A Two-Stream Stacked Autoencoder With Inter-Class Separability for Bilinear Hyperspectral Unmixing

Hyperspectral unmixing is a significant task in remote sensing image analysis. Existing learning-based methods for hyperspectral unmixing generally are in the form of an autoencoder and take geometric distances, such as spectral angle distance (SAD) as loss functions. These methods ignored the distribution similarity between the observation and the reconstruction, which might help improve the unmixing performance. Besides, the autoencoder is trained by directly comparing the difference between the observation and the reconstruction, and the difference between their features has been neglected. Based on the above considerations, we propose a joint metric neural network for hyperspectral unmixing, by introducing the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Wasserstein distance</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">feature matching</i> as regularization terms and SAD as the underlying loss. The proposed neural network consists of two parts: an autoencoder is used for endmember extraction and abundance estimation, while a discriminator is used to compute the Wasserstein distance. The Wasserstein distance can stably provide useful gradient information that promotes the autoencoder to reach a solution with better unmixing performance. The feature matching is adapted to an intermediate layer of the discriminator for enforcing the features of the observation and the reconstruction to be equal, which can lead to further improvement of the unmixing performance. The model analysis and the regularization parameter analysis are conducted to demonstrate the effectiveness of our method. Experimental results on four real-world hyperspectral data sets show that our method outperforms the state-of-the-art methods, especially in terms of abundance estimation.

Hyperspectral unmixing aims to estimate endmember spectra and their corresponding abundance fractions at the subpixel scale, which is a critical preprocessing step for quantitative analysis of hyperspectral remote sensing imagery. While deep learning-based methods have achieved remarkable progress, three fundamental challenges remain: (i) reliance on a single shared spatial prior that cannot decouple the heterogeneous spatial patterns of different land covers; (ii) the lack of synergy in jointly optimizing endmember extraction and abundance estimation; (iii) the poor robustness of unsupervised training to complex mixtures, noise, and class imbalance. To address these issues, we propose a novel unsupervised unmixing framework that integrates adaptive orthogonal multi-faceted graph representation with curriculum learning. Specifically, we design an Adaptive Orthogonal Multi-Faceted Graph Generator (AOMFG) to learn a set of independent orthogonal graph structures, achieving spatially informed decoupling of land cover patterns. Then, a dual-branch collaborative optimization network is constructed: a Graph Convolutional Network (GCN) branch that incorporates the learned spatial topological priors for abundance estimation, and a 1D Convolutional Neural Network (1DCNN) branch that employs a query-attention mechanism to adaptively aggregate pure spectral features for endmember extraction. Finally, we introduce a three-stage curriculum learning strategy that progressively fine-tunes the model, which significantly enhances its performance. Extensive experiments on three widely used real-world benchmark datasets demonstrate that our proposed framework consistently outperforms state-of-the-art methods in both endmember extraction and abundance estimation accuracy. Comprehensive ablation studies, parameter sensitivity analysis, and noise robustness tests further validate the effectiveness of each core component.

Hyperspectral image unmixing is an important part of hyperspectral data analysis. The mixed pixel decomposition consists of two steps, endmember (the unique signatures of pure ground components) extraction and abundance (the proportion of each endmember in each pixel) estimation. Recently, a Discrete Particle Swarm Optimization algorithm (DPSO) was proposed for accurately extract endmembers with high optimal performance. However, the DPSO algorithm shows very high computational complexity, which makes the endmember extraction procedure very time consuming for hyperspectral image unmixing. Thus, in this paper, the DPSO endmember extraction algorithm was parallelized, implemented on the CUDA (GPU K20) platform, and evaluated by real hyperspectral remote sensing data. The experimental results show that with increasing the number of particles the parallelized version obtained much higher computing efficiency while maintain the same endmember exaction accuracy.

Hyperspectral unmixing (HU) is a technique for estimating a set of pure source signals (end members) and their proportions (abundances) from each pixel of the hyperspectral image. Non-negative matrix factorization (NMF) can decompose the observation matrix into the product of two non-negative matrices simultaneously and can be used in HU. Unfortunately, a limitation of many traditional NMF-based methods, i.e., the non-convexity of the objective function, may lead to a sub-optimal solution. Thus, we put forward a new unmixing method based on NMF under smoothing and sparse constraints to obtain a better solution. First, considering the sparseness of the abundance matrix, a weight sparse regularization is introduced into the NMF model to ensure the sparseness of the abundance matrix. Second, according to the similarity prior of the same feature in the adjacent pixels, a Total Variation regularization is further added to the NMF model to improve the smoothness of the abundance map. Finally, the signatures of each end member are modified smoothly in spectral space. Moreover, it is noticed that discontinuities may emerge due to the removal of noisy bands. Therefore, the spectral data are piecewise smooth in spectral space. Then, in this paper, a piecewise smoothness constraint is further applied to each column of the end-member matrix. Experiments are conducted to evaluate the effectiveness of the proposed method based on two different datasets, including a synthetic dataset and the real-life Cuprite dataset, respectively. Experimental results show that the proposed method outperforms several state-of-the-art HU methods. In the Cuprite hyperspectral dataset, the proposed method’s Spectral Angle Distance is 0.1694, compared to the TV-RSNMF method’s 0.1703, L1/2NMF method’s 0.1925, and VCA-FCLS method’s 0.1872.

Hyperspectral unmixing is a critical task in remote sensing, challenged by complex mixing mechanisms and long-range spatial dependency modeling. To address the limitations of existing methods in capturing spatial structures and frequency representations, we propose SFMamba, a novel spatial-frequency collaborative unmixing framework. The framework includes two key modules: (1) a multi-view spatial mamba module based on state space model, which captures directional spatial dependencies to enhance contextual representation; and (2) a hyperspectral fourier mixer, which integrates fourier transform-based frequency features to strengthen the spectral modeling of endmembers. Experiments on the Urban and Jasper Ridge datasets demonstrate that the proposed method achieves superior performance in endmember extraction, with competitive results in abundance estimation, thus showing strong potential in hyperspectral unmixing tasks. This work provides a novel and effective solution for hyperspectral unmixing with spatial-frequency collaboration.

The endmember extraction is a challenging problem in spectral unmixing (SU) of a mixed pixel in hyperspectral imagery. There are plenty of attempts to solve the endmember extraction problem. Still, the pure pixel assumption-based algorithms have probably been used most in solving the endmember extraction of SU due to the light computational burden. These pure pixel assumption-based algorithms usually follow one of the criteria: (1) Maximum simplex volume or (2) Extreme projection on a subspace. We propose a novel integrated framework that uses both the criteria mentioned above and the proposed one is referred to as the Convexity-based Pure Index (CPI) algorithm. The CPI generates a fixed number of convex sets based on the number of available bands in the hyperspectral image. The algorithm defines the purity score based on the availability of pixels in the convex sets for the two-band data. The CPI has been compared with contemporary algorithms such as Automatic Target Generation Process (ATGP), Vertex Component Analysis (VCA), Pixel Purity Index (PPI), Successive Volume MAXimization (SVMAX), Alternating Volume MAXimization (AVMAX), TRIple-P: P-norm based Pure Pixel identification (TRIP), Successive Decoupled Volume Max–Min (SDVMM), Negative ABundance-Oriented (NABO), and Entropy-based Convex Set Optimization (ECSO). The metrics, Spectral Angle Distance (SAD) and Spectral Information Divergence (SID) used in the comparison were improved up to 5.9% and 9%, respectively. The CPI outperforms prevailing algorithms on real benchmark data and new AVIRIS-NG data. The robustness of the CPI is also tested for various noisy synthetic data. The efficacy of the proposed algorithm is also tested by using qualitative analysis by visualizing the spectra comparison, and abundance maps for all real data.

With the advancement in technology, hyperspectral images have potential applications in the field of remote sensing due to their high spectral resolution. Despite the hyperspectral image providing abundant information, its analysis suffers from the problem of high dimensionality. Hence, Dimensionality Reduction (DR) is an essential task in all hyperspectral image analysis. Band Selection, which is one of the DR techniques, is still a challenging issue even though many algorithms have been developed. To provide remedy for this issue, this paper explores a novel approach for band selection using K-means clustering on statistical feature in hyperspectral images. The proposed method of clustering based band selection for DR is simple and accurate. A reliable estimate of number of bands to be selected is provided by Virtual Dimensionality (VD). Informative bands preserving maximum information are selected based on the statistical feature, the variance using K-means Clustering technique. Further, our proposed work involves the utilization of the effectiveness of Simplex Growing Algorithm (SGA) on endmember extraction in association with clustering based band selection. Using Fully Constrained Least Squares (FCLS) method, abundance fraction is estimated based on endmember signatures, which are derived using Endmember Extraction Algorithm (EEA). The proposed work is investigated and compared with that of N-FINDR and Vertex Component Analysis (VCA) algorithms. The performance of the proposed algorithm is evaluated using Root Mean Square Error (RMSE), Spectral Angle Distance (SAD) and computation time. Experimental results show that the proposed clustering based band selection with SGA endmember extraction algorithm reduces the average SAD by 8 to 10 % and the average RMSE by nearly 1 %, compared to that of N-FINDR and VCA algorithms. In terms of computation time, the proposed band selection based DR with SGA algorithm is seven times faster than conventional transform based DR with SGA algorithm.

Few-shot hyperspectral classification is a challenging problem that involves obtaining effective spatial–spectral features in an unsupervised or semi-supervised manner. In recent years, as a result of the development of computer vision, deep learning techniques have demonstrated their superiority in tackling the problems of hyperspectral unmixing (HU) and classification. In this paper, we present a new semi-supervised pipeline for few-shot hyperspectral classification, where endmember abundance maps obtained by HU are treated as latent features for classification. A cube-based attention 3D convolutional autoencoder network (CACAE), is applied to extract spectral–spatial features. In addition, an attention approach is used to improve the accuracy of abundance estimation by extracting the diagnostic spectral features associated with the given endmember more effectively. The endmember abundance estimated by the proposed model outperforms other convolutional neural networks (CNNs) with respect to the root mean square error (RMSE) and abundance spectral angle distance (ASAD). Classification experiments are performed on real hyperspectral datasets and compared to several supervised and semi-supervised models. The experimental findings demonstrate that the proposed approach has promising potential for hyperspectral feature extraction and has better performance relative to CNN-based supervised classification under small-sample conditions.

The spatial resolution of hyperspectral data is low, so there are a large number of mixed pixels, which is also one of the main reasons that reduce the accuracy of hyperspectral image target classification. Hyperspectral unmixing is an important subject in the field of remote sensing. Hyperspectral unmixing generally consists of three steps: reduction, endmember extraction and inversion. As one of the key steps of hyperspectral unmixing, efficient and rapid endmember extraction is an important object in hyperspectral remote sensing. In this paper, the endmember extraction of hyperspectral data is implemented based on PCA and a new SGA algorithm, which solves the dimension limitation of traditional SGA algorithm and the new SGA algorithm without data redundancy caused by data dimensionality reduction.

Autoencoder-based methods have gained prominence in Blind hyperspectral Unmixing (BHU), with most approaches based on predefined mixing assumptions, such as the linear mixing model. However, real-world scenes often involve complex nonlinear light-material interactions that are difficult to model explicitly, leading to systematic biases in endmember and abundance estimation when these assumptions deviate from the actual mixing mechanism. In this article, we extend conventional autoencoder-based BHU by jointly and adaptively learning the mixing mechanism directly from hyperspectral images while estimating endmembers and abundances, and propose a novel BHU framework termed UNmixing TRansformer (UNTR). Specifically, an adaptive mixing mechanism modeling module is designed to parameterize the mixing mechanism, in which a specially designed transformer fuses heterogeneous endmember and abundance information. Furthermore, we develop an end-member query mechanism integrated into the adaptive mixing mechanism modeling module under a distribution alignment constraint, enabling robust endmember estimation under random initialization. As the first attempt to adaptively model the mixing mechanism as data-driven network parameters, UNTR achieves remarkable accuracy in both abundance and endmember estimation. Without relying on predefined mixing assumptions and well-initialized endmembers, UNTR exhibits strong adaptability to complex real-world scenarios. Our code will be available at https://github.com/Preston-Dong/UNTR.

In hyperspectral imaging, spectral unmixing aims at decomposing the image into a set of reference spectral signatures corresponding to the materials present in the observed scene and their relative proportions in every pixel. While a linear mixing model was used for a long time, the complex nature of the physicochemical phenomena that affect the spectra of the materials led to shift the community's attention toward algorithms accounting for the variability of the endmembers. Such intraclass variations are mainly due to local changes in the composition of the materials and to illumination changes. In the physical remote sensing community, a popular model accounting for illumination variability is the radiative transfer model proposed by Hapke. It is, however, too complex to be directly used in hyperspectral unmixing in a tractable way. Instead, the extended linear mixing model (ELMM) allows to easily unmix the hyperspectral data accounting for changing illumination conditions and to address nonlinear effects to some extent. In this letter, we show that the ELMM can be obtained from the Hapke model by successively simplifying physical assumptions, whose validity we experimentally examine, thus demonstrating its relevance to handle illumination-induced variability in the unmixing problem.

Endmember extraction is a key step in hyperspectral unmixing. This paper proposes a new endmember extraction framework based on the swarm intelligence algorithm. We adopt a discrete structure because pixels exist within a discrete frame. Traditional swarm intelligence algorithms produce stacked solutions based on similar endmembers in the same class. We introduce a “distance” factor into the objective function to limit the number of endmembers per class. We then propose three endmember extraction methods based on the artificial bee colony (ABC), ant colony optimization (ACO) and particle swarm optimization (PSO) algorithms. Experiments with both simulated and actual hyperspectral image data indicate that the proposed framework can significantly improve the accuracy of endmember extraction.

Endmember extraction (EE) plays a crucial part in the hyperspectral unmixing (HU) process. To obtain satisfactory EE results, the EE can be considered as the multiobjective optimization problem to optimize the volume maximization (VM) and root-mean-square error (RMSE) simultaneously. However, it is often quite challenging to balance the conflict of these objectives. In order to tackle the challenges of multiobjective EE, we present a (μ + λ) multiobjective differential evolution algorithm ((μ + λ)-MODE) based on ranking multiple mutations. In the (μ + λ)-MODE algorithm, ranking multiple mutations are adopted to create the mutant vectors via the scaling factor pool to enhance the population diversity. Moreover, mutant vectors employ the binary crossover operator to generate the trial vectors through a crossover control parameter pool in (μ + λ)-MODE to take advantage of the good information of the population. In addition, (μ + λ)-MODE utilizes the fast nondominated sorting approach to sort the parent and trial vectors, and then selects the elitism offspring as the next population via the (μ + λ) selection strategy. Eventually, experimental comparative results in three real HSIs reveal that our proposed (μ + λ)-MODE is superior to other EE methods.

Hyperspectral Unmixing (HU), also known as spectral mixture analysis, is a challenging problem that decomposes a mixed spectrum into a collection of endmembers and their abundance fractions. In this paper, we extended the autoencoder network (Palsson et al. in IEEE Access 6:25646–25656, [1]) for blind hyperspectral nonlinear unmixing. The proposed autoencoder architecture consists of two networks encoder and decoder. The encoder network has the same as the original architecture. The architecture of the decoder network was altered to handle nonlinear unmixing. Our proposed encoder network has four fully connected layers, each with the number of neurons equal to the dimension of the end members. Experiments were conducted using nonlinear synthetic dataset sampled from the USGS library, and the performance was evaluated using both SAD and SID metrics. Four categories of experiments were carried out; accuracy assessment, weight initialization techniques, learning rate, and robustness to the noise. Experimental results show that the proposed autoencoder outperforms traditional endmember extraction algorithms in nonlinear cases. Finally, we introduced the application of hyperspectral image unmixing algorithm in the Internet of things (IoT) environment.

The adequacy of quantification of the components in non-homogeneous pharmaceutical tablets using near infrared (NIR) linear hyperspectral unmixing has been studied with and without the presence of the tablet coating and an inefficient blending process. NIR images of six coated tablets of different formulations and of sections thereof, extracted at specific depths, were acquired. The quantification of the compounds present was performed via the classical least squares criterion. The results presented show that given the low depth of penetration of the NIR radiation, the coating represents as much as 30% of the mass fraction of the sampled tablet, even though it is commonly less than 3% of the mass fraction of the total tablet. This deviation negatively impacts the estimates of the compounds of interest. Estimates of the compounds obtained in sections approached the true values and were consistent at each depth. Both scenarios (coated and uncoated) were found to be well explained by a linear mixing model, as the errors in spectral estimates were small. The pixels showing the highest fraction of energy not explained by the linear model were found to be spatially located in areas where the surface curvature was high and a high reflectivity was observed; factors known to contribute non-linearities to the mixing scenario. The outcomes of this study have practical importance for the pharmaceutical industry: first, tablets should always be uncoated or microtomed before being imaged, in order to remove the high contribution of the coating and to obtain a flat surface. These steps reduce the above-mentioned non-linearities that introduce errors when using a linear mixing model. Second, the mixing scale shall be taken into account, as a poor blending may not show a similar in-depth pattern and thus provide different estimates at each depth and, on the other hand, over-blending may lead to a non-linear mixing scenario, depending on the spatial resolution used. An appropriate prior study will direct analysis either to linear or non-linear approaches.