Set Of Endmembers Research Articles

Frost Damage Assessment in Wheat Using Spectral Mixture Analysis

Frost damage to broadacre crops can cause up to an 85% loss in productivity. Although growers have few options for crop protection from frost, a rapid method for assessing frost-induced sterility would allow for timely management decisions (e.g., cutting for hay and altering marketing strategies). Spectral mixture analysis (SMA) has shown success in mapping landscape components and was used with hyperspectral data collected on the canopy, heads, and leaves of wheat at different sites to determine if this could quantify frost damage. Spectral libraries were assembled from canopy components collected from local field sites to generate spectral libraries for SMA from which a series of fraction sets was derived. The frost (Fr) fraction was then used to estimate final yield as a means of measuring frost damage. The best-fitting Fr fractions to yield were derived from the same data set as the source Fr spectra, and these ranged over R2 = 0.58–0.75 at the canopy scale. It was clear that spectral signatures need to be collected at scale to assess frost damage. While Fr fractions were able to estimate yield there was no “universal” endmember set from which a Fr fraction could be derived. The normalized difference vegetation index (NDVI) was not able to estimate frost damage consistently. Future work requires determining whether there is a “universal” set of endmembers and a minimum set of targeted wavebands that could lead to multispectral instruments for frost assessment for use in ground and aerial sensors.

Incorporating band selection in the spatial selection of spectral endmembers

The impact of band selection on endmember selection is seldom explored in the analysis of hyperspectral imagery. This study incorporates the N-dimensional Spectral Solid Angle (NSSA) band selection tool into the Spectral-Spatial Endmember Extraction (SSEE) tool to determine a band set that can be used to better define endmembers classes used in spectral mixture analysis. The incorporation aims to define a band set that improves the spectral contrast between endmembers at each step of the spatial-spectral endmember search and ultimately captures key features for discriminating spectrally similar materials. The proposed method (NSSA-SSEE) was evaluated for lithological mapping using a hyperspectral image encompassing a range of spectrally similar mafic and ultramafic rock units. The band selected by NSSA-SSEE showed a good agreement with known features of scene components identified by experts. Results showed an improvement in the selection of detailed endmembers, endmembers that are similar and that can be significant for mapping. The incorporation of NSSA into SSEE was feasible because both methods are well suited for this process. NSSA is one of the few methods of band selection that is suitable for the analysis of a small number of endmembers and SSEE provides such endmember sets via spatial subsetting. The automated NSSA-SSEE approach can reduce the need for field-based information to guide the feature selection process.

Optimal Endmember-Based Super-Resolution Land Cover Mapping

Super-resolution mapping (SRM) aims to determine the spatial distribution of the land cover classes contained in the area represented by mixed pixels to obtain a more appropriate and accurate map at a finer spatial resolution than the input remotely sensed image. The image-based SRM models directly use the observed images as input and can mitigate the uncertainty caused by class fraction errors. However, existing image-based SRM models always adopt a fixed set of endmembers used in the entire image, ignoring the spatial variability and spectral uncertainty of endmembers. To address this problem, this letter proposed an optimal endmember-based SRM (OESRM) model, which considers the spatial variations in endmembers, and determines the best-fit one for each coarse resolution pixel using the spectral angle and the spectral distance as the spectral similarity indexes. A Sentinel-2A and a Landsat-8 multispectral images were used to analyze the performance of OESRM, by comparing with three other SRM methods which adopt a fixed endmember set or multiple endmember sets. The results showed that OESRM generated resultant land cover maps with more spatial detail, and reduced the confusion between land cover classes with similar spectral features. The proposed OESRM model produced the results with the highest overall accuracy in both experiments, showing its effectiveness in reducing the effect of endmember uncertainty on SRM.

Covariance Similarity Approach for Semiblind Unmixing of Hyperspectral Image

Hyperspectral sparse unmixing methods estimate abundance of endmembers, assuming spectral library as an overcomplete set of endmembers. In this letter, we present a novel, fast and efficient dictionary pruning approach for hyperspectral unmixing. We quantify the change in the latent structure of data due to augmentation of spectral library element using covariance similarity measure. Since the covariance matrices form a nonlinear manifold, choosing an appropriate similarity measure is a nontrivial task. We explored prevalent similarity measures, which motivated us to employ Jeffrey’s Kullback–Leibler divergence measure due to its tighter bounds and better noise performance. We also present analytical formulations for faster implementation of covariance similarity. We evaluate the performance of dictionary pruning algorithms on several synthetic and real hyperspectral images and demonstrate the proficiency of our proposed work in diverse scenarios.

Snow Cover Estimation From Image Time Series Based on Spectral Unmixing

A method based on spectral unmixing (SU) for snow cover estimation from a time series of optical images is proposed in this letter. Specifically, we have developed an endmember estimation procedure that exploits the temporal continuity of a scene. Consecutive dates are jointly processed for a more precise description of background materials improving the estimation of a fractional snow cover map. The proposed workflow relies on up to three consecutive acquisitions over the same area to extract an appropriate set of background spectra to be considered as endmembers. In greater details, multiple sets of endmembers are extracted from different images in the time series by a geometrical automated endmember extraction algorithm and the most relevant one is selected in terms of reconstruction error. Snow cover maps are then estimated by SU considering as endmembers the snow spectra coming from a spectral library and those associated with the background materials as estimated by the proposed procedure. The proposed technique is quantitatively validated considering Moderate-Resolution Imaging Spectroradiometer Terra data over the French Alps and Moroccan High Atlas image time series and comparing the estimated snow cover maps with high-resolution reference data. The experiment clearly demonstrates the effectiveness of the generated set of endmembers using three different approaches to abundance estimation.

Hyperspectral unmixing using double-constrained multilayer NMF

ABSTRACTHyperspectral unmixing (HU) refers to the process decomposing the entire hyperspectral image into a set of endmembers and the corresponding abundance fractions. Nonnegative matrix factorization (NMF) has been widely used in HU due to its simplicity and effectiveness. Many extensions of NMF have been also developed since traditional NMF has a large solution space. On the other hand, the multilayer structure has shown great advantages in learning data representation. Inspired by these considerations, we added sparsity and geometric structure constraints to the multilayer NMF structure and proposed a double-constrained multilayer NMF (DCMLNMF) method for HU in this paper. The multilayer NMF structure was obtained by iteratively decomposing the target matrix into a number of layers. To improve the unmixing performance, a sparsity constraint term on the abundance matrix and a graph regularization term were both incorporated to each layer. Besides, a layer-wise optimization method based on Nesterov’s optimal gradient method was further proposed to solve the multi-factor NMF problem. Experimental results based on both synthetic data and real data demonstrate that the proposed method outperforms several other state-of-art approaches.

N-PSO: endmember extraction using advance particle swarm optimization for NLMM

This paper presents a fully unsupervised endmember extraction technique for hyperspectral image unmixing using nonlinear mixing model. The underlying idea of the model is that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive noise. These nonlinear functions are approximated using polynomial functions, leading to a polynomial post-nonlinear mixing model (PPNM). In an unknown environment, the evaluation of the parameters involved in PPNM model is a tedious task, which is categorized as an NP hard problem. A method based on the combination of swarm intelligence, least-square (LS) and sub-gradient-based optimization (SO) is proposed to estimate the parameters involved in the model. The particle swarm optimization (PSO) is used to search the optimal endmember combination in the feasible solution space. The nonlinearity and respective abundances are evaluated using the LS and SO method, respectively. The proposed method is equipped with an adaptive tuning parameter-free mechanism and modified updating strategy. This strategy not only improves the result in terms of overall accuracy but also maintains physical constraints on the value of the resultant endmember set. The proposed method has been evaluated using simulated and real hyperspectral scenes. The experimental results on the hyperspectral scenes show that the proposed method obtains a higher extraction precision than those of the existing endmember extraction algorithms. Statistical analysis on a real hyperspectral image shows that the results obtain using N-PSO are 20–40% better than those from the existing approaches.

Fast Semi-Supervised Unmixing of Hyperspectral Image by Mutual Coherence Reduction and Recursive PCA

Dictionary pruning step is often employed prior to the sparse unmixing process to improve the performance of library aided unmixing. This paper presents a novel recursive PCA approach for dictionary pruning of linearly mixed hyperspectral data motivated by the low-rank structure of a linearly mixed hyperspectral image. Further, we propose a mutual coherence reduction method for pre-unmixing to enhance the performance of pruning. In the pruning step we, identify the actual image endmembers utilizing the low-rank constraint. We obtain an augmented version of the data by appending each image endmember and compute PCA reconstruction error, which is a convex surrogate of matrix rank. We identify the pruned library elements according to PCA reconstruction error ratio (PRER) and PCA reconstruction error difference (PRED) and employ a recursive formulation for repeated PCA computation. Our proposed formulation identifies the exact endmember set at an affordable computational requirement. Extensive simulated and real image experiments exhibit the efficacy of the proposed algorithm in terms of its accuracy, computational complexity and noise performance.

Evaluation of Unmixing Methods for Impervious Surface Area Extraction From Simulated EnMAP Imagery

Distribution of impervious surface area (ISA) is an important input in a wide range of urban ecosystem studies. The future launch of the German hyperspectral satellite environmental mapping and analysis program (EnMAP) in 2019 provides new opportunities for timely and global ISA extraction. The previously proposed EnMAP applications heavily relied on existing reference endmembers, which may be impractical on a global scale. To overcome this defect, we suggest to use the nonnegative matrix factorization (NMF) method to extract the endmember directly from EnMAP imagery. Three traditional unmixing method (e.g., N-Findr, pixel purity index, and independent component analysis) and four NMF-based methods with different constraints (e.g., sparseness, convex volume, and nonlinearity) were used to obtain series of endmember sets, ISA fraction, and classification maps. In results, the NMF-based methods outperformed the three traditional unmixing method, by achieving 0.5–0.6 R-squared values in the linear regression models between predicted and reference ISA percentages, and over 85% overall accuracy in ISA classification maps. We found that the NMF-based spectral unmixing methods are suitable to work with the EnMAP image, when reference endmember data are unavailable. In addition, we processed the widely used Hydice urban test image with the same methods and compared the resulting ISA percentage/classification maps with the EnMAP results, considering the different features of the Hydice and EnMAP sensors. In the results, it is proved that the EnMAP image has great potential in ISA mapping on a global scale, with reasonable overall accuracy and economical efficiency.

Linear spectral unmixing using endmember coexistence rules and spatial correlation

ABSTRACTMixed pixels are often formed when surface materials are smaller than the spatial resolution of a sensor, or two or more ground features fall within a pixel. Spectral unmixing, decomposing a mixed pixel into a set of endmembers and their corresponding abundance fractions, is an important method for extracting the underlying spectral and spatial information from remote sensing images. Recent studies have shown that it is difficult to increase the accuracy of unmixing using single pixel processing. Here, we suggest combining information on the fundamental interrelations of ground components and a priori knowledge on how ground components co-exist or exclude each other according to general geographic and geomorphic relations with spectral information may allow improved unmixing. Therefore, we propose a novel spectral unmixing method to estimate endmember abundances based on linear spectral mixing model with endmember coexistence rules and spatial correlation (LSMM-R&C). This method was implemented by incorporating endmember coexistence rules along with spatial correlation into a weighted least square method. Experiments with both synthetic and real satellite images were carried out to verify the proposed method, and its performance was also evaluated in comparison to the commonly used LSMM (linear spectral mixture method), LAU (local adaptive unmixing), ISU (iterative spectral unmixing) and ISMA (iterative spectral mixture analysis) methods. LSMM-R&C showed the smallest error, and was more effective at revealing the detailed spatial distribution of endmembers’ abundance, showing high potential for solving the problem of spatial heterogeneity among neighbouring pixels.

Unifying Concepts Linking Dissolved Organic Matter Composition to Persistence in Aquatic Ecosystems.

The link between composition and reactivity of dissolved organic matter (DOM) is central to understanding the role aquatic systems play in the global carbon cycle; yet, unifying concepts driving molecular composition have yet to be established. We characterized 37 DOM isolates from diverse aquatic ecosystems, including their stable and radiocarbon isotopes (δ13C-dissolved organic carbon (DOC) and Δ14C-DOC), optical properties (absorbance and fluorescence), and molecular composition (ultrahigh resolution mass spectrometry). Isolates encompassed end-members of allochthonous and autochthonous DOM from sites across the United States, the Pacific Ocean, and Antarctic lakes. Modern Δ14C-DOC and optical properties reflecting increased aromaticity, such as carbon specific UV absorbance at 254 nm (SUVA254), were directly related to polyphenolic and polycyclic aromatic compounds, whereas enriched δ13C-DOC and optical properties reflecting autochthonous end-members were positively correlated to more aliphatic compounds. Furthermore, the two sets of autochthonous end-members (Pacific Ocean and Antarctic lakes) exhibited distinct molecular composition due to differences in extent of degradation. Across all sites and end-members studied, we find a consistent shift in composition with aging, highlighting the persistence of certain biomolecules concurrent with degradation time.

A Gaussian Mixture Model Representation of Endmember Variability in Hyperspectral Unmixing

Hyperspectral unmixing while considering endmember variability is usually performed by the normal compositional model, where the endmembers for each pixel are assumed to be sampled from unimodal Gaussian distributions. However, in real applications, the distribution of a material is often not Gaussian. In this paper, we use Gaussian mixture models (GMM) to represent endmember variability. We show, given the GMM starting premise, that the distribution of the mixed pixel (under the linear mixing model) is also a GMM (and this is shown from two perspectives). The first perspective originates from random variable transformations and gives a conditional density function of the pixels given the abundances and GMM parameters. With proper smoothness and sparsity prior constraints on the abundances, the conditional density function leads to a standard maximum a posteriori (MAP ) problem which can be solved using generalized expectation maximization. The second perspective originates from marginalizing over the endmembers in the GMM, which provides us with a foundation to solve for the endmembers at each pixel. Hence, compared to the other distribution based methods, our model can not only estimate the abundances and distribution parameters, but also the distinct endmember set for each pixel. We tested the proposed GMM on several synthetic and real datasets, and showed its potential by comparing it to current popular methods.

Nonnegative Matrix Factorization With Data-Guided Constraints For Hyperspectral Unmixing

Hyperspectral unmixing aims to estimate a set of endmembers and corresponding abundances in pixels. Nonnegative matrix factorization (NMF) and its extensions with various constraints have been widely applied to hyperspectral unmixing. L 1 / 2 and L 2 regularizers can be added to NMF to enforce sparseness and evenness, respectively. In practice, a region in a hyperspectral image may possess different sparsity levels across locations. The problem remains as to how to impose constraints accordingly when the level of sparsity varies. We propose a novel nonnegative matrix factorization with data-guided constraints (DGC-NMF). The DGC-NMF imposes on the unknown abundance vector of each pixel with either an L 1 / 2 constraint or an L 2 constraint according to its estimated mixture level. Experiments on the synthetic data and real hyperspectral data validate the proposed algorithm.

Endmember search and proportion estimates from airborne hyperspectral surveys

ABSTRACTThe estimation of areas of land-cover elements is required for many natural resource management programmes and is also used by the mineral and petroleum resource communities either for detection of mineral abundances or monitoring of environmental remediation and other off-site impacts. When the identification of many constituent elements is desired, remote sensors that possess many spectral bands are often deployed, providing data that can be used in a spectroscopic (or other) analysis. At the size of a (remotely sensed) ground sample (represented as an image pixel), which with current technology is typically a few metres, the sample is heterogeneous and typically composed of several biological and geological constituents. It is of interest to first identify the constituent elements and their number and, second, to estimate their relative abundance. When no suitable spectral library is available for a particular data set, an exploratory approach using a blind unmixing method may be used to detect and estimate the endmembers themselves – an exploratory approach because there is no guarantee that the spectral endmembers fitted using blind unmixing will correspond to the ‘pure’ materials of interest to a particular application. Further, if employing a blind unmixing technique to each image in a large multi-image survey independently, there is no guarantee that compatible sets of endmembers will be found to produce maps that are seamless across contiguous images. The aim of this article is to examine the potential for applying blind unmixing at the whole-of-survey level as a way to finding endmembers and proportion maps that are cross-swath consistent and broadscale applicable. We demonstrate that a mosaic of many radiometrically block-adjusted swaths of data from the HyMap airborne hyperspectral imager (HyVista Corporation) can be unmixed as a single image using the Iterated Constrained Endmembers blind unmixing algorithm. The major endmembers are validated against available Analytical Spectral Devices ground spectra and broadscale abundance maps of the type targeted by both vegetation and soil mapping communities are produced.

A Stepwise Analytical Projected Gradient Descent Search for Hyperspectral Unmixing and Its Code Vectorization

We present, in this paper, a new methodology for spectral unmixing, where a vector of fractions, corresponding to a set of endmembers (EMs), is estimated for each pixel in the image. The process first provides an initial estimate of the fraction vector, followed by an iterative procedure that converges to an optimal solution. Specifically, projected gradient descent (PGD) optimization is applied to (a variant of) the spectral angle mapper objective function, so as to significantly reduce the estimation error due to amplitude (i.e., magnitude) variations in EM spectra, caused by the illumination change effect. To improve the computational efficiency of our method over a commonly used gradient descent technique, we have analytically derived the objective function’s gradient and the optimal step size (used in each iteration). To gain further improvement, we have implemented our unmixing module via code vectorization, where the entire process is “folded” into a single loop, and the fractions for all of the pixels are solved simultaneously. We call this new parallel scheme vectorized code PGD unmixing (VPGDU). VPGDU has the advantage of solving (simultaneously) an independent optimization problem per image pixel, exactly as other pixelwise algorithms, but significantly faster. Its performance was compared with the commonly used fully constrained least squares unmixing (FCLSU), the generalized bilinear model (GBM) method for hyperspectral unmixng, and the fast state-of-the-art methods, sparse unmixing by variable splitting and augmented Lagrangian (SUnSAL) and collaborative SUnSAL (CLSUnSAL) based on the alternating direction method of multipliers. Considering all of the prospective EMs of a scene at each pixel (i.e., without a priori knowledge which/how many EMs are actually present in a given pixel), we demonstrate that the accuracy due to VPGDU is considerably higher than that obtained by FCLSU, GBM, SUnSAL, and CLSUnSAL under varying illumination, and is, otherwise, comparable with respect to these methods. However, while our method is significantly faster than FCLSU and GBM, it is slower than SUnSAL and CLSUnSAL by roughly an order of magnitude.

Reducing the Effect of the Endmembers’ Spectral Variability by Selecting the Optimal Spectral Bands

Variable environmental conditions cause different spectral responses of scene endmembers. Ignoring these variations affects the accuracy of fractional abundances obtained from linear spectral unmixing. On the other hand, the correlation between the bands of hyperspectral data is not considered by conventional methods developed for dealing with spectral variability. In this paper, a novel approach is proposed to simultaneously mitigate spectral variability and reduce correlation among different endmembers in hyperspectral datasets. The idea of the proposed method is to utilize the angular discrepancy of bands in the Prototype Space (PS), which is constructed using the endmembers of the image. Using the concepts of PS, in which each band is treated as a space point, we proposed a method to identify independent bands according to their angles. The proposed method comprised two main steps. In the first step, which aims to alleviate the spectral variability issue, image bands are prioritized based on their standard deviations computed over some sets of endmembers. Independent bands are then recognized in the prototype space, employing the angles between the prioritized bands. Finally, the unmixing process is done using the selected bands. In addition, the paper presents a technique to form a spectral library of endmembers’ variability (sets of endmembers). The proposed method extracts endmembers sets directly from the image data via a modified version of unsupervised spatial–spectral preprocessing. The performance of the proposed method was evaluated by five simulated images and three real hyperspectral datasets. The experiments show that the proposed method—using both groups of spectral variability reduction methods and independent band selection methods—produces better results compared to the conventional methods of each group. The improvement in the performance of the proposed method is observed in terms of more appropriate bands being selected and more accurate fractional abundance values being estimated.

SPECTRAL UNMIXING BASED CONSTRUCTION OF LUNAR MINERAL ABUNDANCE MAPS

Abstract. In this study we apply a nonlinear spectral unmixing algorithm to a nearly global lunar spectral reflectance mosaic derived from hyper-spectral image data acquired by the Moon Mineralogy Mapper (M3) instrument. Corrections for topographic effects and for thermal emission were performed. A set of 19 laboratory-based reflectance spectra of lunar samples published by the Lunar Soil Characterization Consortium (LSCC) were used as a catalog of potential endmember spectra. For a given spectrum, the multi-population population-based incremental learning (MPBIL) algorithm was used to determine the subset of endmembers actually contained in it. However, as the MPBIL algorithm is computationally expensive, it cannot be applied to all pixels of the reflectance mosaic. Hence, the reflectance mosaic was clustered into a set of 64 prototype spectra, and the MPBIL algorithm was applied to each prototype spectrum. Each pixel of the mosaic was assigned to the most similar prototype, and the set of endmembers previously determined for that prototype was used for pixel-wise nonlinear spectral unmixing using the Hapke model, implemented as linear unmixing of the single-scattering albedo spectrum. This procedure yields maps of the fractional abundances of the 19 endmembers. Based on the known modal abundances of a variety of mineral species in the LSCC samples, a conversion from endmember abundances to mineral abundances was performed. We present maps of the fractional abundances of plagioclase, pyroxene and olivine and compare our results with previously published lunar mineral abundance maps.

Stratified spectral mixture analysis of medium resolution imagery for impervious surface mapping

Linear spectral mixture analysis (LSMA) is widely employed in impervious surface estimation, especially for estimating impervious surface abundance in medium spatial resolution images. However, it suffers from a difficulty in endmember selection due to within-class spectral variability and the variation in the number and the type of endmember classes contained from pixel to pixel, which may lead to over or under estimation of impervious surface. Stratification is considered as a promising process to address the problem. This paper presents a stratified spectral mixture analysis in spectral domain (Sp_SSMA) for impervious surface mapping. It categorizes the entire data into three groups based on the Combinational Build-up Index (CBI), the intensity component in the color space and the Normalized Difference Vegetation Index (NDVI) values. A suitable endmember model is developed for each group to accommodate the spectral variation from group to group. The unmixing into the associated subset (or full set) of endmembers in each group can make the unmixing adaptive to the types of endmember classes that each pixel actually contains. Results indicate that the Sp_SSMA method achieves a better performance than full-set-endmember SMA and prior-knowledge-based spectral mixture analysis (PKSMA) in terms of R, RMSE and SE.

Identifying geochemical processes using End Member Mixing Analysis to decouple chemical components for mixing ratio calculations

Mixing calculations (i.e., the calculation of the proportions in which end-members are mixed in a sample) are essential for hydrological research and water management. However, they typically require the use of conservative species, a condition that may be difficult to meet due to chemical reactions. Mixing calculation also require identifying end-member waters, which is usually achieved through End Member Mixing Analysis (EMMA). We present a methodology to help in the identification of both end-members and such reactions, so as to improve mixing ratio calculations. The proposed approach consists of: (1) identifying the potential chemical reactions with the help of EMMA; (2) defining decoupled conservative chemical components consistent with those reactions; (3) repeat EMMA with the decoupled (i.e., conservative) components, so as to identify end-members waters; and (4) computing mixing ratios using the new set of components and end-members. The approach is illustrated by application to two synthetic mixing examples involving mineral dissolution and cation exchange reactions. Results confirm that the methodology can be successfully used to identify geochemical processes affecting the mixtures, thus improving the accuracy of mixing ratios calculations and relaxing the need for conservative species.

A New Approach for Endmember Extraction and Clustering Addressing Inter- and Intra-Class Variability via Multiscaled-Band Partitioning

In this paper, a new method is introduced for detecting and clustering spectrally similar but physically distinct materials. The method exploits the spectral information by dividing the spectral domain into band subsets whose width varies from broad to narrower wavelength ranges. Multiple candidate endmembers containing intraclass spectral variability are extracted using a maximum volume-based endmember extraction method at each band subset. Spectral clustering of the extracted spectra is also accomplished by using a multiscaled-band partitioning approach. This allows for the generation of multiscaled clustering identification vectors that can be used to remove partial mixtures and also be used to derive the final set of endmember bundles which retain interclass endmember variability. The proposed method was evaluated using simulated and real hyperspectral data and in comparison with well-known methods for extracting a fixed set or multiple sets of endmembers. Results revealed the advantages of the multiscaled-band partitioning on both multiple endmember extraction and clustering with the latter being an independent module that can be applicable to endmember candidate libraries derived from other methods.