weights. Thus, the abundances are sparse and we propose a sparse regression model to realize the sparse unmixing analysis. We apply random projection technique to accelerate the sparse unmixing process and use split Bregman iteration to optimize the objective function. Our algorithm is tested and compared with other classic algorithms by using simulated hyperspectral images and a real-world image.     

基于差分搜索的高光谱图像解混算法

针对高光谱图像解混问题进行研究,发现高光谱图像中各个端元的分布不完全独立,不能将盲源分离方法直接应用于高光谱图像解混。为此,提出了一种基于差分搜索的高光谱图像解混算法。该算法根据高光谱图像丰度非负和丰度和为一特性构造相应的约束项,与互信息相结合作为目标函数,利用差分搜索算法对该目标函数进行优化求解来实现高光谱图像解混。仿真数据和实际数据实验表明,该算法能够有效解决高光谱图像解混问题,与已有其它算法相比,提高了图像解混的精度,并且针对不含纯像元的高光谱图像具有很好的解混效果。     

基于光谱距离聚类的高光谱图像解混算法

为了解决实际高光谱解混（HU）中噪声对解混精度的影响和光谱、空间信息利用不足的问题,提出了一种改进的基于光谱距离聚类的群稀疏非负矩阵分解的解混算法。首先,引入了基于最小误差的高光谱信号辨识算法（Hysime）,通过计算特征值的方式估计信号矩阵和噪声矩阵;然后,提出了一种简单的基于光谱距离的聚类算法,对多个波段生成的光谱反射率距离值小于某一值的相邻像元进行合并聚类生成空间群结构;最后,在生成的群结构基础上进行稀疏化非负矩阵分解。实验分析表明,对于模拟数据和实际数据而言,该算法都比传统算法产生更小的均方根误差（RMSE）和光谱角距离（SAD）,能够产生优于同类算法的解混效果。     

Spatial-Spectral Preprocessing based on Nonnegative Matrix Factorization to Unmix Hyperspectral Data

Non-negative Matrix Factorization (NMF)method of blind spectral unmixing can obtain the spectrum and abundance of the endmember by synchronous optimization,without supervising the selection of endmember.Therefore,NMF has been developed rapidly in the application of hyperspectral unmixing.However,traditional blind spectral unmixing NMF method tends to fall into the local optimum and it is difficult to obtain a stable optimal solution.In this paper,we propose an improved Non-negative Matrix Factorization (NMF)method based on Spatial\|Spectal Preprocessing for spectral unmixing of hyperspectral data (SSPP-NMF).First,the SSPP algorithm is used to combine spatial and spectral information to select reasonable and effective dataset.Then,the NMF algorithm is used to unmix this dataset to obtain the final optimized endmember spectrum.Finally,the Non\|Negative Least Squares (NNLS)method is used to obtain the final abundance of the whole study area.The validity and applicability of the proposed method were analyzed based on a set of synthetic hyperspectral data and real hyperspectral images;and then the results were compared with that from three algorithms including the existing NMF algorithm,MVC\|NMF algorithm and ATGP-NMF algorithm.Results show that compared with ATGP-NMF and MVC-NMF,the SSPP algorithm can effectively suppress the influence of noise,significantly improve the performance of the NMF method of blind spectral unmixing algorithm.     

基于ANN端元估计的高光谱图像解混算法

针对高光谱图像解混问题进行研究,发现传统解混算法在保持端元数目不变的情况下,得到的解混精度不高。为此,基于人工神经网络（ANN）提出一种估计单像素点中端元数目和类别的解混算法。首先利用人工神经网络对遥感图像中各个像素的端元数目和类别进行估计;之后依据估计结果确定解混算法的目标函数,并引入改进的差分搜索算法对目标函数进行优化求解;最终获取地物丰度和待求参数,实现高光谱图像的解混。仿真数据和真实遥感数据实验表明,与现有的解混算法相比,所提解混算法具有更高的解混性能,更加符合实际场景的情况。     

基于Hessian图正则稀疏NMF的高光谱解混

基于非负矩阵分解(Nonnegative Matrix Factorization, NMF)的高光谱解混(Hyperspectral Unmixing,HU)方法引起了大家的关注,因为可以将一个非负高光谱图像(Hyperspectral Imagery, HSI)数据矩阵分解为两个非负矩阵的乘积,分别对应于端元矩阵和丰度系数矩阵。目前,图约束的NMF算法已经被证明对高光谱解混是有效的,因为它们可以捕获HSI的几何特性。为了挖掘数据在混合过程中的几何结构和稀疏性,提出了一种稀疏的Hessian图正则化NMF(SHGNMF)算法。SHGNMF算法是将丰度矩阵的L1/2正则化器和Hessian图正则化项都添加到每个NMF模型中,同时采用乘法更新规则。最后用模拟数据和真实数据进行实验,验证了所提出的SHGNMF算法相对于其他NMF算法的优越性。     

Unmixing-based content retrieval system for remotely sensed hyperspectral imagery on GPUs

This paper presents a new unmixing-based retrieval system for remotely sensed hyperspectral imagery. The need for this kind of system is justified by the exponential growth in the volume and number of remotely sensed data sets from the surface of the Earth. This is particularly the case for hyperspectral images, which comprise hundreds of spectral bands at different (almost contiguous) wavelength channels. To deal with the high computational cost of extracting the spectral information needed to catalog new hyperspectral images in our system, we resort to efficient implementations of spectral unmixing algorithms on commodity graphics processing units (GPUs). Spectral unmixing is a very popular approach for interpreting hyperspectral data with sub-pixel precision. This paper particularly focuses on the design of the proposed framework as a web service, as well as on the efficient implementation of the system on GPUs. In addition, we present a comparison of spectral unmixing algorithms available in the system on both CPU and GPU architectures.     

A comparative study of signal transformation techniques in automated spectral unmixing of infrared spectra for remote sensing applications

From geological and planetary exploration perspectives, automated sub-pixel classification of hyperspectral data is the most difficult task as it involves blind unmixing with library spectra of minerals. In this study, we demonstrate a procedure involving spectral transformation and linear unmixing to achieve the above task. For this purpose, infrared spectra of rocks from the spectral library, field, and remotely sensed hyperspectral image cube were used. Potential spectra of minerals for unmixing rock spectra were drawn from the library based on similarity of absorption features measured using Pearson correlation coefficient. Eight transformation techniques namely, first derivative, fast Fourier transform, discrete wavelet transform, Hilbert–Huang transform, crude low pass filter, S-transform, binary encoding, spectral effective peak matching, and two sparsity-based techniques (orthogonal matching pursuit, sparse unmixing via variable splitting, and augmented Lagrangian) were evaluated. Subsequently, minerals identified by above techniques were unmixed by linear mixture model (LMM) to decipher mineralogical composition and abundance. Results of LMM achieved using fully constrained least-square-estimation-based quadratic programming optimization approach were evaluated by conventional procedures such as X-ray diffraction and microscopy. In the case of image cube, endmembers derived using minimum noise fraction and pixel purity index were subjected to above procedure. It is evident that the discrete-wavelet-transformation-based approach produced excellent and meaningful results due to its flexibility in scaling the data and capability to handle noisy spectra. It is interesting to note that the adopted procedure could perform sub-pixel classification of image cube automatically and identify predominance of dolomite in limestone and sodium in alunite based on subtle differences in absorption positions.     

嵌入式深度神经网络高光谱图像聚类

目的 高光谱图像的高维特性和非线性结构给聚类任务带来了"维数灾难"和线性不可分问题，以往的工作将特征提取过程与聚类过程互相剥离，难以同时优化。为了解决上述问题，提出了一种新的嵌入式深度神经网络模糊C均值聚类方法（EDFCC）。方法 EDFCC算法为了提取更加有效的深层特征，联合优化高光谱图像的特征提取和聚类过程，将模糊C均值聚类算法嵌入至深度自编码器网络中，可以保持两任务联合优化的优势，同时利用深度自编码器网络降维以及逼近任意非线性函数的能力，逐步将原始数据映射到潜在特征空间，提取数据的深层特征。所提方法采用模糊C均值聚类算法约束特征提取过程，学习适用于聚类的高光谱数据深层特征，动态调整聚类指示矩阵。结果 实验结果表明，EDFCC算法在Indian Pines和Pavia University两个高光谱数据集上的聚类精度分别达到了42.95%和60.59%，与当前流行的低秩子空间聚类算法（LRSC）相比分别提高了3%和4%，相比于基于自编码器的数据聚类算法（AEKM）分别提高了2%和3%。结论 EDFCC算法能够从高光谱图像的高维光谱信息中提取更加有效的深层特征，提升聚类精度，并且由于EDFCC算法不需要额外的训练过程，大大提升了聚类效率。     

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。     

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。     

A novel l 1/2 sparse regression method for hyperspectral unmixing

Hyperspectral unmixing (HU) is a popular tool in remotely sensed hyperspectral data interpretation, and it is used to estimate the number of reference spectra (end-members), their spectral signatures, and their fractional abundances. However, it can also be assumed that the observed image signatures can be expressed in the form of linear combinations of a large number of pure spectral signatures known in advance (e.g. spectra collected on the ground by a field spectro-radiometer, called a spectral library). Under this assumption, the solution of the fractional abundances of each spectrum can be seen as sparse, and the HU problem can be modelled as a constrained sparse regression (CSR) problem used to compute the fractional abundances in a sparse (i.e. with a small number of terms) linear mixture of spectra, selected from large libraries. In this article, we use the l _1/2 regularizer with the properties of unbiasedness and sparsity to enforce the sparsity of the fractional abundances instead of the l ₀ and l ₁ regularizers in CSR unmixing models, as the l _1/2 regularizer is much easier to be solved than the l ₀ regularizer and has stronger sparsity than the l ₁ regularizer (Xu et al. 2010). A reweighted iterative algorithm is introduced to convert the l _1/2 problem into the l ₁ problem; we then use the Split Bregman iterative algorithm to solve this reweighted l ₁ problem by a linear transformation. The experiments on simulated and real data both show that the l _1/2 regularized sparse regression method is effective and accurate on linear hyperspectral unmixing.     

高光谱图像非线性解混方法的研究进展

由于空间分辨率的限制,高光谱遥感图像中存在大量混合像元,对混合像元的解混是实现地物精确分类和识别的前提。与传统的线性解混方法相比,非线性解混方法在寻找组成混合像元的端元以及每个端元的丰度时具有较高的精度。分析了光谱非线性混合的原理,总结了近年来提出的非线性解混算法,重点对双线性模型、神经网络、基于核函数的非线性解混算法以及基于流形学习的非线性解混算法进行了介绍和分析。最后总结了混合像元非线性解混未来发展的趋势。     

Spectral clustering with fuzzy similarity measure

Spectral clustering algorithms have been successfully used in the field of pattern recognition and computer vision. The widely used similarity measure for spectral clustering is Gaussian kernel function which measures the similarity between data points. However, it is difficult for spectral clustering to choose the suitable scaling parameter in Gaussian kernel similarity measure. In this paper, utilizing the prototypes and partition matrix obtained by fuzzy c-means clustering algorithm, we develop a fuzzy similarity measure for spectral clustering (FSSC). Furthermore, we introduce the K-nearest neighbor sparse strategy into FSSC and apply the sparse FSSC to texture image segmentation. In our experiments, we firstly perform some experiments on artificial data to verify the efficiency of the proposed fuzzy similarity measure. Then we analyze the parameters sensitivity of our method. Finally, we take self-tuning spectral clustering and Nyström methods for baseline comparisons, and apply these three methods to the synthetic texture and remote sensing image segmentation. The experimental results show that the proposed method is significantly effective and stable.     

基于超像素的流形正则化稀疏约束NMF混合像元分解算法

针对传统非负矩阵分解（NMF）法用于高光谱图像混合像元分解时产生的分解结果精度不高、对噪声敏感等问题，提出一种基于超像素的流形正则化稀疏约束NMF混合像元分解算法——MRS-NMF。首先，通过基于熵率的超像素分割来构造高光谱图像的流形结构，把原图像分割为k个超像素块并把每个超像素块中具有相似性质的数据点标上相同的标签，定义像素块内有相同标签的任意两个数据点之间的权重矩阵，然后将权重矩阵应用于NMF的目标函数中以构造出流形正则化约束项；第二，在目标函数中添加二次抛物线函数以完成稀疏约束；最后，采用乘法迭代更新法则求解目标函数以得到端元矩阵和丰度矩阵的求解公式，同时设置最大迭代次数和容忍误差阈值，迭代运算得到最终结果。该方法有效利用了高光谱图像的光谱和空间信息。实验结果表明，在模拟的高光谱数据中，与传统的流形稀疏约束的非负矩阵分解（GLNMF）、L1/2-NMF和顶点成分分析-全约束最小二乘法（VCA-FCLS）等方法相比，MRS-NMF可以提高0.016~0.063的端元分解精度和0.01~0.05的丰度分解精度；而在真实的高光谱图像中，MRS-NMF较传统的GLNMF、顶点成分分析法（VCA）、最小体积约束的非负矩阵分解（MVCNMF）等方法可以平均提高0.001~0.0437的端元分解精度。所提MRS-NMF算法有效地提高了混合像元分解的精度，同时具有较好的抗噪性能。     

结合空间光谱预处理和约束非负矩阵分解的高光谱图像混合像元分解

目的 混合像元问题在高光谱遥感图像处理分析中普遍存在,非负矩阵分解的方法被引入到高光谱图像解混中。本文提出结合空间光谱预处理和约束非负矩阵分解的混合像元分解流程。方法 结合空间光谱预处理的约束非负矩阵分解,如最小体积约束、流行约束等,通过加入邻域的空间和光谱信息进行预处理获得更优的预选端元,从而对非负矩阵分解的解混结果进行优化。结果 在5组不同信噪比的模拟数据实验中,空间预处理（SPP）和空间光谱预处理（SSPP）均能够有效提高约束非负矩阵分解（最小体积约束的非负矩阵分解和图正则非负矩阵分解）的解混结果,其中SPP在不同信噪比的情况下都能优化约束非负矩阵分解的结果,而SSPP在低信噪比的情况下,预处理效果更佳。利用美国内华达州Cuprite矿区数据进行真实数据实验,SPP提高了约束非负矩阵分解的解混精度,而SSPP在复杂场景下,解混精度更佳。模拟数据和真实数据的实验均表明,空间光谱预处理能够有效地提高约束非负矩阵分解的解混精度,特别是对于信噪比较低的情况下,融合空间和光谱信息对噪声有很好的鲁棒性。结论 本文对约束非负矩阵分解的解混算法添加空间光谱预处理,利用高光谱遥感数据的空间和光谱信息,优化预选端元,加入空间光谱预处理的非负矩阵解混实验流程,在复杂场景情况下,对噪声具有较好的鲁棒性。     

Hyperspectral unmixing employing l1−l2 sparsity and total variation regularization

ABSTRACT

Hyperspectral unmixing is essential for image analysis and quantitative applications. To further improve the accuracy of hyperspectral unmixing, we propose a novel linear hyperspectral unmixing method based on l₁?l₂ sparsity and total variation (TV) regularization. First, the enhanced sparsity based on the l₁?l₂ norm is explored to depict the intrinsic sparse characteristic of the fractional abundances in a sparse regression unmixing model because the l₁?l₂ norm promotes stronger sparsity than the l₁ norm. Then, TV is minimized to enforce the spatial smoothness by considering the spatial correlation between neighbouring pixels. Finally, the extended alternating direction method of multipliers (ADMM) is utilized to solve the proposed model. Experimental results on simulated and real hyperspectral datasets show that the proposed method outperforms several state-of-the-art unmixing methods.     

基于稀疏和正交约束非负矩阵分解的高光谱解混

针对基于非负矩阵分解（NMF）的高光谱解混存在的容易陷入局部极小值和受初始值影响较大的问题，提出一种稀疏和正交约束相结合的NMF的线性解混算法SONMF。首先，从传统的基于NMF的高光谱线性解混方法出发，分析高光谱数据本身的理化特性；然后，结合丰度的稀疏性和端元的独立性两个方面，将稀疏非负矩阵分解（SNMF）和正交非负矩阵分解（ONMF）两种方法结合应用到高光谱解混当中。模拟数据和真实数据实验表明，相比顶点成分分析法（VCA）、SNMF和ONMF这三种参考解混算法，所提算法提高了线性解混的性能；其中，评价指标光谱角距离（SAD）降低了0.012~0.145。SONMF能够结合两种约束条件的优势，弥补传统基于NMF线性解混方法对高光谱数据表达的不足，取得较好的效果。