Hyperspectral Unmixing Method Research Articles

A Novel Hyperspectral Unmixing Method based on Least Squares Twin Support Vector Machines

ABSTRACT In hyperspectral images, endmembers characterizing one class of ground object may vary due to illumination, weathering, slight variations of the materials. This phenomenon is called intra-class endmember variability which is one of the important factors affecting the performance of unmixing. However, intra-class endmember variability is often ignored in unmixing, which causes a decrease in the accuracy of unmixing. How to deal with intra-class endmember variability is the focus. To address this problem, we propose a novel hyperspectral unmixing method based on Least Squares Twin Support Vector Machines (ULSTWSVM). ULSTWSVM uses multiple training samples (endmembers) to model a pure class, which takes intra-class endmember variability into account in unmixing. At the same time, ULSTWSVM obtains abundances by calculating the distances from the mixed pixels to the classification hyperplanes, which is simple and efficient. ULSTWSVM mainly comprises three steps: (1) to obtain the two non-parallel classification hyperplanes by solving two quadratic programming problems (QPPs) in least squares sense, (2) to calculate distances from the mixed pixels to classification hyperplanes, and (3) to normalize the distances and convert them to abundances. Experimental results on both synthetic and real hyperspectral data show that the proposed method outperforms the methods used for comparison.

A linear hyperspectral unmixing method by means of autoencoder networks

ABSTRACT Hyperspectral unmixing technique is a conventional approach addressing the mixed pixel issue. In this paper, we present an autoencoder (AE) network that deals with estimating the abundances in hyperspectral images (HSIs) given the endmembers. In the suggested network, the mixed pixel issue in a supervised scenario is investigated since the weights of the decoder are set equal to the endmembers. More importantly, the network is trained by a blend of two celebrated objective functions, mean squared error and spectral angle distance, in order to have both privileges of sensitivity to small errors and being scale invariant. To assure the convenience, the sparsity and physical constraints are imposed on the abundances, and the regularization techniques are employed. The abundances are initialized via the fully constrained least squares method thanks to the setting of the initial encoder weights. The superiority of the presented AE is demonstrated via conducting several experiments on synthetic and real HSIs and comparing the results quantitatively and visually with several existing methods.

Hyperspectral Image Unmixing Method Based on Multiple Kernel Graph Non-negative Matrix Factorization

In order to improve the accuracy of non-negative matrix factorization (NMF) in hyperspectral images unmixing, this paper proposes a hyperspectral image unmixing method based on multiple kernel graph NMF. Using multiple kernel learning (MKL), the hyperspectral data is mapped to the high-dimensional feature space, so that the linearly inseparable hyperspectral data in the low-dimensional space is linearly separable. Introducing the graph regular terms that characterizes the spatial structure relationship between pixels, the internal manifold structure of the hyperspectral image is effectively expressed. The results of both simulated dataset and real dataset show that compared with other method, the proposed method can improve the unmixing accuracy.

A comparative study of hyperspectral unmixing using different algorithm approaches

<span>Hyperspectral unmixing (HU) is an important technique for remotely sensed hyperspectral data exploitation. Hyperspectral unmixing is required to get an accurate estimation due to low spatial resolution of hyperspectral cameras, microscopic material mixing, and multiple scattering that cause spectra measured by hyperspectral cameras are mixtures of spectra of materials in a scene. It is a process of estimating constituent endmembers and their fractional abundances present at each pixel in hyperspectral image. Researchers have devised and investigated many models searching for robust, stable, tractable and accurate unmixing algorithm. Such algorithm are highly desirable to avoid propagation of errors within the process. This paper presents the comparison of hyperspectral unmixing method by using different kind of algorithms. These algorithms are named VCA, NFINDR, SISAL, and CoNMF. The performance of unmixing process is evaluated by calculating the SAD (spectral angle distance) for each endmembers by using same input of hyperspectral data for different algorithm.</span>

Homogeneous region regularized multilayer non-negative matrix factorization for hyperspectral unmixing

Hyperspectral unmixing is one of the most important procedures for remote sensing image processing. The multilayer non-negative matrix factorization (MLNMF)-based method has been widely used for hyperspectral unmixing due to its good performance for highly mixed data with multiple-decomposition structure. However, few works consider the spatial information in the image, which may enhance the performance. In order to solve this issue, we propose a homogeneous region regularized multilayer non-negative matrix factorization (HR-MLNMF) method for hyperspectral unmixing. In HR-MLNMF, the spatial information, depicted by the homogeneous region, is applied to regularize MLNMF, which could enhance the smoothness of each homogeneous spatial field to achieve better performance. Experiments on both synthetic and real datasets have validated the effectiveness of our method and shown that it has outperformed several state-of-the-art approaches of hyperspectral unmixing.

Superpixel-Based Graph Laplacian Regularization for Sparse Hyperspectral Unmixing

An efficient spatial regularization method using superpixel segmentation and graph Laplacian regularization is proposed for the sparse hyperspectral unmixing method. Since it is likely to find spectrally similar pixels in a homogeneous region, we use a superpixel segmentation algorithm to extract the homogeneous regions by considering the image boundaries. We first extract the homogeneous regions, which are called superpixels, and then, a weighted graph in each superpixel is constructed by selecting <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -nearest pixels in each superpixel. Each node in the graph represents the spectrum of a pixel, and edges connect the similar pixels inside the superpixel. The spatial similarity is investigated using the graph Laplacian regularization. Sparsity regularization for an abundance matrix is provided using a weighted sparsity promoting norm. Experimental results on simulated and real data sets show the superiority of the proposed algorithm over the well-known algorithms in the literature.

Hyperspectral Image Super-Resolution Based on Spatial Group Sparsity Regularization Unmixing

A hyperspectral image (HSI) contains many narrow spectral channels, thus containing efficient information in the spectral domain. However, high spectral resolution usually leads to lower spatial resolution as a result of the limitations of sensors. Hyperspectral super-resolution aims to fuse a low spatial resolution HSI with a conventional high spatial resolution image, producing an HSI with high resolution in both the spectral and spatial dimensions. In this paper, we propose a spatial group sparsity regularization unmixing-based method for hyperspectral super-resolution. The hyperspectral image (HSI) is pre-clustered using an improved Simple Linear Iterative Clustering (SLIC) superpixel algorithm to make full use of the spatial information. A robust sparse hyperspectral unmixing method is then used to unmix the input images. Then, the endmembers extracted from the HSI and the abundances extracted from the conventional image are fused. This ensures that the method makes full use of the spatial structure and the spectra of the images. The proposed method is compared with several related methods on public HSI data sets. The results demonstrate that the proposed method has superior performance when compared to the existing state-of-the-art.

Low-Rank Tensor Modeling for Hyperspectral Unmixing Accounting for Spectral Variability

Traditional hyperspectral unmixing methods neglect the underlying variability of spectral signatures often observed in typical hyperspectral images (HI), propagating these mismodeling errors throughout the whole unmixing process. Attempts to model material spectra as members of sets or as random variables tend to lead to severely ill-posed unmixing problems. Although parametric models have been proposed to overcome this drawback by handling endmember (EM) variability through generalizations of the mixing model, the success of these techniques depends on employing appropriate regularization strategies. Moreover, the existing approaches fail to adequately explore the natural multidimensinal representation of HIs. Recently, tensor-based strategies considered low-rank decompositions of HIs as an alternative to impose low-dimensional structures on the solutions of standard and multitemporal unmixing problems. These strategies, however, present two main drawbacks: 1) they confine the solutions to low-rank tensors, which often cannot represent the complexity of real-world scenarios and 2) they lack guarantees that EMs and abundances will be correctly factorized in their respective tensors. In this article, we propose a more flexible approach, called unmixing with low-rank tensor regularization algorithm accounting for EM variability (ULTRA-V), that imposes low-rank structures through regularizations whose strictness is controlled by scalar parameters. Simulations attest the superior accuracy of the method when compared with state-of-the-art unmixing algorithms that account for spectral variability.

A Supervised Method for Nonlinear Hyperspectral Unmixing

Due to the complex interaction of light with the Earth’s surface, reflectance spectra can be described as highly nonlinear mixtures of the reflectances of the material constituents occurring in a given resolution cell of hyperspectral data. Our aim is to estimate the fractional abundance maps of the materials from the nonlinear hyperspectral data. The main disadvantage of using nonlinear mixing models is that the model parameters are not properly interpretable in terms of fractional abundances. Moreover, not all spectra of a hyperspectral dataset necessarily follow the same particular mixing model. In this work, we present a supervised method for nonlinear spectral unmixing. The method learns a mapping from a true hyperspectral dataset to corresponding linear spectra, composed of the same fractional abundances. A simple linear unmixing then reveals the fractional abundances. To learn this mapping, ground truth information is required, in the form of actual spectra and corresponding fractional abundances, along with spectra of the pure materials, obtained from a spectral library or available in the dataset. Three methods are presented for learning nonlinear mapping, based on Gaussian processes, kernel ridge regression, and feedforward neural networks. Experimental results conducted on an artificial dataset, a data set obtained by ray tracing, and a drill core hyperspectral dataset shows that this novel methodology is very promising.

Cauchy sparse NMF with manifold regularization: A robust method for hyperspectral unmixing

Recently, nonnegative matrix factorization (NMF) has achieved a great success in hyperspectral image (HSI) unmixing tasks. However, existing NMF based unmixing methods commonly suffer from two main drawbacks: 1) the lack of robustness, which leads to the failure when dealing with the noise contamination in practical HSI data; and 2) the neglect of manifold preservation, resulting in the corruption of the intrinsic structure of HSI data. Accordingly, to address these two issues, we propose a robust hyperspectral unmixing model called Cauchy Sparse NMF with manifold regularization (MCSNMF), which incorporates the prior geometric structure into robust subspace learning. More specifically, in order to filter out the outliers when extracting endmembers, we measure the reconstruction error via the sparse Truncated Cauchy function. Meanwhile, to preserve the manifold structure of original HSI data, we incorporate the graph regularization over the abundances into MCSNMF. Furthermore, from the optimization viewpoint, we conduct a theoretical analysis to confirm the robustness of the proposed method. Optimized by an efficient half-quadratic based algorithm, MCSNMF outperforms the state-of-the-art NMF based unmixing methods on both simulated datasets and real scene images.

Joint hyperspectral unmixing for urban computing

Recently, many methods for hyperspectral unmixing have been proposed. These methods are often based on nonnegative matrix factorization (NMF), which naturally inherits the non-negative advantage and is in line with the common sense of physics. Although there are many ways to perform NMF-based hyperspectral unmixing, these methods can only unmix one hyperspectral image at a time. In practice, we may often collect two or more similar hyperspectral images, and the end of the hyperspectral images of the signal could be only slightly different. Traditional NMF-based hyperspectral unmixing methods cannot take advantage of the fact that different hyper-spectral images may have similar or even the same end-element signals. Accordingly, in order to improve the performance of NMF-based hyperspectral unmixing, we present an algorithm in this paper that can process two hyperspectral images, simultaneously, and makes full use of the available information when most of the signals at the two end-points are similar. This improves the effect of end-element extraction in hyperspectral unmixing evidenced by experimental results on both synthetic and real-world data.

Error Approximation of Hyperspectral Unmixing via Correntropy-Induced Metric

In this letter, a sparse-constrained hyperspectral unmixing method via reconstruction error approximation is proposed. In the presented method, all the noises and the outliers are treated as diverse interferences and addressed to minimize the regularization error. Several techniques are involved in our presented approach: 1) to attenuate the interference of noise, an auxiliary variable is introduced; 2) based on the relative noiseless hyperspectral image, a sparse constraint is employed to achieve the sparsity; and 3) besides, the correntropy-induced metric (CIM), instead of the $L_{2}$ - or $L_{2,1}$ -norm loss function, is utilized to measure the quality of the unmixing model approximation. A series of experiments on the synthetic and real hyperspectral images is conducted, and all the experiment results show the efficacy of the proposed approach.

Covariance Similarity Approach for Semiblind Unmixing of Hyperspectral Image

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

Constrained Nonnegative Tensor Factorization for Spectral Unmixing of Hyperspectral Images: A Case Study of Urban Impervious Surface Extraction

In recent years, a new genre of hyperspectral unmixing methods based on nonnegative matrix factorization (NMF) have been proposed. Unlike traditional spectral unmixing methods, the NMF-based hyperspectral unmixing methods no longer depend on pure pixels in the original image. The NMF is based on linear algebra, which requires that the hyperspectral data cube is converted from 3-D cube to a 2-D matrix. Due to this conversion, the spatial information in the relative positions of the pixels is lost. With the emergence of multilinear algebra, the tensorial representation of hyperspectral imagery that preserves spectral and spatial information has become popular. The tensor-based spectral unmixing was first realized in 2017 using the matrix-vector nonnegative tensor factorization (MVNTF) decomposition. Using the construction of MVNTF spectral unmixing, this letter proposes to integrate three additional constraints (sparseness, volume, and nonlinearity) to the cost function. As we show in this letter, we found that the three constraints greatly improved the impervious surface area fraction/classification results. The constraints also shortened the processing time.

A Multiscale Hierarchical Model for Sparse Hyperspectral Unmixing

Due to the complex background and low spatial resolution of the hyperspectral sensor, observed ground reflectance is often mixed at the pixel level. Hyperspectral unmixing (HU) is a hot-issue in the remote sensing area because it can decompose the observed mixed pixel reflectance. Traditional sparse hyperspectral unmixing often leads to an ill-posed inverse problem, which can be circumvented by spatial regularization approaches. However, their adoption has come at the expense of a massive increase in computational cost. In this paper, a novel multiscale hierarchical model for a method of sparse hyperspectral unmixing is proposed. The paper decomposes HU into two domain problems, one is in an approximation scale representation based on resampling the method’s domain, and the other is in the original domain. The use of multiscale spatial resampling methods for HU leads to an effective strategy that deals with spectral variability and computational cost. Furthermore, the hierarchical strategy with abundant sparsity representation in each layer aims to obtain the global optimal solution. Both simulations and real hyperspectral data experiments show that the proposed method outperforms previous methods in endmember extraction and abundance fraction estimation, and promotes piecewise homogeneity in the estimated abundance without compromising sharp discontinuities among neighboring pixels. Additionally, compared with total variation regularization, the proposed method reduces the computational time effectively.

Spectral-Spatial Hyperspectral Unmixing Using Multitask Learning

Hyperspectral unmixing is an important and challenging task in the field of remote sensing which arises when the spatial resolution of sensors is insufficient for the separation of spectrally distinct materials. Hyperspectral images, like other natural images, have highly correlated pixels and it is very desirable to make use of this spatial information. In this paper, a deep learning based method for blind hyperspectral unmixing is presented. The method uses multitask learning through multiple parallel autoencoders to unmix a neighborhood of pixels simultaneously. Operating on image patches instead of single pixels enables the method to take advantage of spatial information in the hyperspectral image. The method is the first in its class to directly utilize the spatial structure of hyperspectral images (HSIs) for the estimation of the spectral signatures of endmembers in the data cube. We evaluate the proposed method using two real HSIs and compare it to seven state-of-the-art methods that either rely only on spectral or both on spectral and spatial information in the HSIs. The proposed method outperforms all the baseline unmixing methods in experiments.

Efficient quantitative hyperspectral image unmixing method for large-scale Raman micro-spectroscopy data analysis

Vibrational micro-spectroscopy is a powerful optical tool, providing a non-invasive label-free chemically specific imaging for many chemical and biomedical applications. However, hyperspectral image produced by Raman micro-spectroscopy typically consists of thousands discrete pixel points, each having individual Raman spectrum at thousand wavenumbers, and therefore requires appropriate image unmixing computational methods to retrieve non-negative spatial concentration and corresponding non-negative spectra of the image biochemical constituents. Here, we present a new efficient Quantitative Hyperspectral Image Unmixing (Q-HIU) method for large-scale Raman micro-spectroscopy data analysis. This method enables to simultaneously analyse multi-set Raman hyperspectral images in three steps: (i) Singular Value Decomposition with innovative Automatic Divisive Correlation which autonomously filters spatially and spectrally uncorrelated noise from data; (ii) a robust subtraction of fluorescent background from the data using a newly developed algorithm called Bottom Gaussian Fitting; (iii) an efficient Quantitative Unsupervised/Partially Supervised Non-negative Matrix Factorization method, which rigorously retrieves non-negative spatial concentration maps and spectral profiles of the samples' biochemical constituents with no a priori information or when one or several samples’ constituents are known. As compared with state-of-the-art methods, our approach allows to achieve significantly more accurate results and efficient quantification with several orders of magnitude shorter computational time as verified on both artificial and real experimental data. We apply Q-HIU to the analysis of large-scale Raman hyperspectral images of human atherosclerotic aortic tissues and our results show a proof-of-principle for the proposed method to retrieve and quantify the biochemical composition of the tissues, consisting of both high and low concentrated compounds. Along with the established hallmarks of atherosclerosis including cholesterol/cholesterol ester, triglyceride and calcium hydroxyapatite crystals, our Q-HIU allowed to identify the significant accumulations of oxidatively modified lipids co-localizing with the atherosclerotic plaque lesions in the aortic tissues, possibly reflecting the persistent presence of inflammation and oxidative damage in these regions, which are in turn able to promote the disease pathology. For minor chemical components in the diseased tissues, our Q-HIU was able to detect the signatures of calcium hydroxyapatite and β-carotene with relative mean Raman concentrations as low as 0.09% and 0.04% from the original Raman intensity matrix with noise and fluorescent background contributions of 3% and 94%, respectively.

Multiharmonic Postnonlinear Mixing Model for Hyperspectral Nonlinear Unmixing

In this letter, a new method for higher order nonlinear hyperspectral unmixing is introduced. The proposed scheme relies on the harmonic description of the endmembers contributions to characterize the interactions among the materials showing up in the given scenes. Moreover, it aims at directly estimating the probability of occurrence of each material in the images, so to provide an accurate quantification of the endmembers also in complex scenarios. Experimental results carried out on synthetic and real data sets show that the proposed method is able to obtain good unmixing performance when compared to other state-of-the-art architectures.

Inertia-Constrained Pixel-by-Pixel Nonnegative Matrix Factorisation: A Hyperspectral Unmixing Method Dealing with Intra-Class Variability

Blind source separation is a common processing tool to analyse the constitution of pixels of hyperspectral images. Such methods usually suppose that pure pixel spectra (endmembers) are the same in all the image for each class of materials. In the framework of remote sensing, such an assumption is no longer valid in the presence of intra-class variability due to illumination conditions, weathering, slight variations of the pure materials, etc. In this paper, we first describe the results of investigations highlighting intra-class variability measured in real images. Considering these results, a new formulation of the linear mixing model is presented leading to two new methods. Unconstrained pixel-by-pixel NMF (UP-NMF) is a new blind source separation method based on the assumption of a linear mixing model, which can deal with intra-class variability. To overcome the limitations of UP-NMF, an extended method is also proposed, named Inertia-constrained Pixel-by-pixel NMF (IP-NMF). For each sensed spectrum, these extended versions of NMF extract a corresponding set of source spectra. A constraint is set to limit the spreading of each source’s estimates in IP-NMF. The proposed methods are first tested on a semi-synthetic data set built with spectra extracted from a real hyperspectral image and then numerically mixed. We thus demonstrate the interest of our methods for realistic source variabilities. Finally, IP-NMF is tested on a real data set and it is shown to yield better performance than state of the art methods.

Hyperspectral unmixing employing l1−l2 sparsity and total variation regularization

ABSTRACTHyperspectral unmixing is essential for image analysis and quantitative applications. To further improve the accuracy of hyperspectral unmixing, we propose a novel linear hyperspectral unmixing method based on l1−l2 sparsity and total variation (TV) regularization. First, the enhanced sparsity based on the l1−l2 norm is explored to depict the intrinsic sparse characteristic of the fractional abundances in a sparse regression unmixing model because the l1−l2 norm promotes stronger sparsity than the l1 norm. Then, TV is minimized to enforce the spatial smoothness by considering the spatial correlation between neighbouring pixels. Finally, the extended alternating direction method of multipliers (ADMM) is utilized to solve the proposed model. Experimental results on simulated and real hyperspectral datasets show that the proposed method outperforms several state-of-the-art unmixing methods.