Unmixing Of Hyperspectral Data Research Articles

Structured low-rank representation learning for hyperspectral sparse unmixing

ABSTRACT Sparse unmixing methods have been widely used to estimate the abundance of each material component from hyperspectral images. However, conventional sparse unmixing approaches only consider matrix factorization without limited explorations on the high-dimensional structures of the third-order tensors. To address this issue, we propose SUnSLRR, a novel approach to sparse unmixing of hyperspectral data based on structured low-rank tensor modelling. In contrast to traditional methods, SUnSLRR leverages the low-rank property underlying the abundance tensor to exploit structural details from multiple modes. By incorporating sparsity regularization and a low-rank constraint, SUnSLRR can effectively extract the intrinsic features of hyperspectral data. We apply the alternating direction method of multipliers framework to solve the optimization problem induced by SUnSLRR, and experiments conducted on simulated and real hyperspectral images demonstrate the superior effectiveness of our proposed method compared to traditional methods in terms of both accuracy and efficiency.

The Influence of Noise Intensity in the Nonlinear Spectral Unmixing of Hyperspectral Data

The Influence of Noise Intensity in the Nonlinear Spectral Unmixing of Hyperspectral Data

Selection of essential spectra to improve the multivariate curve resolution of minor compounds in complex pharmaceutical formulations

Multivariate curve resolution unmixing of hyperspectral imaging data can be challenging when low sources of variance are present in complex samples, as for minor (low-concentrated) chemical compounds in pharmaceutical formulations. In this work, it was shown how the reduction of hyperspectral imaging data matrices through the selection of essential spectra can be crucial for the analysis of complex unknown pharmaceutical formulation applying Multivariate Curve Resolution – Alternating Least Squares (MCR-ALS). Results were obtained on simulated datasets and on real FT-IR and Raman hyperspectral images of both genuine and falsified tablets. When simulating the presence of minor compounds, different situations were investigated considering the presence of single pixels of pure composition as well as binary and ternary mixtures. The comparison of the results obtained applying MCR-ALS on the reduced data matrices with those obtained on the full matrices revealed unequivocal: more accurate decomposition could be achieved when only essential spectra were analyzed. Indeed, when analyzing the full dataset, MCR-ALS failed resolving minor compounds even though pure spectra were provided as initial estimation, as shown for Raman hyperspectral imaging data obtained on a medicine sample containing 7 chemical compounds. In contrast, when considering the reduced dataset, all minor contributions (down to 1 pixel over 17,956) were successfully unmixed. The same conclusion could be drawn from the results obtained analysing FT-IR hyperspectral imaging data of a falsified medicine.

Semi-Supervised Unmixing of Hyperspectral Data via Spectral-Spatial Factorization

Due to the limited spatial resolution of hyperspectral sensors, each pixel in hyperspectral image often consists of several components, called endmembers. Hyperspectral unmixing aims at extracting these endmembers and corresponding fractional abundances from the hyperspectral image (HSI) data. With the availability of spectral libraries, semi-supervised unmixing which estimates the abundance from given endmember matrix, have become more and more popular. General semi-supervised methods take advantage of the sparsity constraint on the abundance matrix and consider the pixels as independent trials. However, the spatial information for example the correlation between pixels often cannot be taken into consideration. In this paper, we derive a semi-supervised hyperspectral image unmixing algorithm which handles both spectral and spatial prior efficiently using matrix factorization. The abundance matrix is recast as a multiplication of two variables, in which the spectral and spatial priors are captured respectively. Numerical tests in both simulated and real datasets show that compared to state-of-the-art unmixing algorithms, the proposed spectral-spatial factorization method has lower computation cost, better unmixing results, and is more robust to regularization parameter selection.

Improved minimum volume simplex analysis algorithm for unmixing of hyperspectral data

Some of the robust and high-ability processing methods like the improved Minimum Simplex Volume Analysis (MVSA) algorithm are generally time-consuming in hyperspectral data dealing especially the ground resolution is higher. In this research, MVSA was conducted for spectral analysis of HyMap and Hyperion data after a proposed data reduction to overcome the mentioned problem. The data cloud was therefore clustered based on the spectral angle mapper and Multi-Attribute Decision Making (MADM) based methods were used to determine the best threshold angle. Consequently, four indicators were applied as evaluation attributes for selecting the appropriate alternative, and “Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)” and “ELimination Et Choice Translating REality (ELECTRE)” were employed to finalize the decision. The methods resulted in 0.8 and 1.3 degrees as optimal spectral angles for HyMap and Hyperion, respectively. In this case, the image processing computational burden and the noise effect were considerably alleviated and the procedure led to accurate endmember identification.

Non-linear spectral unmixing of hyperspectral data using Modified PPNMM

Spectral unmixing is one of the unique advantages of hyperspectral images to map the type of species. Such images contain a high spectral resolution making it a classical problem of signal processing at each pixel, which is supposedly formed by the interaction of variously constituted end-members (also known as mixed pixels). Finding the abundance of any feature (or class or end-member) may require these mixed pixels to be unmixed through mixing models. This study proposes a linear mixing model and a non-linear mixing model combined for spectral unmixing and suggests a modified mixing model. We proposed linearly unmixed abundances to be used as prior probabilities for non-linear mixing models. We have applied these methods to synthetic data to check performance and robustness. Synthetic data was created using the reflectance spectra of various end-members collected in the study region through rigorous field surveys. Abundance accuracy, reconstruction accuracy, and other statistical measures were used to assess overall accuracy, with results showing that Modified PPNMM performs better than PPNMM and LMM. The performance outcome is further validated with a satellite dataset (hyperspectral data of Hyperion) with randomly distributed points.

Deep Autoencoders With Multitask Learning for Bilinear Hyperspectral Unmixing

Hyperspectral unmixing is an important problem for remotely sensed data interpretation. It amounts at estimating the spectral signatures of the pure spectral constituents in the scene (endmembers) and their corresponding subpixel fractional abundances. Although the unmixing problem is inherently nonlinear (due to multiple scattering), the nonlinear unmixing of hyperspectral data has been a very challenging problem. This is because nonlinear models require detailed knowledge about the physical interactions between the sunlight scattered by multiple materials. In turn, bilinear mixture models (BMMs) can reach good accuracy with a relatively simple model for scattering. In this article, we develop a new BMM and a corresponding unsupervised unmixing approach which consists of two main steps. In the first step, a deep autoencoder is used to linearly estimate the endmember signatures and their associated abundance fractions. The second step refines the initial (linear) estimates using a bilinear model, in which another deep autoencoder (with a low-rank assumption) is adapted to model second-order scattering interactions. It should be noted that in our developed BMM model, the two deep autoencoders are trained in a mutually interdependent manner under the multitask learning framework, and the relative reconstruction error is used as the stopping criterion. The effectiveness of the proposed method is evaluated using both synthetic and real hyperspectral data sets. Our experimental results indicate that the proposed approach can reasonably estimate the nature of nonlinear interactions in real scenarios. Compared with other state-of-the-art unmixing algorithms, the proposed approach demonstrates very competitive performance.

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.

Hierarchical Sparse Nonnegative Matrix Factorization for Hyperspectral Unmixing with Spectral Variability

Accounting for endmember variability is a challenging issue when unmixing hyperspectral data. This paper models the variability that is associated with each endmember as a conical hull defined by extremal pixels from the data set. These extremal pixels are considered as so-called prototypal endmember spectra that have meaningful physical interpretation. Capitalizing on this data-driven modeling, the pixels of the hyperspectral image are then described as combinations of these prototypal endmember spectra weighted by bundling coefficients and spatial abundances. The proposed unmixing model not only extracts and clusters the prototypal endmember spectra, but also estimates the abundances of each endmember. The performance of the approach is illustrated thanks to experiments conducted on simulated and real hyperspectral data and it outperforms state-of-the-art methods.

Attention-Based Residual Network with Scattering Transform Features for Hyperspectral Unmixing with Limited Training Samples

This paper proposes a framework for unmixing of hyperspectral data that is based on utilizing the scattering transform to extract deep features that are then used within a neural network. Previous research has shown that using the scattering transform combined with a traditional K-nearest neighbors classifier (STFHU) is able to achieve more accurate unmixing results compared to a convolutional neural network (CNN) applied directly to the hyperspectral images. This paper further explores hyperspectral unmixing in limited training data scenarios, which are likely to occur in practical applications where the access to large amounts of labeled training data is not possible. Here, it is proposed to combine the scattering transform with the attention-based residual neural network (ResNet). Experimental results on three HSI datasets demonstrate that this approach provides at least 40% higher unmixing accuracy compared to the previous STFHU and CNN algorithms when using limited training data, ranging from 5% to 30%, are available. The use of the scattering transform for deriving features within the ResNet unmixing system also leads more than 25% improvement when unmixing hyperspectral data contaminated by additive noise.

Scattering Transform Framework for Unmixing of Hyperspectral Data

The scattering transform, which applies multiple convolutions using known filters targeting different scales of time or frequency, has a strong similarity to the structure of convolution neural networks (CNNs), without requiring training to learn the convolution filters, and has been used for hyperspectral image classification in recent research. This paper investigates the application of the scattering transform framework to hyperspectral unmixing (STFHU). While state-of-the-art research on unmixing hyperspectral data utilizing scattering transforms is limited, the proposed end-to-end method applies pixel-based scattering transforms and preliminary three-dimensional (3D) scattering transforms to hyperspectral images in the remote sensing scenario to extract feature vectors, which are then trained by employing the regression model based on the k-nearest neighbor (k-NN) to estimate the abundance of maps of endmembers. Experiments compare performances of the proposed algorithm with a series of existing methods in quantitative terms based on both synthetic data and real-world hyperspectral datasets. Results indicate that the proposed approach is more robust to additive noise, which is suppressed by utilizing the rich information in both high-frequency and low-frequency components represented by the scattering transform. Furthermore, the proposed method achieves higher accuracy for unmixing using the same amount of training data with all comparative approaches, while achieving equivalent performance to the best performing CNN method but using much less training data.

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.

Sparse unmixing of hyperspectral data with bandwise model

Sparse unmixing has long been a hot research topic in the area of hyperspectral image (HSI) analysis. Most of the traditional sparse unmixing methods usually assume to only take the Gaussian noise into consideration. However, there are also other types of noise in real HSI, i.e., impulse noise, stripes, dead lines and so on. In addition, the intensity of Gaussian noise is usually different for each band of real HSI. To this end, we propose a novel sparse unmixing method with the bandwise model (SUBM) to address the above mentioned problems simultaneously. Besides, the alternative direction method of multipliers (ADMM) is adopted for solving the proposed SUBM. Moreover, we conduct extensive experiments on synthetic and real datasets to demonstrate effectiveness of the proposed sparse unmixing method under the bandwise model.

Kronecker least angle regression for unsupervised unmixing of hyperspectral imaging data

Spectral unmixing is an important data processing task that is commonly applied to hyperspectral imaging data. It uses a set of spectral pixels, i.e., multichannel data, to separate each spectral pixel, a multicomponent signal comprised of a linear mixture of pure spectral signatures, into its individual spectral signatures commonly known as endmembers. When no prior information about the required endmembers is available, the resulting unsupervised unmixing problem will be underdetermined, and additional constraints become necessary. A recent approach to solving this problem required that these endmembers be sparse in some dictionary. Sparse signal recovery is commonly solved using a basis pursuit optimization algorithm that requires specifying a data-dependent regularization parameter. Least angle regression (LARS) is a very efficient method to simultaneously solve the basis pursuit optimization problem for all relevant regularization parameter values. However, despite this efficiency of LARS, it has not been applied to the spectral unmixing problem before. This is likely because the application of LARS to large multichannel data could be very challenging in practice, due to the need for generation and storage of extremely large arrays (~ 1010 bytes in a relatively small area of spectral unmixing problem). In this paper, we extend the standard LARS algorithm, using Kronecker products, to make it suitable for practical and efficient recovery of sparse signals from large multichannel data, i.e., without the need to construct or process very large arrays, or the need for trial and error to determine the regularization parameter value. We then apply this new Kronecker LARS (K-LARS) algorithm to successfully achieve spectral unmixing of both synthetic and AVIRIS hyperspectral imaging data. We also compare our results to ones obtained using an earlier basis pursuit-based spectral unmixing algorithm, generalized morphological component analysis (GMCA). We show that these two results are similar, albeit our results were obtained without trial and error, or arbitrary choices, in specifying the regularization parameter. More important, our K-LARS algorithm could be a very valuable research tool to the signal processing community, where it could be used to solve sparse least squares problems involving large multichannel data.

NON-MATRIX FACTORIZATION FOR BLIND IMAGE SEPARATION

Hyperspectral unmixing is a process to identify the constituent materials and estimate the corresponding fractions from the mixture, nonnegative matrix factions ( NMF ) is suitable as a candidate for the linear spectral mixture mode, has been applied to the unmixing hyperspectral data. Unfortunately, the local minima is cause by the nonconvexity of the objective function makes the solution nonunique, thus only the nonnegativity constraint is not sufficient enough to lead to a well define problems. Therefore, two inherent characteristic of hyperspectal data, piecewise smoothness ( both temporal and spatial ) of spectral data and sparseness of abundance fraction of every material, are introduce to the NMF. The adaptive potential function from discontinuity adaptive Markov random field model is used to describe the smoothness constraint while preserving discontinuities is spectral data. At the same time two NMF algorithms, non smooth NMS and NMF with sparseness constraint, are used to quantify the degree of sparseness of material abundances. Experiment using the synthetic and real data demonstrate the proposed algorithms provides an effective unsupervised technique for hyperspectial unmixing.

Supervised Kernel Based Nonlinear Unmixing of Hyperspectral Data

In hyperspectral imagery problem, pixels are mixtures of spectral component associated with pure materials. Recently, nonlinear models have been taken into consideration to surmount some limitations of linear model. In this paper, the nonlinear hyperspectral image unmixing problem is formulated with kernel learning theory, with the number of kernels being controlled by the coherence rule. To be more physically interpretable, a relationship between endmembers and abundance vectors is introduced as a constraint of the optimization problem. An iterative learning algorithm derived from augmented Lagrangian method is proposed to solve the defined problem. Simulation results show the efficacy of the proposed model and algorithm.

Clustered multitask non-negative matrix factorization for spectral unmixing of hyperspectral data

The algorithm based on a clustered multitask network is proposed to solve spectral unmixing problem in hyperspectral imagery. In the proposed algorithm, the clustered network is employed. Each pixel in the hyperspectral image is considered as a node in this network. The nodes in the network are clustered using the fuzzy c-means clustering method. Diffusion least mean square strategy has been used to optimize the proposed cost function. To evaluate the proposed method, experiments are conducted on synthetic and real datasets. Simulation results based on spectral angle distance, abundance angle distance, and reconstruction error metrics illustrate the advantage of the proposed algorithm, compared with other methods.

Sparsity-Constrained Distributed Unmixing of Hyperspectral Data

Spectral unmixing (SU) is a technique to characterize mixed pixels in hyperspectral images measured by remote sensors. Most of the spectral unmixing algorithms are developed using the linear mixing models. To estimate endmembers and fractional abundance matrices in a blind problem, nonnegative matrix factorization (NMF) and its developments are widely used in the SU problem. One of the constraints which was added to NMF is sparsity, that was regularized by L q norm. In this paper, a new algorithm based on distributed optimization is suggested for spectral unmixing. In the proposed algorithm, a network including single-node clusters is employed. Each pixel in the hyperspectral images is considered as a node in this network. The sparsity-constrained distributed unmixing is optimized with diffusion least mean p-power (LMP) strategy, and then the update equations for fractional abundance and signature matrices are obtained. Afterward, the proposed algorithm is analyzed for different values of LMP power and L q norms. Simulation results based on defined performance metrics illustrate the advantage of the proposed algorithm in spectral unmixing of hyperspectral data compared with other methods.

Hapke-based computational method to enable unmixing of hyperspectral data of common salts

Environmental scientists are currently assessing the ability of hyper-spectral remote sensing to detect, identify, and analyze natural components, including minerals, rocks, vegetation and soil. This paper discusses the use of a nonlinear reflectance model to distinguish multicomponent particulate mixtures. Analysis of the data presented in this paper shows that, although the identity of the components can often be found from diagnostic wavelengths of absorption bands, the quantitative abundance determination requires knowledge of the complex refractive indices and average particle scattering albedo, phase function and size. The present study developed a method for spectrally unmixing halite and gypsum combinations. Using the known refractive indexes of the components, and with the assistance of Hapke theory and Legendre polynomials, the authors develop a method to find the component particle sizes and mixing coefficients for blends of halite and gypsum. Material factors in the method include phase function parameters, bidirectional reflectance, imaginary index, grain sizes, and iterative polynomial fitting. The obtained Hapke parameters from the best-fit approach were comparable to those reported in the literature. After the optical constants (n, the so-called real index of refraction and k, the coefficient of the imaginary index of refraction) are derived, and the geometric parameters are determined, single-scattering albedo (or ω) can be calculated and spectral unmixing becomes possible.

Nonlinear Unmixing of Hyperspectral Datasets for the Study of Painted Works of Art.

Nonlinear unmixing of hyperspectral reflectance data is one of the key problems in quantitative imaging of painted works of art. The approach presented is to interrogate a hyperspectral image cube by first decomposing it into a set of reflectance curves representing pure basis pigments and second to estimate the scattering and absorption coefficients of each pigment in a given pixel to produce estimates of the component fractions. This two-step algorithm uses a deep neural network to qualitatively identify the constituent pigments in any unknown spectrum and, based on the pigment(s) present and Kubelka-Munk theory to estimate the pigment concentration on a per-pixel basis. Using hyperspectral data acquired on a set of mock-up paintings and a well-characterized illuminated folio from the 15th century, the performance of the proposed algorithm is demonstrated for pigment recognition and quantitative estimation of concentration.