Set Of Endmembers Research Articles

Evolutionary multitasking cooperative transfer for multiobjective hyperspectral sparse unmixing

Evolutionary multiobjective optimization is vigorous but not efficient in solving the hyperspectral sparse unmixing problem, while most related algorithms suffer from high computational complexity. This limitation becomes more pronounced in dealing with multiple complex hyperspectral sparse unmixing tasks (HSUTs) concurrently. In fact, different HSUTs are interrelated on spectral libraries and search spaces. However, there is currently no evolutionary algorithm-based approach that explores the cooperativity of multiple HSUTs. Taking advantage of this opportunity, we propose a novel evolutionary multitasking cooperative transfer (EMCT) framework for multiobjective hyperspectral sparse unmixing in this paper. EMCT can handle different HSUTs simultaneously with a uniformly coded population, and discover the correlation between different tasks to promote their convergence. To overcome the issue of unequal dimensions and non-corresponding spectra in the spectral libraries utilized by different tasks, we propose a novel library alignment strategy to alleviate the multitasking negative transfer. In addition, we design novel initialization strategy and genetic operators to improve the population diversity and the efficiency of population evolution between different HSUTs. We utilize the reconstruction error of every endmember in the spectral library for each task as prior knowledge to evenly distribute the population within the sparsity interval to be explored. In initialization and population evolution, EMCT prefers those decision variables with lower error scores, guiding the population to explore more probable active endmember sets. On the three most commonly used simulated datasets and one real dataset, EMCT achieves state-of-the-art (SOTA) or competitive experimental results. Furthermore, the potential of the EMCT framework is also demonstrated in combination with other multiobjective sparse unmixing algorithms and evolutionary multitasking explicit transfer strategy.

Spatial and Temporal Variation of Mars South Polar Ice Composition From Spectral Endmember Classification of CRISM Mapping Data

AbstractMultispectral mapping data from the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) provide a unique opportunity to characterize south polar ice deposits at higher spectral sampling, spatial resolution, or spatiotemporal coverage than previous work. This new perspective can help constrain the nature and distribution of different mixtures of CO2 ice, H2O ice, and dust that influence the formation, evolution, and preservation of Mars climate records. We processed 1,103 CRISM observations spanning the southern summer of six Mars Years (MYs) through a combination of k‐means clustering and random forest classification. Using a set of 12 spectral endmembers directly tied to previous work with high‐resolution CRISM targeted data, we made a series of temporally restricted mosaics showing surface spectral variation over time. The mosaics show the effects of the MY 28 dust storm on the removal of the seasonal CO2 ice cap that year and reveal how this process differed from the years that followed. A mosaic showing residual ice surfaces displays broad agreement with previous compositional maps while resolving new details in the distribution of H2O ice‐rich material around the periphery of the bright CO2 ice cap. By showing how surface composition varies across a broad swath of the south polar region through time, the endmember set and classified mosaics produced in this work can provide critical context for future studies of the dynamic processes that shape south polar ice deposits.

Mapping Abandoned Uranium Mine Features Using Worldview-3 Imagery in Portions of Karnes, Atascosa and Live Oak Counties, Texas

Worldview-3 (WV3) 16-band multispectral data were used to map exposed bedrock and mine waste piles associated with legacy open-pit mining of sandstone-hosted roll-front uranium deposits along the South Texas Coastal Plain. We used the “spectral hourglass” approach to extract spectral endmembers representative of these features from the image. This approach first requires calibrating the imagery to reflectance, then masking for vegetation, followed by spatial and spectral data reduction using a principal component analysis-based procedure that reduces noise and identifies homogeneous targets which are “pure” enough to be considered spectral endmembers. In this case, we used a single WV3 image which covered an ~11.5 km by ~19.5 km area of Karnes, Atascosa and Live Oak Counties, underlain by mined rocks from the Jackson Group and Catahoula Formation. Up to 58 spectral endmembers were identified using a further multi-dimensional class segregation method and were used as inputs for spectral angle mapper (SAM) classification. SAM classification resulted in the identification of at least 117 mine- and mine waste-related features, most of which were previously unknown. Class similarity was further evaluated, and the dominant minerals in each class were identified by comparison to spectral libraries and measured samples of actual Jackson Group uranium host rocks. Redundant classes were eliminated, and SAM was run a second time using a reduced set of 23 endmembers, which were found to map these same features as effectively as using the full 58 set of endmembers, but with significantly reduced noise and spectral outliers. Our classification results were validated by evaluating detailed scale mapping of three known mine sites (Esse-Spoonamore, Wright-McCrady and Garbysch-Thane) with published ground truth information about the vegetation cover, extent of erosion and exposure of waste pile materials and/or geologic information about host lithology and mineralization. Despite successful demonstration of the utility of WV3 data for inventorying mine features, additional landscape features such as bare agricultural fields and oil and gas drill pads were also identified. The elimination of such features will require combining the spectral classification maps presented in this study with high-quality topographic data. Also, the spectral endmembers identified during the course of this study could be useful for larger-scale mapping efforts using additional well-calibrated WV3 images beyond the coverage of our initial study area.

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.

The Sentinel 2 MSI Spectral Mixing Space

A composite spectral feature space is used to characterize the spectral mixing properties of Sentinel 2 Multispectral Instrument (MSI) spectra over a wide diversity of landscapes. Characterizing the linearity of spectral mixing and identifying bounding spectral endmembers allows the Substrate Vegetation Dark (SVD) spectral mixture model previously developed for the Landsat and MODIS sensors to be extended to the Sentinel 2 MSI sensors. The utility of the SVD model is its ability to represent a wide variety of landscapes in terms of the areal abundance of their most spectrally and physically distinct components. Combining the benefits of location-specific spectral mixture models with standardized spectral indices, the physically based SVD model offers simplicity, consistency, inclusivity and applicability for a wide variety of land cover mapping applications. In this study, a set of 110 image tiles compiled from spectral diversity hotspots worldwide provide a basis for this characterization, and for identification of spectral endmembers that span the feature space. The resulting spectral mixing space of these 13,000,000,000 spectra is effectively 3D, with 99% of variance in 3 low order principal component dimensions. Four physically distinct spectral mixing continua are identified: Snow:Firn:Ice, Reef:Water, Evaporite:Water and Substrate:Vegetation:Dark (water or shadow). The first 3 continua exhibit complex nonlinearities, but the geographically dominant Substrate:Vegetation:Dark (SVD) continuum is conspicuous in the linearity of its spectral mixing. Bounding endmember spectra are identified for the SVD continuum. In a subset of 80 landscapes, excluding the 3 nonlinear mixing continua (reefs, evaporites, cryosphere), a 3 endmember (SVD) linear mixture model produces endmember fraction estimates that represent 99% of modeled spectra with <6% RMS misfit. Two sets of SVD endmembers are identified for the Sentinel 2 MSI sensors, allowing Sentinel 2 spectra to be unmixed globally and compared across time and space. In light of the apparent disparity between the 11D spectral feature space and the statistically 3D spectral mixing space, the relative contribution of 11 Sentinel 2 MSI spectral bands to the information content of this space is quantified using both parametric (Pearson Correlation) and nonparametric (Mutual Information) metrics. Comparison of linear (principal component) and nonlinear (Uniform Manifold Approximation and Projection) projections of the SVD mixing space reveal both physically interpretable spectral mixing continua and geographically distinct spectral properties not resolved in the linear projection.

Characterizing Seasonal and Residual Ices at the South Pole of Mars Using a Universal Set of CRISM Spectral Endmembers

AbstractCurrent maps of compositional variation across south polar ice exposures on Mars do not resolve the meter‐scales at which erosional processes are most active, ultimately limiting our understanding of how the deposits form and evolve and how they can be used to interpret long‐term climate records. In this study, we use k‐means clustering and random forest classification to identify and map a set of universal spectral endmembers across 167 high‐resolution observations acquired during southern summer by the Compact Reconnaissance Imaging Spectrometer for Mars. The 21 endmembers show distinct combinations and strengths of key infrared absorption features reflecting diverse mixtures of CO2 ice, H2O ice, and dust. The resulting compositional framework can be used to characterize the nature of both seasonal CO2 frost and the residual ices it overlies across a variety of terrains. Following the large dust event of Mars Year 28, the residual CO2‐ice deposits (RCD) were covered by an unusually thick or long‐lived deposit of seasonal frost. Within the RCD, low‐albedo material around erosional features display H2O ice absorptions consistent with exposures around the outer margins of the RCD. These peripheral water‐ice deposits show unexpected variation in CO2 ice and dust content. Most notably, regions within several km of the edge of the RCD display spectral contributions from CO2 ice even after seasonal frost has been removed. These results can inform investigations focused on the dynamics of seasonal CO2 deposition, the development of erosional morphologies, and the creation of climate records in south polar stratigraphy.

Hyperspectral Unmixing Based on Nonnegative Matrix Factorization: A Comprehensive Review

Hyperspectral unmixing has been an important technique that estimates a set of endmembers and their corresponding abundances from a hyperspectral image (HSI). Nonnegative matrix factorization (NMF) plays an increasingly significant role to solve this problem. In this article, we present a comprehensive survey of the NMF-based methods proposed for hyperspectral unmixing. Taking the NMF model as a baseline, we show how to improve NMF by utilizing the main properties of HSIs (e.g., spectral, spatial, and structural information). We categorize three important development directions including constrained NMF, structured NMF, and generalized NMF. Furthermore, several experiments are conducted to illustrate the effectiveness of associated algorithms. Finally, we conclude the paper with possible future directions with the purposes of providing guidelines and inspiration to promote the development of hyperspectral unmixing.

Zirconolite from Larvik Plutonic Complex, Norway, its relationship to stefanweissite and nöggerathite, and contribution to the improvement of zirconolite end-member systematics

Abstract The very first description of zirconolite, originally called polymignyte, discovered in alkaline pegmatites within the Larvik Plutonic Complex (LPC), Norway, was published almost 200 yr ago. We studied zirconolite from three occurrences located in this region using modern techniques—X-ray powder diffraction (XRPD) upon thermal annealing of initially radiation-damaged mineral, electron probe microanalysis, and Mössbauer spectroscopy. The initial XRPD pattern lacked any sharp diffraction maxima, as the accumulated radiation dose exceeded a critical value of ca. 1016 α-decays/mg. Annealing at 400–800 °C induced recrystallization to a transitional, cubic phase interpreted to have a disordered, defect fluorite structure [space group Fm3m; unit-cell parameters: a = 5.1047(4) Å, V = 133.02(2) Å3], with its XRPD pattern being very similar to that of cubic ZrO2. Rietveld analysis of the XRPD pattern obtained after a phase transition at 900 °C shows a mixture of -3O [wt. fraction of ca. 60%, space group Cmca, unit-cell parameters: a = 7.2664(8) Å, b = 14.1877(15) Å, c = 10.1472(12) Å, V = 1046.1(2) Å3], and -3T [wt. fraction of ca. 40%, space group P3121, unit-cell parameters: a = 7.2766(6) Å, c = 17.0627(15) Å, V = 752.42(11) Å3] zirconolite polytypes. However, the crystal habits of zirconolite from the LPC show a distinct orthorhombic symmetry. Although their chemical compositions are far from the ideal zirconolite composition and a large number of elements are involved in high concentrations [up to ca. 17 wt% REE2O3, ≤7 wt% ACTO2, ≤18 wt% Me25+O5, ≤9 wt% Me2+O + Me23+O3, Fe3+/(Fe3++Fe2+) ≈ 0.2, where ACT = Th + U, Me5+ = Nb ± Ta, Me2+ = Fe2+ ± Mg, Me3+ ≈ Fe3+], the compositional variability is relatively limited. To quantitatively describe the two distinct compositional trends observed, we introduced a concept called “edgemembers,” so that mixing is approximated to occur between two terminal compositions situated at two edges of the zirconolite composition space. These marginal compositions were determined from observed compositional trends, i.e., heterovalent substitution of Me5+ for Ti in octahedral sites and ACT enrichment associated with increasing Ti/Me5+ ratio. This approach provides general substitution vectors for both, Håkestad-type mode (ACT + 3 Ti + Me3+ = Ca + 3 Me5+ + Me2+), and Stålaker-type mode (0.7 ACT + 0.5 REE + 0.9 Ti + 0.7 Me3+ + 0.05 Zr = 1.2 Ca + 1.3 Me5+ + 0.3 Me2+ + 0.05 Mn). In terms of chemical composition, the studied zirconolite corresponds to recently approved zirconolite-related minerals stefanweissite (for Ca > REE) and nöggerathite (for REE > Ca). Based on a careful analysis of zirconolite composition space, we show that our observed Håkestad-type compositional trend, as well as a high number of published zirconolite compositions worldwide (with Me2+ + Me3+ sum of ca. 1 atom per 14 O), can be well approximated by a modified end-member set comprising Ca2Zr2Me25+TiMe2+O14, REE2Zr2Ti3Me2+O14, CaACTZr2Ti3Me2+O14, CaREEZr2Ti3Me3+O14, and Ca2Zr2Ti2Me5+Me3+O14 without a need to involve the ideal zirconolite formula Ca2Zr2Ti4O14. The redefined composition space constrained by end-members from this set, together with ideal zirconolite, may be representative of the vast majority of more than 450 published zirconolite compositions worldwide with Me2+ + Me3+ totaling ≤1 atom per 14 O. The equation XMe3+ = 2 – 2XREE* – 3XMe5+* provides an independent calculation of iron oxidation state or XMe3+ = Me3+/(Me2+ + Me3+) for this remarkable group of zirconolites, where XREE* is derived from XREE = REE/(REE + Ca) and XMe5+* from XMe5+ = Me5+/(Me5+ + Ti). Understanding the oxidation state of iron in zirconolite may be helpful to characterize redox conditions during its crystallization.

Multi-fidelity evolutionary multitasking optimization for hyperspectral endmember extraction

Endmember extraction plays an indispensable role in hyperspectral image processing, which is also an important step to decompose the mixed pixels in spectral unmixing. Most of the existing methods based on the principle of convex geometry and intelligent optimization algorithms have achieved an excellent result, but they also suffer from the influence of outliers and expensive computation respectively. Furthermore, it is difficult to determine the number of endmembers in a hyperspectral image without any prior conditions. In order to alleviate these problems, we propose a multi-fidelity evolutionary multitasking optimization framework for hyperspectral endmember extraction in this article. In the proposed framework, multiple tasks to extract different numbers of endmembers are uniformly coded into a single population, aiming to process these similar tasks simultaneously with the implicit genetic transfer. Accordingly, our proposed algorithm is capable of extracting the best endmember set within a certain range of the number of endmembers without any prior knowledge. In addition, an ensemble surrogate model is firstly built to approximate the high-fidelity fitness with the low-fidelity fitness in endmember extraction, which greatly alleviates the time-consuming problem of individual evaluation. The experimental results on the simulated and the real hyperspectral data demonstrate the effectiveness of the proposed framework. The accuracy and the efficiency of endmember extraction are greatly improved compared with other classic endmember extraction methods.

Nonnegative matrix factorization with entropy regularization for hyperspectral unmixing

ABSTRACT Nonnegative matrix factorization (NMF) has been one of the most widely used techniques for hyperspectral unmixing (HU), which aims at decomposing each mixed pixel into a set of endmembers and their corresponding fractional abundances. However, the standard NMF model is ill-posed with only considering the non-negativity constraint. Therefore, many kinds of regularization (e.g. Tikhonov or sparsity regularization) have been imposed into NMF to well-define the model. Different from the general regularization, we introduce the entropy regularization into the NMF and propose an entropy regularized NMF (ERNMF) model for HU. In ERNMF, we minimize the entropy of that abundances on each pixel, which can achieve the sparsity of abundances. We also introduce a strategy to adaptively adjust the regularization parameter. In addition, we explore the proposed ERNMF with two optimization algorithms and provide the corresponding convergence and complexity analysis. Experimental results on both simulated and real-world data sets demonstrate the effectiveness of our proposed model and algorithms in comparison to the state-of-the-art approaches.

Using a Panchromatic Image to Improve Hyperspectral Unmixing

Hyperspectral unmixing is a widely studied field of research aiming at estimating the pure material signatures and their abundance fractions from hyperspectral images. Most spectral unmixing methods are based on prior knowledge and assumptions that induce limitations, such as the existence of at least one pure pixel for each material. This work presents a new approach aiming to overcome some of these limitations by introducing a co-registered panchromatic image in the unmixing process. Our method, called Heterogeneity-Based Endmember Extraction coupled with Local Constrained Non-negative Matrix Factorization (HBEE-LCNMF), has several steps: a first set of endmembers is estimated based on a heterogeneity criterion applied on the panchromatic image followed by a spectral clustering. Then, in order to complete this first endmember set, a local approach using a constrained non-negative matrix factorization strategy, is proposed. The performance of our method, in regards of several criteria, is compared to those of state-of-the-art methods obtained on synthetic and satellite data describing urban and periurban scenes, and considering the French HYPXIM/HYPEX2 mission characteristics. The synthetic images are built with real spectral reflectances and do not contain a pure pixel for each endmember. The satellite images are simulated from airborne acquisition with the spatial and spectral features of the mission. Our method demonstrates the benefit of a panchromatic image to reduce some well-known limitations in unmixing hyperspectral data. On synthetic data, our method reduces the spectral angle between the endmembers and the real material spectra by 46% compared to the Vertex Component Analysis (VCA) and N-finder (N-FINDR) methods. On real data, HBEE-LCNMF and other methods yield equivalent performance, but, the proposed method shows more robustness over the data sets compared to the tested state-of-the-art methods. Moreover, HBEE-LCNMF does not require one to know the number of endmembers.

Fluvial gravel bar mapping with spectral signal mixture analysis

ABSTRACT The paper presents a method for mapping fluvial gravel bars based on Sentinel-2 and Landsat imagery. The proposed method therefore uses spectral signal mixture analysis (SSMA) because its results allow the development of land cover fraction maps for surface water, gravel, and vegetation. The method is validated on a spatially heterogeneous mountainous area in the upper Soča river basin in north-west Slovenia, Central Europe. Unmixing results in highly accurate fraction maps with MAE of around 0.1. Gravel fractions are mapped the most accurately, indicating that the approach can be used successfully for fluvial gravel bar mapping. Endmember sets selected automatically perform slightly worse (MAE higher by at most 0.05) than sets selected manually based on high resolution reference data. Both Sentinel-2 and Landsat imagery can be used for accurate mapping with differences between the two remote sensing systems within 0.05 MAE. For the study area, the SSMA-based soft classification method is more accurate for land cover mapping than a Spectral Angle Mapping-based hard classification. The method is promising for an effective use in other cases where highly accurate subpixel information is needed, because it is able to detect small-scale changes that could go unnoticed with hard classification mapping.

Super-resolution mapping of hyperspectral data using Artificial Neural Network and wavelet

Hyperspectral images are characterized by high spectral but moderate spatial resolution and are therefore contains mixed pixels. Hyperspectral is capable of detecting the type of material represented by endmembers by utilizing the unique absorption dip in the reflected wavelength spectra. The quantification of present endmembers in mixed pixel has been investigated widely in the recent times. This quantification is known as Hyperspectral unmixing which also refers to the decomposition of these mixed pixels into the set of endmembers and abundance fractions. Estimation of abundance fraction has often been solved based on the linear mixing model because of their simplicity while on many occasions non-linear spectral unmixing has been utilized to enhance the simulation of spectral mixing. In this study, we have proposed a novel approach (cum algorithm) to super resolved the fractional images (generated through spectral unmixing). We have used Artificial Neural Network (ANN) coupled with wavelet, that decomposes the images into different level of frequencies. These frequency components are further fed to ANN to learn the network. A learned network is then used to predict coarser and finer features separately thereby preserving the smaller features and produces a better representation of higher resolution map. The accuracy of the super-resolved map was compared using a high resolution image. Object characterization is adopted for metric accuracy measure and positional accuracy for spatial consistency. We also performed metric comparison for few features in original image, high resolution image (obtained from Google Earth image at best resolution) and super-resolved image. We found the algorithm is performing very well for comparatively larger features and satisfactory for others. We also found the very good metric accuracy and positional accuracy to represent the features in super-resolved images. The results shows, features are better represented in super-resolved image than original image when compared their dimensions with high resolution Google Earth image. Since we have degraded the original image to collect the training data so this approach may not be suitable for small features however performing very well for relatively bigger features.

AVIRIS-NG hyperspectral data analysis for pre- and post-MNF transformation using per-pixel classification algorithms

The hyperspectral image such as AVIRIS-NG provides a lot of spectral information and fine resolution that identify and discriminate similar objects based on their spectral reflectance. This study reveals a comparative analysis of multiple classification algorithms for AVIRIS-NG data, before and after minimum noise fraction (MNF) transformation for land use land cover classification. Applied distance methods are entirely based upon the availability of a complete set of endmembers for the data and used to classify the pixels in terms of endmembers. Applied classifiers yield more accurate results especially in terms of the overall accuracy after dimensionality reduction. As a result, minimum distance achieved highest 97.76% overall accuracy with a Kappa coefficient of 0.97, whereas Mahalanobis distance yields more precise results before MNF with 95.34% overall accuracy and a Kappa coefficient of 0.94. This study also indicates the importance of data dimensionality reduction for hyperspectral imagery.

Spectral Mixture Model Inspired Network Architectures for Hyperspectral Unmixing

In many statistical hyperspectral unmixing approaches, the unmixing task is essentially an optimization problem given a defined linear or nonlinear spectral mixture model. However, most of the model inference algorithms require a time-consuming iterative procedure. On the other hand, neural networks have been recently used to estimate abundances given some training samples, or directly estimate endmembers and abundances simultaneously in an unsupervised setting. However, their disadvantages are clear: lack of interpretability and reliance on the large training set. Model-inspired neural networks are constructed by the problem model and its corresponding inference algorithm. It incorporates the prior knowledge of physical model and algorithm into network architecture, combining the advantages of model-based and learning-based methods. This article deeply unfolds the linear mixture model and the corresponding iterative shrinkage-thresholding algorithm (ISTA) to build two unmixing network architectures. The first assumes that the set of endmembers are known, and the deep unfolded ISTA model is only for abundance estimation; and the second is used for blind unmixing to estimate both endmembers and abundances at the same time. The networks can be trained by supervised and unsupervised schemes, respectively, with a small-size training set, and then, unmixing becomes a feedforward process, which is very fast since no iteration is required. The experimental results show their competitive performance compared with the state-of-the-art unmixing approaches.

Nonlocal Low-Rank Abundance Prior for Compressive Spectral Image Fusion

Compressive spectral imaging (SI) (CSI) acquires few random projections of an SI reducing acquisition, storage, and, in some cases, processing costs. Then, this acquisition framework has been widely used in various tasks, such as target detection, video processing, and fusion. Particularly, compressive spectral image fusion (CSIF) aims at obtaining a high spatial-spectral resolution SI from two sets of compressed measurements: one from a hyperspectral image with a high-spectral low-spatial resolution, and one from a multispectral image with high-spatial low-spectral resolution. Most of the literature approaches include prior information, such as global low rank, smoothness, and sparsity, to solve the resulting ill-posed CSIF inverse problem. More recently, the high self-similarities exhibited by SIs have been successfully used to improve the performance of CSI inverse problems, including a nonlocal low-rank (NLLR) prior. However, to the best of our knowledge, this NLLR prior has not been implemented in the solution of the CSIF inverse problem. Therefore, this article formulates an approach that jointly includes the global low rank, the smoothness, and the NLLR priors to solve the CSIF inverse problem. The global low-rank prior is introduced with the linear mixture model that describes the SI as a linear combination of a set of few end-members to specific abundances. In this article, either the end-members are accurately estimated from the compressed measurements or initialized from a fast reconstruction of the hyperspectral image. Also, it assumes that the abundances preserve the smoothness and NLLR priors of the SI so that the fused image is obtained from the end-members and abundances that result when minimizing a cost function including the sum of two data fidelity terms and two regularizations: the smoothness and the NLLR. Simulations over three data sets show that the proposed approach increases the CSIF performance compared with literature approaches.

Simultaneously Counting and Extracting Endmembers in a Hyperspectral Image Based on Divergent Subsets

Most existing endmember extraction techniques require prior knowledge about the number of endmembers in a hyperspectral image. The number of endmembers is normally estimated by a separate procedure, whose accuracy has a large influence on the endmember extraction performance. In order to bridge the two seemingly independent but, in fact, highly correlated procedures, we develop a new endmember estimation strategy that simultaneously counts and extracts endmembers. We consider a hyperspectral image as a hyperspectral pixel set and define the subset of pixels that are most different from one another as the divergent subset (DS) of the hyperspectral pixel set. The DS is characterized by the condition that any additional pixel would increase the likeness within the DS and, thus, reduce its divergent degree. We use the DS as the endmember set, with the number of endmembers being the subset cardinality. To render a practical computation scheme for identifying the DS, we reformulate it in terms of a quadratic optimization problem with a numerical solution. In addition to operating as an endmember estimation algorithm by itself, the DS method can also co-operate with existing endmember extraction techniques by transforming them into a novel and more effective schemes. Experimental results validate the effectiveness of the DS methodology in simultaneously counting and extracting endmembers not only as an individual algorithm but also as a foundation algorithm for improving existing methods. Our full code is released for public evaluation. 1 1 https://github.com/xuanwentao/DivergentSubset

Spatially Enhanced Spectral Unmixing Through Data Fusion of Spectral and Visible Images from Different Sensors

We propose an unmixing framework for enhancing endmember fraction maps using a combination of spectral and visible images. The new method, data fusion through spatial information-aided learning (DFuSIAL), is based on a learning process for the fusion of a multispectral image of low spatial resolution and a visible RGB image of high spatial resolution. Unlike commonly used methods, DFuSIAL allows for fusing data from different sensors. To achieve this objective, we apply a learning process using automatically extracted invariant points, which are assumed to have the same land cover type in both images. First, we estimate the fraction maps of a set of endmembers for the spectral image. Then, we train a spatial-features aided neural network (SFFAN) to learn the relationship between the fractions, the visible bands, and rotation-invariant spatial features for learning (RISFLs) that we extract from the RGB image. Our experiments show that the proposed DFuSIAL method obtains fraction maps with significantly enhanced spatial resolution and an average mean absolute error between 2% and 4% compared to the reference ground truth. Furthermore, it is shown that the proposed method is preferable to other examined state-of-the-art methods, especially when data is obtained from different instruments and in cases with missing-data pixels.

Analyses of Namibian Seasonal Salt Pan Crust Dynamics and Climatic Drivers Using Landsat 8 Time-Series and Ground Data

Salt pans are highly dynamic environments that are difficult to study by in situ methods because of their harsh climatic conditions and large spatial areas. Remote sensing can help to elucidate their environmental dynamics and provide important constraints regarding their sedimentological, mineralogical, and hydrological evolution. This study utilizes spaceborne multitemporal multispectral optical data combined with spectral endmembers to document spatial distribution of surface crust types over time on the Omongwa pan located in the Namibian Kalahari. For this purpose, 49 surface samples were collected for spectral and mineralogical characterization during three field campaigns (2014–2016) reflecting different seasons and surface conditions of the salt pan. An approach was developed to allow the spatiotemporal analysis of the salt pan crust dynamics in a dense time-series consisting of 77 Landsat 8 cloud-free scenes between 2014 and 2017, covering at least three major wet–dry cycles. The established spectral analysis technique Sequential Maximum Angle Convex Cone (SMACC) extraction method was used to derive image endmembers from the Landsat time-series stack. Evaluation of the extracted endmember set revealed that the multispectral data allowed the differentiation of four endmembers associated with mineralogical mixtures of the crust’s composition in dry conditions and three endmembers associated with flooded or muddy pan conditions. The dry crust endmember spectra have been identified in relation to visible, near infrared, and short-wave infrared (VNIR–SWIR) spectroscopy and X-ray diffraction (XRD) analyses of the collected surface samples. According these results, the spectral endmembers are interpreted as efflorescent halite crust, mixed halite–gypsum crust, mixed calcite quartz sepiolite crust, and gypsum crust. For each Landsat scene the spatial distribution of these crust types was mapped with the Spectral Angle Mapper (SAM) method and significant spatiotemporal dynamics of the major surface crust types were observed. Further, the surface crust dynamics were analyzed in comparison with the pan’s moisture regime and other climatic parameters. The results show that the crust dynamics are mainly driven by flooding events in the wet season, but are also influenced by temperature and aeolian activity in the dry season. The approach utilized in this study combines the advantages of multitemporal satellite data for temporal event characterization with advantages from hyperspectral methods for the image and ground data analyses that allow improved mineralogical differentiation and characterization.

A manifold Hessian-regularized NMF for hyperspectral data unmixing

ABSTRACTHyperspectral unmixing (HU) has drawn remarkable attention because it can decompose mixed pixels into a set of endmembers and abundance fractions. And the nonnegative matrix factorization (NMF) algorithm has been widely used for solving hyperspectral spectral unmixing problem. This letter proposes a Hessian graph regularized NMF (HGNMF) algorithm, which relies upon the construction of a Hessian graph representation, to solve the hyperspectral unmixing problem. According to the HGNMF algorithm, the smoothness in the estimated abundance maps is well promoted. Moreover, the optimized problem of HGNMF algorithm is also solved by employing the multiplicative updating rules. Compared to other algorithms, the proposed HGNMF algorithm demonstrates lots of advantages based on the simulated results of the synthetic data and real data sets.