Traditional target detection (TD) algorithms for hyperspectral imagery (HSI) typically suffer from background interference. To alleviate this problem, we propose a novel preprocessing method based on tensor principal component analysis (TPCA) to separate the background and target apart. With the use of TPCA, HSI is decomposed into a principal component part and a residual part with the spatial-spectral information of the HSI being fully exploited, and TD is performed on the latter. Moreover, an effective distinction in scheme can be made between a HSI tensor’s spatial and spectral domains, which is in line with the physical meanings. Experimental results from both synthetic and real hyperspectral data show that the proposed method outperforms other preprocessing methods in improving the TD accuracies. Further, target detectors that combine the TPCA preprocessing approach with traditional target detection methods can achieve better results than those of state-of-the-art methods aiming at background suppression.

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.

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.

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.

Hyperspectral unmixing has received increasing attention as a technique for estimating endmember spectra and fractional abundances of land covers. Encoding high-dimensional hyperspectral data into a low-dimensional latent space to generate reasonable abundances, autoencoder (AE) has shown its great potential and attractive advantages in spectral unmixing. AEs decode abundances back to spectra, which can effectively reflect the general spectral mixing process. However, most existing AE-based unmixing methods often do not fully exploit the spatial information of hyperspectral images, hindering the improvement of unmixing accuracy. This paper proposes a graph attention convolutional autoencoder architecture for hyperspectral unmixing. By incorporating graph attention convolution into AE, the proposed method performs better in leveraging both long-range and short-range spatial information of hyperspectral images. Accurate abundances with global and local spatial consistency can be efficiently learned by the network. Moreover, the decoder is further improved based on the post-polynomial nonlinear mixing (PPNM) model to make the network have stronger physical interpretability to deal with the issue of nonlinear blind unmixing. Experimental results indicate that the proposed method has good unmixing performance. It can reduce the root mean squared error of estimated abundances for synthetic data by over 10% compared to other methods. In experiments with real hyperspectral data, the difference between its unmixing results' accuracy and the best is less than 5%.

Spectral unmixing is an important technique for exploiting hyperspectral data. The presence of nonlinear mixing effects poses an important problem when attempting to provide accurate estimates of the abundance fractions of pure spectral components (endmembers) in a scene. This problem complicates the development of algorithms that can address all types of nonlinear mixtures in the scene. In this paper, we develop a new strategy to simultaneously estimate both the endmember signatures and their corresponding abundances using a biswarm particle swarm optimization (BiPSO) bilinear unmixing technique based on Fan's model. Our main motivation in this paper is to explore the potential of the newly proposed bilinear mixture model based on particle swarm optimization (PSO) for nonlinear spectral unmixing purposes. By taking advantage of the learning mechanism provided by PSO, we embed a multiobjective optimization technique into the algorithm to handle the more complex constraints in simplex volume minimization algorithms for spectral unmixing, thus avoiding limitations due to penalty factors. Our experimental results, conducted using both synthetic and real hyperspectral data, demonstrate that the proposed BiPSO algorithm can outperform other traditional spectral unmixing techniques by accounting for nonlinearities in the mixtures present in the scene.