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In a previous paper, we introduced (i) a specific hyperspectral mixing model for the sea bottom, based on a detailed physical analysis that includes the adjacency effect, and (ii) an associated unmixing method that is supervised (i.e., not blind) in the sense that it requires a prior estimation of various parameters of the mixing model, which is constraining. We here proceed much further, by first analytically showing that the above model can be seen as a specific member of the general class of mixing models involving spectral variability. Therefore, we then process such data with the IP-NMF unsupervised (i.e., blind) unmixing method that we proposed in previous works to handle spectral variability. Such variability especially occurs when the sea depth significantly varies over the considered scene. We show that IP-NMF then yields significantly better pure spectra estimates than a classical method from the literature that was not designed to handle such variability. We present test results obtained with realistic synthetic data. These tests address several reference water depths, up to 7.5 m, and clear or standard water. For instance, they show that when the reference depth is set to 7.5 m and the water is clear, the proposed approach is able to distinguish various classes of pure materials when the water depth varies up to ±0.2 m around this reference depth, over all pixels of the analyzed scene or over a “subscene”: the overall scene may first be segmented, to obtain smaller depths variations over each subscene. The proposed approach is therefore effective and can be used as a building block in performing the subpixel classification of the sea bottom for shallow water.

Hyperspectral unmixing plays a fundamental role in mining meaningful information from hyperspectral data. It promotes advancements in various scientific, environmental, and industrial applications by extracting meaningful information from hyperspectral data. However, it is still hindered by several challenges, including accurately identifying the number of endmembers in a hyperspectral image, extracting the endmembers, and estimating their abundance fractions. This research addresses these challenges by employing a convolutional-neural-network-based autoencoder that leverages both the spatial and spectral information present in the hyperspectral image. Additionally, a self-learning module utilizing a fuzzy clustering algorithm is designed to determine the number of endmembers. A novel approach is also introduced that estimates the abundances of the endmembers from the autoencoder and the clustering output. Real datasets and relevant performance metrics were used to validate and evaluate the performance of the proposed method. The results demonstrate that our approach outperforms related methods, achieving improvements of 47% in Spectral Angle Distance (SAD) and 42% in root-mean-square error (RMSE).

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.

Nonnegative matrix factorization (NMF) has been applied in hyperspectral unmixing. The nonconvexity of the NMF’s cost function leads to solutions that are only locally optimal. Adding regularized terms to the NMF helps improve the solutions. In this study, we proposed a regularized NMF model, the regularized tern is the minimum volume constraint with perturbation. The NMF model is solved with multiplicative updated rules. Numerical results verified that adding a disturbance term to the minimum volume constraint effectively improves the spectral curve’s local accuracy while maintaining the original model’s advantages.

Sparse unmixing plays a crucial role in the field of hyperspectral image unmixing technology, leveraging the availability of pre-existing endmember spectral libraries. In recent years, there has been a growing trend in incorporating spatial information from hyperspectral images into sparse unmixing models. There is a strong spatial correlation between pixels in hyperspectral images (that is, the spatial information is very rich), and many sparse unmixing algorithms take advantage of this to improve the sparse unmixing effect. Since hyperspectral images are susceptible to noise, the feature separability of ground objects is reduced, which makes most sparse unmixing methods and models face the risk of degradation or even failure. To address this challenge, a novel robust dual spatial weighted sparse unmixing algorithm (RDSWSU) has been proposed for hyperspectral image unmixing. This algorithm effectively utilizes the spatial information present in the hyperspectral images to mitigate the impact of noise during the unmixing process. For the proposed RDSWSU algorithm, which is based on ℓ1 sparse unmixing framework, a pre-calculated superpixel spatial weighting factor is used to smooth the noise, so as to maintain the original spatial structure of hyperspectral images. The RDSWSU algorithm, which builds upon the ℓ1 sparse unmixing framework, employs a pre-calculated spatial weighting factor at the superpixel level. This factor aids in noise smoothing and helps preserve the inherent spatial structure of hyperspectral images throughout the unmixing process. Additionally, another spatial weighting factor is utilized in the RDSWSU algorithm to capture the local smoothness of abundance maps at the sub-region level. This factor helps enhance the representation of piecewise smooth variations within different regions of the hyperspectral image. Specifically, the combination of these two spatial weighting factors in the RDSWSU algorithm results in an enhanced sparsity of the abundance matrix. The RDSWSU algorithm, which is a sparse unmixing model, offers an effective solution using the alternating direction method of multiplier (ADMM) with reduced requirements for tuning the regularization parameter. The proposed RDSWSU method outperforms other advanced sparse unmixing algorithms in terms of unmixing performance, as demonstrated by the experimental results on synthetic and real hyperspectral datasets.

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.

The complexity of land types and the limited spatial resolution of Synthetic Aperture Radar (SAR) imagery have led to widespread mixed-pixel contamination in radar backscatter images. The radar backscatter echo signals from a mixed pixel are often a combination of backscattering contributions from multiple endmembers. The signal mixture of endmembers within mixed pixels hinders the establishment of accurate relationships between pure endmembers’ parameters and the corresponding backscatter coefficient, thereby significantly reducing the accuracy of surface parameter inversion. However, few studies have focused on decomposing and estimating the pure backscatter signals within mixed pixels. This paper proposes a novel approach based on hyperspectral unmixing techniques and the microwave backscatter contribution decomposition (MBCD) model to estimate the pure backscatter coefficients of all Endmembers within mixed pixels. Experimental results demonstrate that the model performance varied significantly with endmember abundance. Specifically, high accuracy was achieved in estimating soil backscattering coefficients when vegetation coverage was below 25% (R2≈0.88, with 98% of pixels showing relative errors within 0–20%); however, this accuracy declined as vegetation coverage increased. For grass endmembers, the model maintained high estimation precision across the entire grassland area (vegetation coverage 0.2–0.8), yielding an of 0.80 with 83% of pixels falling within the 0–20% relative error range. In addition, the model performance is influenced by the number of endmembers.

Transformers have performed favorably in recent hyperspectral unmixing studies in which the self-attention mechanism possesses the ability to retain spectral information and spatial details. However, the lack of reliable prior information for correction guidance has resulted in an inadequate accuracy and robustness of the network. To benefit from the advantages of the Transformer architecture and to improve the interpretability and robustness of the network, a dual-branch network with prior information correction, incorporating a Transformer network (PICT-Net), is proposed. The upper branch utilizes pre-extracted endmembers to provide pure pixel prior information. The lower branch employs a Transformer structure for feature extraction and unmixing processing. A weight-sharing strategy is employed between the two branches to facilitate information sharing. The deep integration of prior knowledge into the Transformer architecture effectively reduces endmember variability in hyperspectral unmixing and enhances the model’s generalization capability and accuracy across diverse scenarios. Experimental results from experiments conducted on four real datasets demonstrate the effectiveness and superiority of the proposed model.

Spectral unmixing attempts to decompose a spectral ensemble into the constituent pure spectral signatures (called endmembers) along with the proportion of each endmember. This is essential for techniques like hyperspectral imaging (HSI) used in environment monitoring, geological exploration, etc. Several spectral unmixing approaches have been proposed, many of which are connected to hyperspectral imaging. However, most extant approaches assume highly diverse collections of mixtures and extremely low-loss spectroscopic measurements. Additionally, current non-Bayesian frameworks do not incorporate the uncertainty inherent in unmixing. We propose a probabilistic inference algorithm that explicitly incorporates noise and uncertainty, enabling us to unmix endmembers in collections of mixtures with limited diversity. We use a Bayesian mixture model to jointly extract endmember spectra and mixing parameters while explicitly modeling observation noise and the resulting inference uncertainties. We obtain approximate distributions over endmember coordinates for each set of observed spectra while remaining robust to inference biases from the lack of pure observations and the presence of non-isotropic Gaussian noise. As a direct impact of our methodology, access to reliable uncertainties on the unmixing solutions would enable robust solutions to noise, as well as informed decision-making for HSI applications and other unmixing problems.

Hyperspectral unmixing (HU) is one of the most active hyperspectral image (HSI) processing research fields, which aims to identify the materials and their corresponding proportions in each HSI pixel. The extensions of the nonnegative matrix factorization (NMF) have been proved effective for HU, which usually uses the sparsity of abundances and the correlation between the pixels to alleviate the non-convex problem. However, the commonly used L 1 / 2 sparse constraint will introduce an additional local minima because of the non-convexity, and the correlation between the pixels is not fully utilized because of the separation of the spatial and structural information. To overcome these limitations, a novel bilateral filter regularized L 2 sparse NMF is proposed for HU. Firstly, the L 2 -norm is utilized in order to improve the sparsity of the abundance matrix. Secondly, a bilateral filter regularizer is adopted so as to explore both the spatial information and the manifold structure of the abundance maps. In addition, NeNMF is used to solve the object function in order to improve the convergence rate. The results of the simulated and real data experiments have demonstrated the advantage of the proposed method.