This letter presents an unsupervised unmixing method to interpret both nonlinear mixing effects and spectral variability (SV). First, the traditional multilinear mixing model (LMM) is augmented by introducing physically meaningful factors representing wavelength-dependent SV into the modeling. This model-driven improvement effectively provides a concise numerical explanation for the nonlinearity and SV, facilitating the consideration of their coupled effects on unmixing. Second, based on the augmented model, total variation (TV) regularizers to improve abundances’ spatial smoothness and scaling factors’ local similarity, and a constraint to confine the perturbations’ energy of SV, are exploited to formulate the unmixing problem. A multiswarm particle swarm optimization (PSO) algorithm is employed as the solver for this problem to achieve robust unmixing results with higher accuracy. Finally, experiments on numerical model-based and physical-based simulated data and real hyperspectral remote sensing images demonstrate the proposed method’s superiority over the state-of-the-art methods.

To mitigate the impact of mixed pixels in hyperspectral images (HSIs), substantial progress has been made in both model- and deep learning-based unmixing methods. However, issues such as complex computational processes and limited interpretability, hinder the improvement of their unmixing performance. Particularly, unsupervised nonlinear hyperspectral unmixing (HU) remains a great challenge. In this paper, we propose an extended multilinear mixing (EMLM) model-inspired dual-stream network for unsupervised nonlinear HU. Firstly, the alternating direction method of multipliers (ADMM) algorithm for the EMLM-based unmixing problem is unfolded to construct an encoder network. Subsequently, it is connected to a decoder network derived from the EMLM, creating an autoencoder-like network architecture. Secondly, the original HSIs and superpixel-averaging-based coarse HSIs are input into two network branches with identical architectures, respectively, to build a novel weight-sharing dual-stream network. Furthermore, estimates of abundances and nonlinear parameters obtained from the two branches are utilized to formulate local spatial similarity regularizers, enhancing the network’s loss function and effectively improving unmixing accuracy. Finally, experiments conducted on the laboratory-created dataset and real-world datasets validate that the proposed method exhibits superior unmixing performance compared to state-of-the-art methods. In addition, our code is available at: https://github.com/I3ab/EMLM-Net.

Recently, the research on nonlinear unmixing for hyperspectral images (HSIs) has received more and more attention. However, unsupervised nonlinear unmixing methods that jointly estimate endmembers and abundances from HSIs are insufficiently studied. Besides, the reasonable description of the wavelength-dependent nonlinear intensity and the effective utilization of the spectral and spatial information of HSIs remain to be improved. Based on an extended multilinear mixing model, a coarse-to-fine scheme is proposed for unsupervised nonlinear hyperspectral unmixing to address the above issues. Coarse HSIs generated based on the superpixel segmentation are unmixed first, and then fine unmixing on the original HSIs is achieved with the guidance of the coarse unmixing results. The endmembers extracted by the coarse unmixing are used to update the endmembers in the fine unmixing, and the coarse abundances and nonlinear parameters are integrated into regularizers. To be specific, a weighted sparse regularizer of abundances and a weighted graph regularizer of nonlinear parameters are constructed and incorporated into the objective function. In this way, some priors can be well modeled and exploited, including that the neighboring pixels share similar sparsity patterns in the abundances and show the consistency in correlations between different bands of the nonlinear parameters. Finally, the alternative optimization strategy and the alternating direction method of multipliers are applied to derive the algorithm. Experimental results on the synthetic, laboratory-created, and real hyperspectral data demonstrate that the proposed method outperforms the state-of-the-art nonlinear unmixing methods.

Due to noisy acquisition and atmospheric effects, some spectral bands in hyperspectral images (HSIs) suffer from low signal-to-noise ratios, thus requiring robust techniques to tackle unmixing problems. Besides, integrating the spatial information of HSIs into the nonlinear unmixing framework remains a challenge. To cope with the above problems, first, the$\ell_{2.1}$norm-based objective function is adopted to suppress the influence of noisy bands. Furthermore, to fully exploit the spatial-spectral information of HSIs, a reweighted collaborative sparse regularizer imposed on the abundances enforces that the pixels in a superpixel-based neighborhood share the same set of endmembers and have similar abundances, and a reweighted spectral total variation regularizer is employed to enhance the spatial-spectral smoothness of the nonlinear parameters. Extensive experiments conducted on the simulated and real datasets verify the superiority of the proposed algorithm over other state-of-the-art ones.

This paper presents a novel kernel-based decomposition model with total variation and sparsity regularizations via union dictionary for nonlinear hyperspectral anomaly detection. It decomposes a hyperspectral imagery into three components: background, anomaly, and noise. By using a union dictionary consisting of background and potential anomalous pixels, each test pixel can be well represented. Further, by utilizing endmember-kernel theory to handle nonlinear interactions between atoms in the dictionary, the complex light scattering effects can be effectively characterized. Besides, to separate these components effectively, the total variation and sparsity regularizations are incorporated into the decomposition model to represent the spatial properties of the background and the anomaly, respectively. The experimental results on simulated and real hyperspectral data sets demonstrated the effectiveness of our proposed method compared to several conventional and state-of-the-art anomaly detection methods.

As a representative structural property, the sparsity of ground covers’ distribution in hyperspectral images (HSIs) has been extensively applied to improve spectral unmixing in years. It is worth leveraging the close relationship between the sparsity of abundances and the spatial information of HSIs to obtain more reasonable sparse unmixing results. In this letter, a novel multi-level reweighted sparse unmixing method using superpixel segmentation and particle swarm optimization is proposed. Three sparse reweighted factors are finely designed at different local and global spatial levels. The first two local reweighted factors are constructed according to the sparseness and the low-rank property of pixels’ abundances in the generated superpixels. The third global reweighted factor is given by considering the change of the sparseness of each material abundance map in the entire HSI. Then, a new sparse constraint is imposed which can effectively facilitate the correct expression of abundances’ sparsity during unmixing. Moreover, particle swarm optimization based on double swarms with dimension division is employed to solve the unmixing problem and enhance the unmixing robustness. Experimental results of both simulated and real hyperspectral data validate that the proposed method can produce accurate unsupervised sparse unmixing results.

Due to the presence of multiple scatterings, linear unmixing methods may not perform well in practical applications, and thus nonlinear unmixing has become an urgent problem to be solved. Usually, the mixing process in the observed scenarios is physically based, and many well-designed models have been proposed to interpret it. Recently, kernel-based nonlinear unmixing methods have been popularly studied to achieve a model-free and flexible representation of the nonlinearity. However, the existing kernel-based methods are mainly data-driven, which could make them fail to match the real physical mixing mechanism and result in the occurrence of overfitting. In this article, a kernel-based bilinear unmixing (KBU) method was proposed to transform the classic bilinear mixing models into their equivalent kernel forms that are more general and effective in expressing second-order scatterings. Two specific types of kernel transformations were designed, and the alternating direction method of multipliers (ADMM) was used to solve the kernel-transformed model-based optimization problem for unmixing. Moreover, the spatial prior was exploited to further improve the unmixing accuracy, and here we employ the total variation (TV) regularization as a paradigm. Experiments on synthetic data sets, physics-based simulated data sets, and real data were conducted to evaluate the algorithms. It is validated that our methods have better performance in abundance estimation and nonlinear reconstruction compared with other nonlinear unmixing methods.

Recently, nonlinear unmixing algorithms have attracted special attention in hyperspectral image (HSI) processing. However, the inherent wavelength-dependent nonlinear intensity and noise effects in real HSIs are often overlooked, and the spatial information of HSIs has not been fully utilized in current studies. In this paper, we propose a spectral-spatial reweighted robust nonlinear unmixing algorithm to solve the above problems. First, a robust unmixing method is built on an extended multilinear mixing model (EMLM), which employs the vectorized nonlinear parameters to describe the nonlinear intensity varying along with spectral bands, and adopts thel2,1norm-based loss function to suppress the influence of noise. Second, to fully exploit the spectral-spatial information of HSIs, the nonlinear unmixing problem is reformulated with two regularizers. Specifically, a reweighted collaborative sparse regularizer is used to make the pixels in a superpixel-based neighborhood share the same subset of endmembers and have similar abundances because the neighboring pixels are usually composed of several materials in similar proportions, and a reweighted spectral total variation regularizer is utilized to improve the spectral-spatial smoothness of the vectorized nonlinear parameters by considering the local-region similarities of the nonlinear mixing effects. Finally, the constrained optimization problem is solved by the alternating direction method of multipliers (ADMM). Experimental results on simulated, semi-simulated, and real hyperspectral datasets demonstrate that the proposed method outperforms several state-of-the-art nonlinear unmixing methods.

The presence of shadows has always been a troublesome problem in image processing and can also affect spectral unmixing with hyperspectral remote sensing images. Traditional unmixing algorithms regard shadows as a special type of ground cover, so they can only estimate real materials’ sunlit abundances, and materials with low reflectance may be wrongly recognized as shadows. Without regarding shadows as ground cover, we propose a supervised nonlinear unmixing method to accurately estimate real materials’ total abundances inside and outside shadow areas. First, sunlit and shadowed constituents in every pixel of an image are modeled explicitly and integrated by a tractable bilinear mixing mechanism. Second, based on the constructed model, the strong sparsity of shadow spatial distribution and the spatial correlation among neighboring material abundances are exploited to produce a constrained optimization problem for nonlinear unmixing. Third, an existing unmixing framework based on particle swarm optimization is extended to calculate unknown variables of the optimization problem. Three alternatingly updated swarms using improved dimensional division strategies are designed to accordingly address the unmixing subproblems with respect to variables to be estimated during the solution search. This process has the potential to be generalized to solve complex nonlinear unmixing optimization problems. Finally, model-based simulated data, virtual citrus orchard data, and real hyperspectral remote sensing images are used in experiments to evaluate the proposed method and compare it with traditional and state-of-the-art nonlinear unmixing algorithms. Experimental results verify that the proposed method can achieve acceptable unmixing performance when managing nonlinear mixing effects and shadows.

Remote sensing image analysis often involves image-level classification and/ or regression. One major problem with remote sensing data is that it is difficult to obtain abundant precise manual annotations to train fully supervised deep networks that have achieved great success in computer vision. Therefore, this paper proposes a novel general semisupervised framework (GSF) which only requires a small amount of annotated samples for training. It employs a new hybrid (dis) similarity to characterize different aspects of the images and realizes label propagation while fine- tuning a deep neural network (NN). As shown by the experimental results, GSF outperforms several supervised baselines and state-of-the-art semisupervised models in classification and regression.

Maximum wind speed (MWS) is an important characteristic of tropical cyclone (TC). Estimation of MWS with remote sensing images of TCs via machine learning is a relatively new and challenging task. Here we propose a novel and effective method, Regularized Tensor Network (RTN), to estimate MWS using multispectral images (MSIs). RTN is a transductive regression model, built on a deep Tensor Network (TN) combined with two regularizations: manifold learning and categorization error. Experimental results showed that RTN outperformed several classic regression methods as well as advanced models based on deep learning.

Bilinear mixture models have shown their effectiveness for nonlinear spectral unmixing in literature. However, the influence of adjacency and shade effects is commonly overlooked. In this paper, an improved bilinear mixture model accounting for this issue is presented. Neighboring pixels of a pixel are linearly combined to represent the adjacency effect which works in both the first-order and second-order scattering parts. Moreover, abundances and the first-order scattering proportions are handled separately to consider the shadows. Model parameters are estimated by alternating projection gradient method. Experimental results on both simulated and real hyperspectral data verify the rationality of the proposed model.

Traditional target detection (TD) methods for hyperspectral imagery (HSI) suffer from background interference. In this paper, we propose a novel preprocessing method based on tensor principal component analysis (TPCA) to separate the background and target apart. In our approach, HSI is decomposed into the sum of the principal component (PC) part and the residual part, and TD is performed on the latter. TPCA takes spatial and spectral information into account jointly, and treats spatial and spectral information differently, which is in line with HSI physical meanings. Experiments on both synthetic and real data indicate that our TPCA-based method outperforms other feature extraction preprocessing methods in terms of TD results.

Wavelength dependent nonlinearity is an essential issue in hyperspectral unmixing, which was overlooked in the past. In this paper, a band-wise nonlinear unmixing method is presented. An extended multilinear mixing model is adopted for interpreting different degrees of nonlinear contributions per band. Moreover, regularizers including abundances' sparsity and nonlinear parameters' smoothness are exploited to formulate the optimization problem and obtain better unmixing results. Finally, unmixing is implemented in the scheme of alternating direction method of multipliers. Experimental results on both simulated and real hyperspectral data validate that the proposed method can improve the unmixing accuracy and reveal the change of nonlinearity at each band as well.

Most nonlinear mixture models and unmixing methods in the literature assume implicitly that the degrees of multiple scatterings at each band are the same. However, it is commonly against the practical situation that spectral mixing is intrinsically wavelength dependent, and the nonlinear intensity varies along with bands. In this paper, a band-wise nonlinear unmixing algorithm is proposed to circumvent this drawback. Pixel dependent probability parameters of the recent multilinear mixing model that represent different orders of nonlinear contributions are vectorized. Therefore, each band can get a scalar probability parameter which explicitly corresponds to the nonlinear intensity at that band. Before solving the extended model, abundances’ sparsity and probability parameters’ smoothness are exploited to build two physical constraints. After incorporating them into the objective function as regularization terms, the issue of local minima can be well alleviated to produce better solutions. Finally, alternating direction method of multipliers is applied to solve the constrained optimization problem and implement the nonlinear spectral unmixing. Experiments are further carried out with current model-based simulated data, physical-based synthetic data of virtual vegetated areas, and real hyperspectral remote sensing images, to provide a more reasonable validation for the developed model and algorithm. In comparison with state-of-the-art nonlinear unmixing methods, this method performs better in explaining the band dependent nonlinear mixing effect for improving the unmixing accuracy.

Recently, many nonlinear spectral unmixing algorithms that use various bilinear mixture models (BMMs) have been proposed. However, the high computational complexity and intrinsic collinearity between true endmembers and virtual endmembers considerably decrease these algorithms’ unmixing performances. In this paper, we come up with a novel abundance estimation algorithm based on the BMMs. Motivated by BMMs’ geometric characteristics that are related to collinearity, we conduct a unique nonlinear vertex${p}$to replace all the virtual endmembers. Unlike the virtual endmembers, this vertex${p}$actually works as an additional true endmember that gives affine representations of pixels with other true endmembers. When the pixels’ normalized barycentric coordinates with respect to true endmembers are obtained, they will be directly projected to be their approximate linear mixture components, which removes the collinearity effectively and enables further linear spectral unmixing. After that, based on the analysis of projection bias, two strategies using the projected gradient algorithm and a traditional linear spectral unmixing algorithm, respectively, are provided to correct the bias and estimate more accurate abundances. The experimental results on simulated and real hyperspectral data show that the proposed algorithm performs better compared with both traditional and state-of-the-art spectral unmixing algorithms. Both the unmixing accuracy and speed have been improved.

Change detection in multitemporal hyperspectral images (HSI) can be regarded as a classification task, consisting of two steps: change feature extraction and identification. To extract clean change features from heavily corrupted spectral change vectors (SCV) of multitemporal HSI, this paper proposes a novel spectrally-spatially regularized low-rank and sparse decomposition model (LRSDSS). It exploits the underlying data structure of SCV by decomposing SCV into three components: spatially smoothed low-rank data, sparse outliers and Gaussian noise. The first component maintains clean change features. The second and the third are corruptions to be removed. The experimental results can validate the effectiveness and the efficiency of LRSD_SS.

Nonnegative matrix factorization (NMF) is often used for unsupervised spectral unmixing in recent years. In this paper, a constrained NMF algorithm based on the bilinear mixture models for unsupervised nonlinear spectral unmixing is proposed. By using a distance measure without dimension reduction, data's projection on a group of constructed hyperplanes representing the nonlinearity are obtained so that the linear parts of data can be approximately determined. Further, we adopt NMF incorporated with a minimum distance constraint for unmixing with the hyperplanes being reconstructed repeatedly during the iteration. Experimental results on synthetic and real hyperspectral data indicate that the proposed algorithm has good unmixing performance.

Nonlinear spectral unmixing based on the bilinear mixture models has received much attention recently. In this paper, an abundance estimation algorithm based on the geometric characteristics of bilinear mixture models is proposed. By representing the models' bilinear terms as the linear contribution of an extra vertex that concentrates the common nonlinear mixing effect, solving the complex bilinear mixture models can be converted to doing the simple linear spectral unmixing. Furthermore, a traditional linear spectral unmixing algorithm is adopted to estimate the abundances directly in an iterative way. Experimental results on synthetic and real hyperspectral data show that the proposed algorithm performs better in both unmixing accuracy and computational speed.

Nonnegative Matrix Factorization (NMF) has been applied to hyperspectral unmixing for a few years. To relieve the non-convex problem, different constraints are imposed on NMF. But these constraints are added only on endmember or abundance. Simultaneously imposing constraints on endmember and abundance has not been tried yet. In this paper, we impose constraints on endmember and abundance at the same time in order to take a more comprehensive consideration of the properties of the hyperspectral image data. The constraints consider not only the geometric feature of endmember but also the sparsity and smoothness of abundance. The experimental performances of our method and other state-of-the-art constrained NMF methods are compared and analyzed, proving that our method is better than only imposing constraints on endmember or abundance and can improve the accuracy of hyperspectral unmixing.