Hyperspectral Unmixing Algorithms Research Articles

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

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

Hyperspectral Unmixing Network Accounting for Spectral Variability Based on a Modified Scaled and a Perturbed Linear Mixing Model

Spectral unmixing is one of the prime topics in hyperspectral image analysis, as images often contain multiple sources of spectra. Spectral variability is one of the key factors affecting unmixing accuracy, since spectral signatures are affected by variations in environmental conditions. These and other factors interfere with the accurate discrimination of source type. Several spectral mixing models have been proposed for hyperspectral unmixing to address the spectral variability problem. The interpretation for the spectral variability of these models is usually insufficient, and the unmixing algorithms corresponding to these models are usually classic unmixing techniques. Hyperspectral unmixing algorithms based on deep learning have outperformed classic algorithms. In this paper, based on the typical extended linear mixing model and the perturbed linear mixing model, the scaled and perturbed linear mixing model is constructed, and a spectral unmixing network based on this model is constructed using fully connected neural networks and variational autoencoders to update the abundances, scales, and perturbations involved in the variable endmembers. Adding spatial smoothness constraints to the scale and adding regularization constraints to the perturbation improve the robustness of the model, and adding sparseness constraints to the abundance determination prevents overfitting. The proposed approach is evaluated on both synthetic and real data sets. Experimental results show the superior performance of the proposed method against other competitors.

Raman Spectroscopic Imaging of Human Bladder Resectates towards Intraoperative Cancer Assessment.

Raman spectroscopy offers label-free assessment of bladder tissue for in vivo and ex vivo intraoperative applications. In a retrospective study, control and cancer specimens were prepared from ten human bladder resectates. Raman microspectroscopic images were collected from whole tissue samples in a closed chamber at 785 nm laser excitation using a 20× objective lens and 250 µm step size. Without further preprocessing, Raman images were decomposed by the hyperspectral unmixing algorithm vertex component analysis into endmember spectra and their abundancies. Hierarchical cluster analysis distinguished endmember Raman spectra that were assigned to normal bladder, bladder cancer, necrosis, epithelium and lipid inclusions. Interestingly, Raman spectra of microplastic particles, pigments or carotenoids were detected in 13 out of 20 specimens inside tissue and near tissue margins and their identity was confirmed by spectral library surveys. Hypotheses about the origin of these foreign materials are discussed. In conclusion, our Raman workflow and data processing protocol with minimal user interference offers advantages for future clinical translation such as intraoperative tumor detection and label-free material identification in complex matrices.

Robust Hyperspectral Unmixing with Practical Learning-Based Hyperspectral Image Denoising

The noise corruption problem commonly exists in hyperspectral images (HSIs) and severely affects the accuracy of hyperspectral unmixing algorithms. The noise formulation existing in HSIs is relatively complex and would change in conjunction with different devices and imaging settings. For real applications, applying denoising approaches without accurate close-to-reality noise modeling before unmixing may not improve, but rather degrade the unmixing performance. This study proposes a robust hyperspectral unmixing method with practical learning-based hyperspectral image denoising. We formulated a close-to-reality noise model for hyperspectral data and provide a calibration approach for the noise parameters. On the basis of the calibrated noise model, synthetic data were generated and used for training a KST-based denoising network. The noisy hyperspectral data were firstly denoised by the trained denoising network and were then used to perform the unmixing process. A variety of unmixing algorithms can be integrated into our method to improve the accuracy of unmixing in noisy situations. In the experiments, several widely used unmixing algorithms were employed to verify the effect of the proposed method. The experimental results on both synthetic and real demonstrated that our proposed method can handle HSI data with various gain settings and helps to improve the unmixing performance effectively.

Realistic Mixing Miniature Scene Hyperspectral Unmixing: From Benchmark Datasets to Autonomous Unmixing

Mixed pixels that contain more than one material type are common in mid/low spatial resolution remote sensing imagery. Hyperspectral unmixing is aimed at decomposing the mixed pixels into endmembers and abundances. However, there are few datasets that are suitable for quantitatively evaluating unmixing accuracies, and the ground-truth abundances of the existing datasets are often generated in an approximate way. To address the lack of real unmixing datasets for quantitative evaluation, we built the realistic mixing miniature scenes (RMMS) dataset, which can be used to quantitatively evaluate the unmixing accuracy of different algorithms. The RMMS dataset consists of a simple mixture scene with homogeneous flat materials and a complex mixture scene with 3-D structural features. The features of the RMMS dataset also take point, line, and polygon characteristics into consideration, and the spectral similarity of the materials increases the challenge of the spectral unmixing. In the RMMS dataset, due to the multiscale observation characteristics of the spatiotemporal scanning modality, it can avoid the registration error between RGB and hyperspectral data, and it can ensure that the endmembers are pure pixels. Most of the autonomous hyperspectral unmixing algorithms focus on solving some of the unmixing problems and have difficulty achieving fully autonomous hyperspectral unmixing (FAHU). In this article, to overcome this shortcoming, a fully autonomous hyperspectral unmixing method called FAHU is proposed to take advantage of the spatial information. Some of the state-of-the-art autonomous hyperspectral unmixing algorithms are used to evaluate the performance with the RMMS dataset, and the experimental results show the advantages and disadvantages of the different autonomous unmixing algorithms.

Benchmark for Hyperspectral Unmixing Algorithm Evaluation

Over the past decades, many methods have been proposed to solve the linear or nonlinear mixing of spectra inside the hyperspectral data. Due to a relatively low spatial resolution of hyperspectral imaging, each image pixel may contain spectra from multiple materials. In turn, hyperspectral unmixing is finding these materials and their abundances. A few main approaches to performing hyperspectral unmixing have emerged, such as nonnegative matrix factorization (NMF), linear mixture modelling (LMM), and, most recently, autoencoder networks. These methods use different approaches in finding the endmember and abundance of information from hyperspectral images. However, due to the huge variation of hyperspectral data being used, it is difficult to determine which methods perform sufficiently on which datasets and if they can generalize on any input data to solve hyperspectral unmixing problems. By trying to mitigate this problem, we propose a hyperspectral unmixing algorithm testing methodology and create a standard benchmark to test already available and newly created algorithms. A few different experiments were created, and a variety of hyperspectral datasets in this benchmark were used to compare openly available algorithms and to determine the best-performing ones.

Adaptive multiscale sparse unmixing for hyperspectral remote sensing image

Sparse unmixing of hyperspectral images aims to separate the endmembers and estimate the abundances of mixed pixels. This approach is the essential step for many applications involving hyperspectral images. The multi-scale spatial sparse hyperspectral unmixing algorithm (MUA) could achieve higher accuracy than many state-of-the-art algorithms. The regularization parameters, whose combinations markedly influence the unmixing accuracy, are determined by manually searching in the broad parameter space, leading to time consuming. To settle this issue, the adaptive multi-scale spatial sparse hyperspectral unmixing algorithm (AMUA) is proposed. Firstly, the MUA model is converted into a new version by using of a maximum a posteriori (MAP) system. Secondly, the theories indicating that andnorms are equivalent to Laplacian and multivariate Gaussian functions, respectively, are applied to explore the strong connections among the regularization parameters, estimated abundances and estimated noise variances. Finally, the connections are applied to update the regularization parameters adaptively in the optimization process of unmixing. Experimental results on both simulated data and real hyperspectral images show that the AMUA can substantially improve the unmixing efficiency at the cost of negligible accuracy. And a series of sensitive experiments were undertook to verify the robustness of the AMUA algorithm.

Hyperspectral image non-linear unmixing using joint extrinsic and intrinsic priors with L1/2-norms to non-negative matrix factorisation

Hyperspectral unmixing (HU) is one of the most active emerging areas in image processing that estimates the hyperspectral image’s endmember and abundance. HU enhances the quality of both spectral and spatial dimensions of the image by modifying the endmember and abundance parameters of the hyperspectral images. There are several HU algorithms available in the literature based on the linear mixing model (LMM) that deals with the microscopic contents of the pixels in the images. Non-negative matrix factorisation (NMF) is the prominent method widely used in LMMs that simultaneously estimates both the endmembers and abundances parameters along with some residual factors of the image to improve the quality of unmixing. In addition to this, the quality of the image is enhanced by incorporating some constraints to both endmember and abundance matrices with the NMF method. However, all the existing methods apply any of these constraints to the endmember and abundance matrices by considering the linearity features of the images. In this paper, we propose an unmixing model called joint extrinsic and intrinsic priors with L1/2 norms to non-negative matrix factorisation (JEIp L1/2-NMF) that applies multiple constraints simultaneously to both endmember and abundance matrices of the hyperspectral image to enhance its quality. Three main external and internal constraints such as minimum volume, sparsity and total variation are applied to both the endmembers and abundance parameters of the image. In addition, a L1/2-norms is imposed to extract good quality spectral data. Therefore, the proposed method enhances spatial as well as spectral data and considers the non-linearity of the pixels in the image by adding a residual term to the model. Performance of our proposed model is measured by using different quality measuring indexes on four benchmark public datasets and found that the proposed method shows outstanding performance compared to all the conventional baseline methods. Further, we also evaluated the performance of our method by varying the number of endmembers empirically and concluded that less than five endmembers provides high-quality spectral and spatial data during the unmixing process.

Hyperspectral sparse unmixing based on multiple dictionary pruning

ABSTRACT When a spectral library is known, hyperspectral sparse unmixing could obtain the abundance images, which estimate the fractional proportions in each pixel in a hyperspectral image scene. Dictionary pruning (DP) methods furtherly improve the performance of the hyperspectral sparse unmixing by reducing the spectral dictionary to a smaller subset. However, the current hyperspectral sparse unmixing algorithms usually only use a single DP method to obtain the subset, which affects the sparse unmixing results. In this study, we propose a multiple dictionary pruning (MDP) method to improve the performance of hyperspectral sparse unmixing algorithms, making them more accurate. MDP consists of three DP methods, namely, spectral angle mapping (SAM), spectral information divergence (SID) and robust multiple signal classification (RMUSIC). In MDP, we first make a difference between SAM and SID to produce the first level subset named as SS, reducing the impact of non-target information spectrums on the accuracy of sparse unmixing. We then use the RMUSIC to handle the SS to obtain the second level subset named as SSTR, reducing the endmember variability and calibration errors. Finally, we introduce the more accurate subset SSTR into the current hyperspectral sparse unmixing algorithms to produce the sparse unmixing results. Experimental results on two simulated data sets and one real data set show that the proposed MDP method is superior to the traditional DP methods.

L₁ Sparsity-Constrained Archetypal Analysis Algorithm for Hyperspectral Unmixing

Hyperspectral unmixing (HU) is widely used to process mixed pixels as an essential technology. Among them, the nonnegative matrix factorization (NMF)-based approach is one typical of the blind unmixing techniques, which can achieve endmembers and abundances simultaneously. Considering the physical meaning of the extracted endmembers, the archetypal analysis (AA) method constructs a new matrix decomposition structure with stronger interpretability than NMF. However, AA ignores the significant sparse property of abundance in unmixing. Therefore, we propose the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> sparsity-constrained AA algorithm for HU. To solve the new optimization problem, we explore a new optimization method for optimizing abundance. The alternating direction method of multipliers (ADMM) is used to increase the strong convexity and convergence of the problem. Then the fast gradient method (FGM) instead of traditional gradient descent is used to speed up algorithm convergence. The experimental results in both the synthesized and real datasets show that the proposed method outperforms several sparse NMF-based and AA-based methods.

Fast Hyperspectral Unmixing Using a Multiscale Sparse Regularization

This letter proposes a simple, fast yet efficient sparse hyperspectral unmixing algorithm. The proposed method consists of three main steps. First, a coarse approximation of the hyperspectral image is built using a off-the-shelf segmentation algorithm. Then, a low-resolution approximation of the abundance map is estimated by solving a weighted ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -regularized problem on this coarse approximation of the hyperspectral data. Finally, this low-resolution abundance map is subsequently used to design a sparsity-promoting penalization which acts as a spatial regularization informed by the coarse abundance map. It is incorporated into another weighted ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -regularized problem whose solution is a higher resolution abundance map. The computational efficiency of the two last steps is ensured by solving the two underlying optimization problems using an alternating direction method of multipliers. Extensive experiments conducted on simulated and real data show the effectiveness of the proposed method.

Hyperspectral linear unmixing based on collaborative sparsity and multi-band non-local total variation

ABSTRACT In recent years, spectral unmixing is a hot issue in the hyperspectral remote sensing technology and applications. Within various methods, sparse regression is one of the most commonly used methods in the hyperspectral unmixing community. In order to overcome the limitation of spatial correlation of existing sparse unmixing methods and improve further the accuracy of sparsity representation, a novel hyperspectral linear unmixing method via fusion of collaborative sparsity and multi-band non-local total variation is proposed. This method analyses the sparsity and spatially geometrical structure of hyperspectral pixels by studying the linear spectral mixed model of hyperspectral images, and reveals the interior spatial correlation of hyperspectral images with the non-local variation framework. Specifically, the sparsity and spatial correlation of hyperspectral imagery are discussed, and a hyperspectral linear sparse unmixing model is afterwards constructed by combining the relaxation technique and non-local total variation framework. Second, the solution procedure of the above spectral unmixing model is divided into two steps under the variable separation method: fractional abundance estimation and abundance map restoration. The alternating direction method of multipliers (ADMM) and split Bregman operator are exploited to obtain the spectral unmixing results. Finally, the proposed hyperspectral unmixing algorithm is evaluated with synthetic and real hyperspectral datasets. In the experiments with a synthetic hyperspectral dataset, the feasibility and effectiveness of the method are analysed quantitatively and qualitatively. The quantitative metrics and visual examination of the estimated fractional abundance map are also better than the performance of the current mainstream hyperspectral sparse unmixing algorithms. Furthermore, two real hyperspectral datasets are applied to the algorithm of this work to prove its practicability.

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.

Evolutionary Multiobjective Optimization with Endmember Priori Strategy for Large-Scale Hyperspectral Sparse Unmixing

Mixed pixels inevitably appear in the hyperspectral image due to the low resolution of the sensor and the mixing of ground objects. Sparse unmixing, as an emerging method to solve the problem of mixed pixels, has received extensive attention in recent years due to its robustness and high efficiency. In theory, sparse unmixing is essentially a multiobjective optimization problem. The sparse endmember term and the reconstruction error term can be regarded as two objectives to optimize simultaneously, and a series of nondominated solutions can be obtained as the final solution. However, the large-scale spectral library poses a challenge due to the high-dimensional number of spectra, it is difficult to accurately extract a few active endmembers and estimate their corresponding abundance from hundreds of spectral features. In order to solve this problem, we propose an evolutionary multiobjective hyperspectral sparse unmixing algorithm with endmember priori strategy (EMSU-EP) to solve the large-scale sparse unmixing problem. The single endmember in the spectral library is used to reconstruct the hyperspectral image, respectively, and the corresponding score of each endmember can be obtained. Then the endmember scores are used as a prior knowledge to guide the generation of the initial population and the new offspring. Finally, a series of nondominated solutions are obtained by the nondominated sorting and the crowding distances calculation. Experiments on two benchmark large-scale simulated data to demonstrate the effectiveness of the proposed algorithm.

Simulation of a Blind Hyperspectral-Unmixing Algorithm Incorporating Spatial Correlation and Spectral Similarity

Simulation of a Blind Hyperspectral-Unmixing Algorithm Incorporating Spatial Correlation and Spectral Similarity

A two-step iterative algorithm for sparse hyperspectral unmixing via total variation

Sparse hyperspectral unmixing is a hot topic in the field of remote sensing. Its goal is to find an optimal spectral subset, from a large spectral library, to properly model the mixed pixels in hyperspectral images. Sparse unmixing via variable splitting augmented Lagrangian and total variation (SUnSAL-TV) incorporates a TV regularizer into sparse unmixing, achieving a promising unmixing performance. Note that, SUnSAL-TV is solved by the framework of the alternating direction method of multipliers (ADMM). In this paper, we first propose a weighted collaborative sparse unmixing via TV model, named as WCSU-TV, for hyperspectral unmixing. Then a two-step iterative strategy, based on ADMM, is designed to solve the proposed model. Its key idea is to compute the current solution by a linear combination of the results of two previous iterates, instead of only using current solution in classic ADMM. Experiments on simulated and real hyperspectral data illustrate the effectiveness of the proposed approach.

A Modified Huber Nonnegative Matrix Factorization Algorithm for Hyperspectral Unmixing

Hypersepctral unmixing (HU) has been one of the most challenging tasks in hyperspectral image research. Recently, nonnegative matrix factorization (NMF) has shown its superiority in hyperspectral unmixing due to its flexible modeling and little prior requirement. But most NMF algorithms tend to use least square function as the objective, which is sensitive to outliers and different kinds of noise. In this article, we propose a modified Huber (mHuber) NMF model to achieve robustness to outliers and different kinds of noise. Under this robust model, we accelerate the half-quadratic optimization algorithm by replacing multiplicative updating rule with a projected nonlinear conjugated gradient rule, which achieves much faster convergence rate. Moreover, a new tuning parameter, rather than a fixed one, is given to adapt to mHuber loss function. Finally, we perform algorithm analysis and experiments in the synthetic and real-world datasets, which confirms the effectiveness and superiority of the proposed method when compared with several state-of-the-art NMF methods in HU.

A Novel Collaborative Representation Algorithm for Spectral Unmixing of Hyperspectral Remotely Sensed Imagery

Hyperspectral unmixing has attracted considerable attentions in recent years and some promising algorithms have been developed. In this paper, collaborative representation-based unmixing (CRU) for hyperspectral images is proposed. Different from imposing the sparseness constraint on training samples in sparse representation, collaborative representation emphasizes the collaboration of training samples. Furthermore, its closed form solution greatly improves computational efficiency. In the experiments, synthetic and the real hyperspectral data are used to evaluate the effectiveness and efficiency of the proposed collaborative representation-based hyperspectral unmixing algorithm.

Sparse and Low-Rank Constrained Tensor Factorization for Hyperspectral Image Unmixing

Third-order tensors have been widely used in hyperspectral remote sensing because of their ability to maintain the 3-D structure of hyperspectral images. In recent years, hyperspectral unmixing algorithms based on tensor factorization have emerged, but these decomposition processes may be inconsistent with physical mechanism of unmixing. To solve this problem, this article proposes a sparse and low-rank constrained tensor factorization unmixing algorithm based on a matrix-vector nonnegative tensor factorization (MV-NTF) framework. Considering the fact that each component tensor obtained by the image decomposition contains only one endmember and the corresponding abundance matrix has sparse property, a sparse constraint is imposed to ensure the accuracy of abundance maps. Since abundance maps also have low-rank attribute, in order to avoid the strict low-rank constraint in the original MV-NTF framework, a low-rank tensor regularization is introduced to flexibly express the low-rank characteristics of the abundance tensors, making the resulting abundance maps more in line with the actual scene. Then, the optimization problem is solved by using the alternating direction method of multipliers. In experiments, simulated datasets are adopted to demonstrate the effectiveness of the sparse and low-rank constraints of the proposed algorithm, and real datasets from different sensors and different scenarios are used to verify its applicability.

Constrained Nonnegative Matrix Factorization for Blind Hyperspectral Unmixing Incorporating Endmember Independence

Hyperspectral unmixing (HU) has become an important technique in exploiting hyperspectral data since it decomposes a mixed pixel into a collection of endmembers weighted by fractional abundances. The endmembers of a hyperspectral image (HSI) are more likely to be generated by independent sources and be mixed in a macroscopic degree before arriving at the sensor element of the imaging spectrometer as mixed spectra. Over the past few decades, many attempts have focused on imposing auxiliary regularizes on the conventional nonnegative matrix factorization (NMF) framework in order to effectively unmix these mixed spectra. As a promising step toward finding an optimum regularizer to extract endmembers, this paper presents a novel blind HU algorithm, referred to as Kurtosis-based Smooth Nonnegative Matrix Factorization (KbSNMF) which incorporates a novel regularizer based on the statistical independence of the probability density functions of endmember spectra. Imposing this regularizer on the conventional NMF framework promotes the extraction of independent endmembers while further enhancing the parts-based representation of data. Experiments conducted on diverse synthetic HSI datasets (with numerous numbers of endmembers, spectral bands, pixels, and noise levels) and three standard real HSI datasets demonstrate the validity of the proposed KbSNMF algorithm compared to several stateof- the-art NMF-based HU baselines. The proposed algorithm exhibits superior performance especially in terms of extracting endmember spectra from hyperspectral data; therefore, it could uplift the performance of recent deep learning HU methods which utilize the endmember spectra as supervisory input data for abundance extraction.