Endmember Extraction Algorithms Research Articles

Endmember extraction and abundance estimation algorithm based on double-compressed sampling

Based on double-compressed sampling, a hyperspectral spectral unmixing algorithm (SU_DCS) is proposed, which could directly complete the endmember extraction and abundance estimation. On the basis of the linear mixed model (LMM), we designed spatial and spectral sampling matrices, obtained spatial and spectral measurement data, and constructed a joint unmixing model containing endmember and abundance information. By using operator separation and Lagrangian multiplier algorithm, the endmember matrix, abundance matrix and remixing image can be quickly obtained by matrix operation. The parameters of the unmixing algorithm, including regularization parameter, convergence threshold and spatial sampling rate, are determined using synthetic simulated hyperspectral data. The proposed algorithm is applied to two kinds of real hyperspectral data, with or without ground truth, in order to verify the effectiveness and reliability of the algorithm. Firstly, we provide the performance of the algorithm on real datasets without ground truth. Compared with algorithm VCA_FCLS and algorithm CPPCA_VCA_FCLS, the endmember spectral curve extracted by the proposed SU_DCS is almost consistent with that obtained by VCA_FCLS, and is more smooth than that of obtained by CPPCA_VCA_FCLS. Additionally, the abundance estimation map estimated by the SU_DCS has consistency with the results obtained by VCA_FCLS. Moreover, the proposed SU_DCS has higher peak signal-to-noise ratio (PSNR) for remixing images with higher computational efficiency. Secondly, we provide the performance of the proposed algorithm on four real datasets with ground truth, including dataset Cuprite, dataset Samson, dataset Jasper and dataset Urban. We provide the results of endmember extraction and abundance estimation from the compressed data under different sampling rate conditions. The extracted endmember maintains good consistency with the true spectral curves, and the estimated abundance map can also maintain good spatial consistency with the ground truth. The comparison results with other four comparative algorithms also indicate that the proposed algorithm can obtain relatively accurate endmembers and abundance information from compressed data, the reliability and validity of the proposed algorithm have been proved. In summary, the main innovation of the proposed algorithm is that it can extract endmembers and estimate abundance with high accuracy from a small amount of measurement data.

A comparison of multivariate curve resolution with endmember extraction methods in hyperspectral Raman imaging

Hyperspectral Raman imaging not only offers spectroscopic fingerprints but also reveals morphological information such as spatial distributions in an analytical sample. However, the spectrum-per-pixel nature of hyperspectral imaging (HSI) results in a vast amount of data. Furthermore, HSI often requires pre- and post-processing steps to extract valuable chemical information. To derive pure spectral signatures and concentration abundance maps of the active spectroscopic compounds, both endmember extraction (EX) and Multivariate Curve Resolution (MCR) techniques are widely employed. The objective of this study is to carry out a systematic investigation based on Raman mapping datasets to highlight the similarities and differences between these two approaches in retrieving pure variables, and ultimately provide guidelines for pure variable extraction. Numerical simulations and Raman mapping experiments on a mixture of pharmaceutical powders and on a layered plastic foil sample were conducted to underscore the distinctions between MCR and EX algorithms (in particular Vertex Component Analysis, VCA) and their outputs. Both methods were found to perform well if the dataset contains pure pixels for each of the individual components. However, in cases where such pure pixels do not exist, only MCR was found to be capable of extracting the pure component spectra.

An initially robust minimum simplex volume-based method for linear hyperspectral unmixing

ABSTRACT Initialization plays an important role in the accuracy of endmember extraction algorithms (EEAs) in linear hyperspectral unmixing (LHU). Random initialization can lead to varying endmembers generated by EEAs. To address this challenge, an initialization strategy has been introduced, encompassing vertex component analysis (VCA), automatic target generation process (ATGP), among others. These techniques significantly contribute to enhancing the accuracy of EEAs. However, complex initialization is sometimes less preferable, prompting the unexplored question of whether there exists an EEA robust to initialization. This paper focuses on analyzing this issue within the context of minimum simplex volume-based (MV) methods, which have received considerable attention in the past two decades due to their robustness against the absence of pure pixels. MV methods typically formulate LHU as an optimization problem, most of which includes a non-convex volume term. Additionally, many MV methods use VCA as an initialization strategy. Firstly, this paper demonstrates that the variable splitting augmented Lagrangian approach (SISAL), as a representative non-convex MV method, heavily depends on initialization. To our knowledge, the impact of initialization for MV methods has not been thoroughly analyzed before. Furthermore, this paper proposes an initially robust MV method by introducing a new convex MV term. Numerical experiments conducted on simulated and real datasets demonstrate its outstanding performance in accuracy and robustness to initialization. Throughout the experiments the proposed method proves to be the most stable, which is crucial in real scene where the ground truth is unknown beforehand.

An Unsupervised Feature Extraction Using Endmember Extraction and Clustering Algorithms for Dimension Reduction of Hyperspectral Images

Hyperspectral images (HSIs) provide rich spectral information, facilitating many applications, including landcover classification. However, due to the high dimensionality of HSIs, landcover mapping applications usually suffer from the curse of dimensionality, which degrades the efficiency of supervised classifiers due to insufficient training samples. Feature extraction (FE) is a popular dimension reduction strategy for this issue. This paper proposes an unsupervised FE algorithm that involves extracting endmembers and clustering spectral bands. The proposed method first extracts existing endmembers from the HSI data via a vertex component analysis method. Using these endmembers, it subsequently constructs a prototype space (PS) in which each spectral band is represented by a point. Similar/correlated bands in the PS remain near one another, forming several clusters. Therefore, our method, in the next step, clusters spectral bands into multiple clusters via K-means and fuzzy C-means algorithms. Finally, it combines all the spectral bands in the same cluster using a weighted average operator to decrease the high dimensionality. The extracted features were evaluated by applying an SVM classifier. The experimental results confirmed the superior performance of the proposed method compared with five state-of-the-art dimension reduction algorithms. It outperformed these algorithms in terms of classification accuracy on three widely used hyperspectral images (Indian Pines, KSC, and Pavia Centre). The suggested technique also showed comparable or even stronger performance (up to 9% improvement) compared with its supervised competitor. Notably, the proposed method exhibited higher accuracy even when only a limited number of training samples were available for supervised classification. Using only five training samples per class for the KSC and Pavia Centre datasets, our method’s classification accuracy was higher than that of its best-performing unsupervised competitors by about 7% and 1%, respectively, in our experiments.

A Global-to-Local Evolutionary Algorithm for Hyperspectral Endmember Extraction

Recently, evolutionary algorithms (EAs) have shown their promising performance in solving the hyperspectral endmember extraction (EE) task. Despite that, most of the existing EA-based EE algorithms mainly take advantage of the global search capability of evolutionary computation. Few of them focus on the hyperspectral EE task itself, which is a sparse large-scale problem with constraint. To fill the gap, in this paper, a global-to-local evolutionary algorithm (GL-EA) is proposed, where the global and local search is performed sequentially to extract the endmembers effectively. Specifically, in the first global search stage, two complementary solution generation strategies including asymmetric flip based solution generation and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SAD</i> based solution repair are designed, with which the sparse large-scale search space of hyperspectral EE is fully explored and the endmembers that satisfy the constraint could be achieved. Then in the second stage, a perturbation based local search is suggested, which further enhances the quality of the obtained endmembers. In addition, an endmember repetition based solution selection strategy is also developed for both global and local search stages, by using which good solutions can be selected effectively during the evolution. Experimental results on different hyperspectral data sets demonstrate that when compared with the state-of-the-art EE algorithms, the proposed GL-EA could extract the endmembers with higher quality.

Endmember Bundle Extraction Based on Improved Multiobjective Particle Swarm Optimization

Endmember extraction (EE) is a key task for hyperspectral image unmixing. The majority of EE algorithms extract only one pure spectrum for each class of material, which may lead to a large unmixing error in cases of spectral variability. Endmember bundle extraction (EBE), which identifies a set of endmembers representing the spectral variability within each class, has been developed to solve the spectral variability problem. To date, only a small number of EBE methods have been developed; moreover, these approaches mainly employ traditional convex-geometry-based EE methods to extract endmember bundles from subset data, which may result in the loss of some endmembers and an incomplete endmember bundle set. This paper proposes an improved multi-objective particle swarm optimization method for the identification of multiple endmember bundles, named IMPSO-EBE. The proposed approach follows the framework of the spatial-spectral EBE (SSEBE) method, which extracts endmember candidates first and then applies post-processing to remove redundant endmembers. However, unlike the SSEBE method, which uses the traditional pixel purity index (PPI) method to obtain candidate endmembers from single feature space, IMPSO-EBE proposes to cooperate across multiple dataspaces to obtain candidate endmembers based on multi-objective particle swarm optimization, making it able to extract candidate endmembers that cannot be identified in single feature space. We compare the performance of the proposed method with that of the single dataspace-based endmember bundle extraction methods using two real hyperspectral datasets. Results show that the endmember bundles identified by the proposed method are more complete than those of the comparison method.

Crop type discrimination using Geo-Stat Endmember extraction and machine learning algorithms

The identification of crop diversity in today's world is very crucial to ensure adaptation of the crop with changing climate for better productivity as well as food security. Towards this, Hyperspectral Remote Sensing (HRS) is an efficient technique that offers the opportunity to discriminate crop types based on morphological as well as physiological features due to availability of contiguous spectral bands. The current work utilized the benefits of Airborne Visible Infrared Imaging Spectrometer- New Generation (AVIRIS-NG) data and explored the techniques for classification and identification of crop types. The endmembers were identified using the Geo-Stat Endmember Extraction (GSEE) algorithm for pure pixels identification and to generate the spectral library of the different crop types. Spectral feature comparison was done among AVIRIS-NG, Analytical Spectral Device (ASD)-Spectroradiometer and Continuum Removed (CR) spectra. The best-fit spectra obtained with the Reference ASD-Spectroradiometer and Pure Pixel spectral library were then used for crop discrimination using the ten supervised classifiers namely Spectral Angle Mapper (SAM), Spectral Information Divergence (SID), Support Vector Machine (SVM), Minimum Distance Classifier (MDC), Binary Encoding, deep learning-based Convolution Neural Network (CNN) and different algorithms of Ensemble learning such as Tree Bag, AdaBoost (Adaptive Boosting), Discriminant and RUSBoost (Random Under Sampling). In total, nine crop types were identified, namely, wheat, maize, tobacco, sorghum, linseed, castor, pigeon pea, fennel and chickpea. The performance evaluation of the classifiers was made using various metrics like Overall Accuracy, Kappa Coefficient, Precision, Recall and F1 score. The classifier 2D-CNN was found to be the best with Overall Accuracy, Kappa Coefficient, Precision, Recall and F1 score values of 89.065 %, 0.871, 87.565%, 89.541% and 88.678% respectively. The output of this work can be utilized for large scale mapping of crop types at the species level in a short interval of time with high accuracy.

Quadratic Clustering-Based Simplex Volume Maximization for Hyperspectral Endmember Extraction

The existence of intra-class spectral variability caused by differential scene components and illumination conditions limits the improvement of endmember extraction accuracy, as most endmember extraction algorithms directly find pixels in the hyperspectral image as endmembers. This paper develops a quadratic clustering-based simplex volume maximization (CSVM) approach to effectively alleviate spectral variability and extract endmembers. CSVM first adopts spatial clustering based on simple linear iterative clustering to obtain a set of homogeneous partitions and uses spectral purity analysis to choose pure pixels. The average of the chosen pixels in each partition is taken as a representative endmember, which reduces the effect of local-scope spectral variability. Then an improved spectral clustering based on k-means is implemented to merge homologous representative endmembers to further reduce the effect of large-scope spectral variability, and final endmember collection is determined by the simplex with maximum volume. Experimental results show that CSVM reduces the average spectral angle distance on Samson, Jasper Ridge and Cuprite datasets to below 0.02, 0.06 and 0.09, respectively, provides the root mean square errors of abundance maps on Samson and Jasper Ridge datasets below 0.25 and 0.10, and exhibits good noise robustness. By contrast, CSVM provides better results than other state-of-the-art algorithms.

A Distributed N-FINDR Cloud Computing-Based Solution for Endmembers Extraction on Large-Scale Hyperspectral Remote Sensing Data

In this work, we introduce a novel, distributed version of the N-FINDR endmember extraction algorithm, which is able to exploit computer cluster resources in order to efficiently process large volumes of hyperspectral data. The implementation of the distributed algorithm was done by extending the InterCloud Data Mining Package, originally adopted for land cover classification, through the HyperCloud-RS framework, here adapted for endmember extraction, which can be executed on cloud computing environments, allowing users to elastically administer processing power and storage space for adequately handling very large datasets. The framework supports distributed execution, network communication, and fault tolerance, transparently and efficiently to the user. The experimental analysis addresses the performance issues, evaluating both accuracy and execution time, over the processing of different synthetic versions of the AVIRIS Cuprite hyperspectral dataset, with 3.1 Gb, 6.2 Gb, and 15.1Gb respectively, thus addressing the issue of dealing with large-scale hyperspectral data. As a further contribution of this work, we describe in detail how to extend the HyperCloud-RS framework by integrating other endmember extraction algorithms, thus enabling researchers to implement algorithms specifically designed for their own assessment.

Spatial Potential Energy Weighted Maximum Simplex Algorithm for Hyperspectral Endmember Extraction

Most traditional endmember extraction algorithms focus on spectral information, which limits the effectiveness of endmembers. This paper develops a spatial potential energy weighted maximum simplex algorithm (SPEW) for hyperspectral endmember extraction, combining the relevance of hyperspectral spatial context with spectral information to effectively extract endmembers. Specifically, for pixels in a uniform spatial area, SPEW assigns a high weight to pixels with higher spatial potential energy. For pixels scattered in a spatial area, the high weights are assigned to the representative pixels with a smaller spectral angle distance. Then, the optimal endmember collection is determined by the simplex with maximum volume in the space of representative pixels. SPEW not only reduces the complexity of searching for the maximum simplex volume but also improves the performance of endmember extraction. In particular, compared with other newly proposed spatial-spectral hyperspectral endmember extraction methods, SPEW can effectively extract the hidden endmembers in a spatial area without adjusting any parameters. Experiments on synthetic and real data show that the SPEW algorithm has also provides better results than the traditional algorithms.

An Adaptive Surrogate-Assisted Endmember Extraction Framework Based on Intelligent Optimization Algorithms for Hyperspectral Remote Sensing Images

As the foremost step of spectral unmixing, endmember extraction has been one of the most challenging techniques in the spectral unmixing processing due to the mixing of pixels and the complexity of hyperspectral remote sensing images. The existing geometrial-based endmember extraction algorithms have achieved the ideal results, but most of these algorithms perform poorly when they do not meet the assumption of simplex structure. Recently, many intelligent optimization algorithms have been employed to solve the problem of endmember extraction. Although they achieved the better performance than the geometrial-based algorithms in different complex scenarios, they also suffer from the time-consuming problem. In order to alleviate the above problems, balance the two key indicators of accuracy and running time, an adaptive surrogate-assisted endmember extraction (ASAEE) framework based on intelligent optimization algorithms is proposed for hyperspectral remote sensing images in this paper. In the proposed framework, the surrogate-assisted model is established to reduce the expensive time cost of the intelligent algorithms by fitting the fully constrained evaluation value with the low-cost estimated value. In more detail, three commonly used intelligent algorithms, namely genetic algorithm, particle swarm optimization algorithm and differential evolution algorithm, are specifically designed into the ASAEE framework to verify the effectiveness and robustness. In addition, an adaptive weight surrogate-assisted model selection strategy is proposed, which can automatically adjust the weights of different surrogate models according to the characteristics of different intelligent algorithms. Experimental results on three data sets (including two simulated data sets and one real data set) show the effectiveness and the excellent performance of the proposed ASAEE framework.

Comparison of Image Endmember- and Object-Based Classification of Very-High-Spatial-Resolution Unmanned Aircraft System (UAS) Narrow-Band Images for Mapping Riparian Forests and Other Land Covers

Riparian forests are critical for carbon storage, biodiversity, and river water quality. There has been an increasing use of very-high-spatial-resolution (VHR) unmanned aircraft systems (UAS)-based remote sensing for riparian forest mapping. However, for improved riparian forest/zone monitoring, restoration, and management, an enhanced understanding of the accuracy of different classification methods for mapping riparian forests and other land covers at high thematic resolution is necessary. Research that compares classification efficacies of endmember- and object-based methods applied to VHR (e.g., UAS) images is limited. Using the Sequential Maximum Angle Convex Cone (SMACC) endmember extraction algorithm (EEA) jointly with the Spectral Angle Mapper (SAM) classifier, and a separate multiresolution segmentation/object-based classification method, we map riparian forests/land covers and compare the classification accuracies accrued via the application of these two approaches to narrow-band, VHR UAS orthoimages collected over two river reaches/riparian areas in Austria. We assess the effect of pixel size on classification accuracy, with 7 and 20 cm pixels, and evaluate performance across multiple dates. Our findings show that the object-based classification accuracies are markedly higher than those of the endmember-based approach, where the former generally have overall accuracies of &gt;85%. Poor endmember-based classification accuracies are likely due to the very small pixel sizes, as well as the large number of classes, and the relatively small number of bands used. Object-based classification in this context provides for effective riparian forest/zone monitoring and management.

A New Deep Convolutional Network for Effective Hyperspectral Unmixing

Hyperspectral unmixing extracts pure spectral constituents (endmembers) and their corresponding abundance fractions from remotely sensed scenes. Most traditional hyperspectral unmixing methods require the results of other endmember extraction algorithms to complete the abundance estimation step. Due to the impressive learning and data fitting capabilities of convolutional neural networks (CNNs), deep learning (DL)-based hyperspectral unmixing technologies have rapidly developed in the literature. According to the procedure used to combine different layers (i.e., fully connected layers, convolution layers, and activation layers), these techniques are mainly divided into three main categories, i.e., those based on autoencoder networks, convolutional neural networks, and convolutional autoencoder networks. They usually extract the weight and output of a specific activation layer as endmember signatures and abundance maps, respectively. Moreover, most existing DL-based unmixing approaches usually use 2D CNNs to learn the features contained in hyperspectral images, and very few approaches employ 3D CNNs to extract spectral and spatial information. However, 2D CNN-based techniques cannot capture good discriminative feature maps from the spectral viewpoint, and 3D CNN-based techniques usually have high computational overload. In this work, to further exploit the feature extraction capability of CNNs, we combine 3D and 2D convolutions to propose a cross-convolution unmixing network (CrossCUN) for hyperspectral unmixing. Simultaneously, to better illustrate the improvements of our proposed CrossCUN, we also build the corresponding 2D convolution unmixing network (2DCUN) and 3D convolution unmixing network (3DCUN). We evaluate the performance of our newly developed networks on two types of synthetic data sets and three real hyperspectral images. Experimental results show that the proposed networks not only obtain better results than other DL-based unmixing methods but also do not require any prior knowledge (e.g., the results of other endmember extraction algorithms) to estimate the abundance maps. We release the related codes at https://github.com/xuanwentao to encourage the reproduction of our results.

Pixel Purity Index Applied to the Mapping of Degraded Soils by the Presence of Cangahuas in the Ilaló Volcano, Ecuador

Soil degradation is a severe problem in the northern region of Ecuador. Due to deforestation, expansion of the agricultural frontier, and poor tillage practices, the outcrop of cangahuas further aggravates. Remote Sensing allows mapping this type of subsoil, which is often related to eroded areas; the spatial resolution of free multispectral images contains more than one coverage. This means that techniques to discern the pure spectral signature of the object of interest are required. Pixel Purity Index (PPI) is an endmember extraction algorithm capable of selecting the pure pixel and classifying it better than object-oriented techniques. The study's objective was to map soils with outcrops of cangahua, by PPI applied to Landsat 8 images in Ilaló volcano and later performed a physicochemical characterization to know the magnitude of the soil degradation in the mapped areas. We used two models with PPI: SAM and LSU; both were compared with classifications based on three vegetation indexes. LSU obtained the best result (91.2% accuracy and 0.81 Kappa coefficient). The mapped cangahua was approximately 806.85 ha. The soil had an average porosity of 45%, a relative density of 2.271 g/cm3, low concentrations of nitrates, phosphates, and sulfates, electrical conductivity <500 µS/cm, and alkaline pH, this means there is soil degradation. The PPI method had good accuracy and was achieved in identifying cangahua outcrops, which demonstrated its potentiality in mapping land cover.

Subspace-Based Preprocessing Module for Fast Hyperspectral Endmember Selection

Endmember extraction algorithms (EEAs) play a crucial role in hyperspectral image (HSI) perception, and yet they normally suffer from three flaws: 1) High computational burden, 2) weak noise robustness, and 3) high outlier sensitivity. To solve these problems, this article proposes a fast subspace-based preprocessing module, called fast subspace-based preprocessing module (FSPM), to select a high-quality data subset for subsequent endmember extraction. Specifically, FSPM first transforms an HSI into a low-dimensional data subspace using singular value decomposition. For each component pair, FSPM then detects its convex hull vertices and proposes a local outlier score measurement to remove potential outliers. FSPM finally transforms determined data points into noise-reduced data space for the sake of identifying endmembers. The proposed FSPM sheds new light on the current preprocessing field, which can fast reduce noises and outliers as well as remove redundant data points. Based on various validation metrics, experiments conducted on both synthetic and real HSIs indicate that the proposed FSPM is superior to current state-of-the-art preprocessing techniques.

Interference-Suppressed and Cluster-Optimized Hyperspectral Target Extraction Based on Density Peak Clustering

Target extraction can provide a prior knowledge for spectral unmixing, unsupervised hyperspectral image classification, and unsupervised target detection tasks, which is of great practice. Considering that the traditional endmember extraction algorithms such as automatic target generation process (ATGP) and simplex growing algorithm (SGA) are sensitive to the burst noise caused by hyperspectral sensor imaging and cannot extract the appropriate target set to simultaneously guide the various tasks, a weighted target extraction algorithm based on the density peak clustering (DPC) is proposed in this article. First, DPC is extended to hyperspectral images, and the decision graph is generated according to the density and distance of each pixel to effectively classify the regions with different attributes such as burst noise, cluster center, cluster boundary, and cluster core. On the basis, three DPC-based weighted vectors are designed, and the weighted target extraction algorithms W-ATGP and W-SGA are put forward which allocates a lower weight than the core pixel to the interference so as to reduce its impact on ATGP and SGA while obtaining the high-quality targets for various tasks. The experimental results on three datasets show that the accuracies of the target sets extracted by W-ATGP and W-SGA are higher than that of ATGP and SGA, no matter as the prior knowledge of spectral unmixing, unsupervised hyperspectral image classification, or unsupervised target detection, which verifies the effectiveness of the proposed methods.

A spatial-spectral clustering-based algorithm for endmember extraction and hyperspectral unmixing

ABSTRACT Spectral variability existing in hyperspectral (HS) images reduces the accuracy of unmixing. To mitigate the effect of spectral variability on unmixing, we propose a spatial-spectral clustering-based method (called SP2C) for endmember extraction and HS unmixing. The proposed SP2C adopts a local spatial-spectral clustering strategy to obtain a set of spatially homogenous regions and exploits a spectral purity index calculation strategy to choose pure pixels on the regions, where the average spectra of chosen pure pixels on the regions are taken as endmember candidates to alleviate local spectral variability. Then, an adjusted k-means plus (called AD k-means++) algorithm is employed to cluster candidate endmembers to alleviate global spectral variability, and the final endmembers are achieved by matching the cluster centers and the reference endmembers obtained by the vertex component analysis (VCA)-like methods. Our experiment results, conducted using real HS datasets, confirm that the proposed method considerably improves the HS unmixing performance compared to the state-of-the-art techniques.

The Spatial–Spectral–Environmental Extraction Endmember Algorithm and Application in the MODIS Fractional Snow Cover Retrieval

Endmember extraction is a primary and indispensable component of the spectral mixing analysis model applicated to quantitatively retrieve fractional snow cover (FSC) from satellite observation. In this study, a new endmember extraction algorithm, the spatial–spectral–environmental (SSE) endmember extraction algorithm, is developed, in which spatial, spectral and environmental information are integrated together to automatically extract different types of endmembers from moderate resolution imaging spectroradiometer (MODIS) images. Then, combining the linear spectral mixture analysis model (LSMA), the SSE endmember extraction algorithm is practically applied to retrieve FSC from standard MODIS surface reflectance products in China. The new algorithm of MODIS FSC retrieval is named as SSEmod. The accuracy of SSEmod is quantitatively validated with 16 higher spatial-resolution FSC maps derived from Landsat 8 binary snow cover maps. Averaged over all regions, the average root-mean-square-error (RMSE) and mean absolute error (MAE) are 0.136 and 0.092, respectively. Simultaneously, we also compared the SSEmod with MODImLAB, MODSCAG and MOD10A1. In all regions, the average RMSE of SSEmod is improved by 2.3%, 2.6% and 5.3% compared to MODImLAB for 0.157, MODSCAG for 0.157 and MOD10A1 for 0.189. Therefore, our SSE endmember extraction algorithm is reliable for the MODIS FSC retrieval and may be also promising to apply other similar satellites in view of its accuracy and efficiency.

Convex Polygon Maximization-Based Hyperspectral Endmember Extraction Algorithm

Pure endmember extraction from the hyperspectral image is a very essential step in target detection, classification and unmixing applications. Using the concept of convex geometry, a novel algorithm for endmember extraction is proposed in this paper. The algorithm uses convex polygon maximization to determine a convex set that gives maximum convex polygon area according to the surveyor’s formula. The parallel implementation of the proposed algorithm is useful in finding more effective distinctive pixels. The robustness of the proposed algorithm in the presence of noise is demonstrated with synthetic data. The simulation results, conducted using real hyperspectral data, indicate that the proposed algorithm reduces the Spectral Angle Error (SAE) and Spectral Information Divergence (SID) error by 2.4–8.8%. The effectiveness of the proposed algorithm in abundance mapping is also validated using Root Mean Square Error (RMSE). The RMSE of the proposed algorithm is also improved by 1.7–7.6%.

Convex geometry and K-medoids based noise-robust endmember extraction algorithm

Spectral mixture analysis (SMA) is an effective means of finding a unique spectral signature of constituents called endmembers and approximating their proportion of presence (abundance fractions). In the literature of SMA, the challenging task of endmember extraction from the hyperspectral imagery is approached by different methods. The majority of the endmember extraction algorithms are developed based on the convex geometry of the dataset perhaps due to low computation. But the performance of these convex geometry-based algorithms is degraded in the high-level noise scenario. To make the noise-robust algorithm, we propose an algorithm by introducing K-medoids with convex geometry. The proposed algorithm uses the K-medoids clustering approach in the removal of extra convex points, which leads to improving the endmember extraction efficacy. The proposed algorithm is tested by introducing white Gaussian noise under different signal-to-noise ratio conditions in the synthetic dataset, especially for high-level noise. Our experimental results show that the proposed one improves the endmember extraction efficiency in the high-level noise condition. The proposed algorithm is also tested on the real datasets of Cuprite and Mangalore. The proposed algorithm outperforms others on the real benchmark datasets as well.