Unmixing Of Hyperspectral Data Research Articles

Wavelets Based Simulation and Visualization Approach for Unmixing of Hyperspectral Data

This paper discusses the use of wavelet based simulation and visualization methods to unmix multi-component, intimate, and particulate mixtures. We describe a new approach to simulate the hyperspectral data based on an interpolating wavelet estimation. We choose a very constructive family of a wavelet basis, Duabechies wavelets, of order one and two to analyze the data. We used the discrete wavelet transform (DWT), which the basic tool needed for studying time series via wavelets and plays a role analogue in the theory of spectral analysis. The present paper present parameters and algorithms that successfully simulate the binary system of Na2SO4-MgSO4. This system was selected because of it is importance to us on analogue for Mars salt and salt regolith.

A Phenological Approach to Spectral Differentiation of Low-Arctic Tundra Vegetation Communities, North Slope, Alaska

Arctic tundra ecosystems exhibit small-scale variations in species composition, micro-topography as well as significant spatial and temporal variations in moisture. These attributes result in similar spectral characteristics between distinct vegetation communities. In this study we examine spectral variability at three phenological phases of leaf-out, maximum canopy, and senescence of ground-based spectroscopy, as well as a simulated Environmental Mapping and Analysis Program (EnMAP) and simulated Sentinel-2 reflectance spectra, from five dominant low-Arctic tundra vegetation communities in the Toolik Lake Research Area, Alaska, in order to inform spectral differentiation and subsequent vegetation classification at both the ground and satellite scale. We used the InStability Index (ISI), a ratio of between endmember and within endmember variability, to determine the most discriminative phenophase and wavelength regions for identification of each vegetation community. Our results show that the senescent phase was the most discriminative phenophase for the identification of the majority of communities when using both ground-based and simulated EnMAP reflectance spectra. Maximum canopy was the most discriminative phenophase for the majority of simulated Sentinel-2 reflectance data. As with previous ground-based spectral characterization of Alaskan low-Arctic tundra, the blue, red, and red-edge parts of the spectrum were most discriminative for all three reflectance datasets. Differences in vegetation colour driven by pigment dynamics appear to be the optimal areas of the spectrum for differentiation using high spectral resolution field spectroscopy and simulated hyperspectral EnMAP and multispectral Sentinel-2 reflectance spectra. The phenological aspect of this study highlights the potential exploitation of more extreme colour differences in vegetation observed during senescence when hyperspectral data is available. The results provide insight into both the community and seasonal dynamics of spectral variability to better understand and interpret currently used broadband vegetation indices and also for improved spectral unmixing of hyperspectral aerial and satellite data which is useful for a wide range of applications from fine-scale monitoring of shifting vegetation composition to the identification of vegetation vigor.

Spectral and stratigraphic mapping of hydrated minerals associated with interior layered deposits near the southern wall of Melas Chasma, Mars

Orbital remote sensing data acquired from the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) onboard Mars Reconnaissance Orbiter (MRO), in conjunction with other datasets, are used to perform detailed spectral and stratigraphic analyses over a portion of south Melas Chasma, Mars. The Discrete Ordinate Radiative Transfer (DISORT) model is used to retrieve atmospherically corrected single scattering albedos from CRISM I/F data for mineral identification. A sequence of interbedded poly- and monohydrated sulfates associated with interior layered deposits (ILDs) is identified and mapped. Analyses from laboratory experiments and spectral unmixing of CRISM hyperspectral data support the hypothesis of precipitation and dehydration of multiple inputs of complex Mg-Ca-Fe-SO4-Cl brines. In this scenario, the early precipitated Mg sulfates could dehydrate into monohydrated sulfate due to catalytic effects, and the later-precipitated Mg sulfates from the late-stage “clean” brine could terminate their dehydration at mid-degree of hydration to form a polyhydrated sulfate layer due to depletion of the catalytic species (e.g., Ca, Fe, and Cl). Distinct jarosite-bearing units are identified stratigraphically above the hydrated sulfate deposits. These are hypothesized to have formed either by oxidation of a fluid containing Fe(II) and SO4, or by leaching of soluble phases from precursor intermixed jarosite-Mg sulfate units that may have formed during the later stages of deposition of the hydrated sulfate sequence. Results from stratigraphic analysis of the ILDs show that the layers have a consistent northward dip towards the interior of the Melas Chasma basin, a mean dip angle of ∼6°, and neighboring strata that are approximately parallel. These strata are interpreted as initially sub-horizontal layers of a subaqueous, sedimentary evaporite deposits that underwent post-depositional tilting from slumping into the Melas Chasma basin. The interbedded hydrated sulfate units and jarosite-bearing units, which have distinct stratigraphic relationships, are indicative of a complex sedimentary and aqueous history in south Melas Chasma.

Unmixing of large-scale hyperspectral data based on projected mini-batch gradient descent

The minimization problem of reconstruction error over large hyperspectral image data is one of the most important problems in unsupervised hyperspectral unmixing. A variety of algorithms based on nonnegative matrix factorization (NMF) have been proposed in the literature to solve this minimization problem. One popular optimization method for NMF is the projected gradient descent (PGD). However, as the algorithm must compute the full gradient on the entire dataset at every iteration, the PGD suffers from high computational cost in the large-scale real hyperspectral image. In this paper, we try to alleviate this problem by introducing a mini-batch gradient descent-based algorithm, which has been widely used in large-scale machine learning. In our method, the endmember can be updated pixel set by pixel set while abundance can be updated band set by band set. Thus, the computational cost is lowered to a certain extent. The performance of the proposed algorithm is quantified in the experiment on synthetic and real data.

DISTRIBUTED UNMIXING OF HYPERSPECTRAL DATAWITH SPARSITY CONSTRAINT

Abstract. Spectral unmixing (SU) is a data processing problem in hyperspectral remote sensing. The significant challenge in the SU problem is how to identify endmembers and their weights, accurately. For estimation of signature and fractional abundance matrices in a blind problem, nonnegative matrix factorization (NMF) and its developments are used widely in the SU problem. One of the constraints which was added to NMF is sparsity constraint that was regularized by L1/2 norm. In this paper, a new algorithm based on distributed optimization has been used for spectral unmixing. In the proposed algorithm, a network including single-node clusters has been employed. Each pixel in hyperspectral images considered as a node in this network. The distributed unmixing with sparsity constraint has been optimized with diffusion LMS strategy, and then the update equations for fractional abundance and signature matrices are obtained. Simulation results based on defined performance metrics, illustrate advantage of the proposed algorithm in spectral unmixing of hyperspectral data compared with other methods. The results show that the AAD and SAD of the proposed approach are improved respectively about 6 and 27 percent toward distributed unmixing in SNR=25dB.

Hybrid Spectral Unmixing: Using Artificial Neural Networks for Linear/Non-Linear Switching

Spectral unmixing is a key process in identifying spectral signature of materials and quantifying their spatial distribution over an image. The linear model is expected to provide acceptable results when two assumptions are satisfied: (1) The mixing process should occur at macroscopic level and (2) Photons must interact with single material before reaching the sensor. However, these assumptions do not always hold and more complex nonlinear models are required. This study proposes a new hybrid method for switching between linear and nonlinear spectral unmixing of hyperspectral data based on artificial neural networks. The neural networks was trained with parameters within a window of the pixel under consideration. These parameters are computed to represent the diversity of the neighboring pixels and are based on the Spectral Angular Distance, Covariance and a non linearity parameter. The endmembers were extracted using Vertex Component Analysis while the abundances were estimated using the method identified by the neural networks (Vertex Component Analysis, Fully Constraint Least Square Method, Polynomial Post Nonlinear Mixing Model or Generalized Bilinear Model). Results show that the hybrid method performs better than each of the individual techniques with high overall accuracy, while the abundance estimation error is significantly lower than that obtained using the individual methods. Experiments on both synthetic dataset and real hyperspectral images demonstrated that the proposed hybrid switch method is efficient for solving spectral unmixing of hyperspectral images as compared to individual algorithms.

Sparsity-Based Unsupervised Unmixing of Hyperspectral Imaging Data Using Basis Pursuit

Sparsity-Based Unsupervised Unmixing of Hyperspectral Imaging Data Using Basis Pursuit

RCMF: Robust Constrained Matrix Factorization for Hyperspectral Unmixing

We propose a constrained matrix factorization approach for linear unmixing of hyperspectral data. Our approach factorizes a hyperspectral cube into its constituent endmembers and their fractional abundances such that the endmembers are sparse nonnegative linear combinations of the observed spectra themselves. The association between the extracted endmembers and the observed spectra is explicitly noted for physical interpretability. To ensure reliable unmixing, we make the matrix factorization procedure robust to outliers in the observed spectra. Our approach simultaneously computes the endmembers and their abundances in an efficient and unsupervised manner. The extracted endmembers are nonnegative quantities, whereas their abundances additionally follow the sum-to-one constraint. We thoroughly evaluate our approach using synthetic data with white and correlated noise as well as real hyperspectral data. Experimental results establish the effectiveness of our approach.

Multilayer NMF for Blind Unmixing of Hyperspectral Imagery with Additional Constraints

Due to the coincidence of hyperspectral reflectance nonnegativity (and its corresponding abundance) with nonnegative matrix factorization (<small>NMF</small>) methods, <small>NMF</small> has been widely applied to unmix hyperspectral images in recent years. However, many local minima persist because of the nonconvexity of the objective function. Thus, the nonnegativity constraint is not sufficient and additional auxiliary constraints should be applied to objective functions. In this paper, a new approach we call constrained multilayer <small>NMF</small> (<small>CMLNMF</small>), is proposed for hyperspectral data. In this approach, the mixed spectra are regarded as endmember signatures that has been contaminated by multiplicative noise. The purpose of <small>CMLNMF</small> is to eliminate noise by hierarchical processing until the endmember spectra are obtained. Also, the hierarchical processing is self-adaptive to make the algorithm more effective. Furthermore, in each layer two constraints are implemented on the objective function. One is sparseness on the abundance matrix and the other is minimum volume on the spectral matrix. The hierarchical processing separates the abundance matrix into a series of matrices that make the characteristic of sparseness more obvious and meaningful. The proposed algorithm is applied to synthetic data and real hyperspectral data for quantitative evaluation. According to the comparison with other algorithms, <small>CMLNMF</small> has better performance and provides effective solutions for blind unmixing of hyperspectral image data.

A Multiobjective Cooperative Coevolutionary Algorithm for Hyperspectral Sparse Unmixing

Sparse unmixing of hyperspectral data is an important technique aiming at estimating the fractional abundances of the endmembers. Traditional sparse unmixing is faced with the $\boldsymbol {l_{0}}$ -norm problem which is an NP-hard problem. Sparse unmixing is inherently a multiobjective optimization problem. Most of the recent works combine cost functions into single one to construct an aggregate objective function, which involves weighted parameters that are sensitive to different data sets and difficult to tune. In this paper, a novel multiobjective cooperative coevolutionary algorithm is proposed to optimize the reconstruction term, the sparsity term and the total variation regularization term simultaneously. A problem-dependent cooperative coevolutionary strategy is designed because sparse unmixing encounters a large scale optimization problem. The proposed approach optimizes the nonconvex $\boldsymbol {l_{0}}$ -norm problem directly and can find a better compromise between two or more competing cost function terms automatically. Experimental results on simulated and real hyperspectral data sets demonstrate the effectiveness of the proposed method.

Robust Sparse Hyperspectral Unmixing With $\ell_{2,1}$ Norm

Sparse unmixing (SU) of hyperspectral data have recently received particular attention for analyzing remote sensing images, which aims at finding the optimal subset of signatures to best model the mixed pixel in the scene. However, most SU methods are based on the commonly admitted linear mixing model, which ignores the possible nonlinear effects (i.e., nonlinearity), and the nonlinearity is merely treated as outlier. Besides, the traditional SU algorithms often adopt the $\ell _{2}$ norm loss function, which makes them sensitive to noises and outliers. In this paper, we propose a robust SU (RSU) method with $\ell _{2,1}$ norm loss function, which is robust for noises and outliers. Then, the RSU can be solved by the alternative direction method of multipliers. Finally, the experiments on both synthetic data sets and real hyperspectral images demonstrate that the proposed RSU is efficient for solving the hyperspectral SU problem compared with the state-of-the-art algorithms.

Nonlinear Unmixing of Hyperspectral Data With Vector-Valued Kernel Functions.

This paper presents a kernel-based nonlinear mixing model for hyperspectral data, where the nonlinear function belongs to a Hilbert space of vector valued functions. The proposed model extends the existing ones by accounting for band-dependent and neighboring nonlinear contributions. The key idea is to work under the assumption that nonlinear contributions are dominant in some parts of the spectrum, while they are less pronounced in other parts. In addition to this, we motivate the need for taking into account nonlinear contributions originating from the ground covers of neighboring pixels by practical considerations, precisely the adjacency effect. The relevance of the proposed model is that the nonlinear function is associated with a matrix valued kernel that allows to jointly model a wide range of nonlinearities and includes prior information regarding band dependences. Furthermore, the choice of the nonlinear function input allows to incorporate neighboring effects. The optimization problem is strictly convex and the corresponding iterative algorithm is based on the alternating direction method of multipliers. Finally, experiments conducted using synthetic and real data demonstrate the effectiveness of the proposed approach.

Endmember initialization method for hyperspectral data unmixing

Spectral unmixing aims at finding the spectrally pure constituent materials (also called endmembers) and their respective fractional abundances in each pixel of the hyperspectral image scene. One important issue in hyperspectral data unmixing is the initialization of endmembers. Most unmixing methods initialize their endmembers by randomly selecting a specified number of pixels from the data or by vertex component analysis, which limits their performance in practice. We propose an endmember initialization method for hyperspectral data unmixing. Our initial endmembers include some of the true endmembers, which improves the accuracy of hyperpspectral unmixing effectively. The experimental results on both synthetic and real hyperspectral data illustrate the superiority of the proposed method compared with other state-of-the-art approaches.

Hyperspectral Unmixing with Robust Collaborative Sparse Regression

Recently, sparse unmixing (SU) of hyperspectral data has received particular attention for analyzing remote sensing images. However, most SU methods are based on the commonly admitted linear mixing model (LMM), which ignores the possible nonlinear effects (i.e., nonlinearity). In this paper, we propose a new method named robust collaborative sparse regression (RCSR) based on the robust LMM (rLMM) for hyperspectral unmixing. The rLMM takes the nonlinearity into consideration, and the nonlinearity is merely treated as outlier, which has the underlying sparse property. The RCSR simultaneously takes the collaborative sparse property of the abundance and sparsely distributed additive property of the outlier into consideration, which can be formed as a robust joint sparse regression problem. The inexact augmented Lagrangian method (IALM) is used to optimize the proposed RCSR. The qualitative and quantitative experiments on synthetic datasets and real hyperspectral images demonstrate that the proposed RCSR is efficient for solving the hyperspectral SU problem compared with the other four state-of-the-art algorithms.

GEOLOGICAL MAPPING BY COMBINING SPECTRAL UNMIXING AND CLUSTER ANALYSIS FOR HYPERSPECTRAL DATA

Spectral unmixing of hyperspectral data often fails to select some minerals and rocks having flat spectra but no diagnostic absorption features as endmembers, even if they are actually important endmembers. To avoid this problem, we propose a novel approach that combined two methods: spectral unmixing and full-pixel classification. First, all pixels were divided into two categories, hydrothermally altered areas and unaltered rocks based on the absorption depth of 2.0 to 2.5 μm. For the hydrothermally altered areas, endmembers were extracted by the Improved Causal Random Pixel Purity Index (ICRPPI) method, which was improved from the existing Pixel Purity Index (PPI) and Causal Random Pixel Purity Index (CRPPI) methods. Endmember abundance in each pixel was calculated by linear spectral unmixing. In a separate operation, k-means clustering was applied to the unaltered rock areas. Finally, the results of these two methods were combined to generate a single distribution map of rocks and minerals. This approach was applied to the airborne hyperspectral HyMap data of Cuprite, Nevada, U.S.A. We confirmed that our mapping result was consistent with the existing geological map as well as our field survey result.

GEOLOGICAL MAPPING BY COMBINING SPECTRAL UNMIXING AND CLUSTER ANALYSIS FOR HYPERSPECTRAL DATA

Abstract. Spectral unmixing of hyperspectral data often fails to select some minerals and rocks having flat spectra but no diagnostic absorption features as endmembers, even if they are actually important endmembers. To avoid this problem, we propose a novel approach that combined two methods: spectral unmixing and full-pixel classification. First, all pixels were divided into two categories, hydrothermally altered areas and unaltered rocks based on the absorption depth of 2.0 to 2.5 μm. For the hydrothermally altered areas, endmembers were extracted by the Improved Causal Random Pixel Purity Index (ICRPPI) method, which was improved from the existing Pixel Purity Index (PPI) and Causal Random Pixel Purity Index (CRPPI) methods. Endmember abundance in each pixel was calculated by linear spectral unmixing. In a separate operation, k-means clustering was applied to the unaltered rock areas. Finally, the results of these two methods were combined to generate a single distribution map of rocks and minerals. This approach was applied to the airborne hyperspectral HyMap data of Cuprite, Nevada, U.S.A. We confirmed that our mapping result was consistent with the existing geological map as well as our field survey result.

A Comparison Study of ORASIS and VCA for Mineralogical Unmixing of Hyperspectral Data

Hyperspectral datasets are usually composed of different pure materials or endmembers. Endmember extraction is the most challenging stage in the spectral unmixing procedure. In the case of mineral detection studies, due to the absence of pure pixels for some constituent minerals, the common methods based on pure pixel assumption do not yield accurate results. The current study aims to evaluate the efficiency of ORASIS in endmember determination. ORASIS is a collection of stepwise algorithms working together to produce a set of endmembers not necessarily included in the dataset. The ORASIS method was applied to estimate the endmembers of three hyperspectral dataset series: 1) highly mixed synthetic dataset with maximum purity of 0.48 %, 2) AVIRIS dataset of Cuprite, Nevada, 3) Hyperion dataset of the Dost-Bayli area, Ardabil. SAM and SFF techniques were used to identify the unknown endmembers by comparison of them with USGS spectral library. The functionality of the VCA and PPI as pure pixel-based approaches were also investigated along with ORASIS. The number of estimated endmembers of ORASIS that were appropriately matched with reference spectra was more than VCA and PPI so that majority of detected minerals are present in the study areas. So, it can be inferred that ORASIS generally outperforms the VCA and PPI. The Linear Spectral Unmixing algorithm was implemented for demixing of the Cuprite and Dost-Bayli datasets; and abundances maps were generated using mapping methods. The results highly correspond to the geological, geochemical and mineralogical reports of both regions.

Fast Spatial Preprocessing for Spectral Unmixing of Hyperspectral Data on Graphics Processing Units

Spectral unmixing is an important technique for hyperspectral data exploitation. It amounts at finding a set of pure spectral signatures (endmembers) of the most representative materials in the scene, and estimating their abundance fractions. The integration of spatial information prior to spectral unmixing of hyperspectral data has attracted much attention in recent years. Several approaches have been developed for the purpose of guiding endmember identification algorithms to spatially representative, yet spectrally pure endmembers. In particular, the spatial preprocessing (SPP) algorithm can be used prior to most existing spectral-based endmember identification techniques, thus promoting the selection of endmembers in spatially representative areas of the scene. However, most SPP techniques are computationally expensive, which adds significant burden to the spectral unmixing process. In this paper, we present three parallel implementations of SPP that have been specifically developed for commodity graphics processing units (GPUs). We perform an evaluation of these techniques using two GPU architectures from NVidia: GeForce GTX 580 and GeForce GTX 870M, which reveals that real-time processing performance can be obtained for real hyperspectral data sets collected by the airborne visible infra-red imaging spectrometer (AVIRIS).

Uncertainties in Unmixing of Multi-phase Hyperspectral Data in Reflective Region: Effects of Texture and Fabric

The Linear Mixing Model (LMM), based on the assumption of single scattering of light is the most preferred approach to unmix (interpret) hyperspectral data due to its simplicity in implementation. However, in most of the natural situations, the reflection process involves multiple scattering and hence, LMM is not very effective. Therefore, nonlinear spectral unmixing model based on Radiative Transfer Equation (RTE) is necessary to understand the influencing factors and effects associated with shadowing or multiple scattering. The reflected spectrum of two juxtaposed materials is the linear sum of the two individual absorption spectra. However, light reflected off an intimate mixture of particles exhibits a spectra that is a nonlinear combination of the two individual spectra. In this work, we have studied the influence of texture (grain size) and fabric (patterns) on reflectance spectra using RTE based nonlinear unmixing model. For this purpose, three types of geological materials namely basalt, anorthosite, and quartzite representing high, moderate and low albedos were used. Multi-phase reflectance spectra of these rocks were acquired in varying combinations of grain size (2-4 mm, 1-2 mm, and <1mm) and patterns. The complexity of fabric was progressively increased from a three-boundary case to intimate mixture. Bi-directional reflectance spectra for different phase angles were collected using a spectroradiometer mounted on a goniometer setup. Subsequently, salient parameters addressing nonlinearity in Hapke model such as phase function, opposition effect, type of scattering for each combination of texture and fabric were estimated from the iteratively modeled spectra. The condition adopted to evaluate the modeling efficacy is the root mean square error (RMSE) between the measured and modeled spectra. When the desired RMSE (<0.01) is achieved, the iteration process is stopped and Hapke parameters corresponding to the best-fit model were retrieved. Analyses of results indicate that grain size, shape, and the fabric cumulatively influence the Hapke parameters such as Bo, b, and c. This clearly indicates that texture and fabric influence the basic physical properties of light scattering namely opposition effect, phase function, and forward/backward scattering property.

Optimizing the Endmembers Using Volume Invariant Constrained Model.

The linear mixture model (LMM) plays a crucial role in the spectral unmixing of hyperspectral data. Under the assumption of LMM, the solution with the minimum reconstruction error is considered to be the ideal endmember. However, for practical hyperspectral data sets, endmembers that enclose all the pixels are physically meaningless due to the effect of noise. Therefore, in many cases, it is not sufficient to consider only the reconstruction error, some constraints (for instance, volume constraint) need to be added to the endmembers. The two terms can be considered as serving two forces: minimizing the reconstruction error forces the endmembers to move outward and thus enlarges the volume of the simplex while the endmember constraint acts in the opposite direction by driving the endmembers to move inward so as to constrain the volume to be smaller. Many existing methods obtain their solution just by balancing the two contradictory forces. The solution acquired in this way can not only minimize the reconstruction error but also be physically meaningful. Interestingly, we find, in this paper, that the two forces are not completely contradictory with each other, and the reconstruction error can be further reduced without changing the volume of the simplex. And more interestingly, our method can further optimize the solution provided by all the endmember extraction methods (both endmember selection methods and endmember generation methods). After optimization, the final endmembers outperform the initial solution in terms of reconstruction error as well as accuracy. The experiments on simulated and real hyperspectral data verify the validation of our method.