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 Wasserstein distance and feature matching 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 image (HSI) classification is a challenging task due to subtle interclass difference and large intraclass variability, especially when the available training samples are scarce. To overcome this barrier, this paper proposes a novel deep similarity network (DSN) for HSI classification, which not only ensures enough samples for training but also extracts more discriminative features. Unlike other classification methods, our essential idea is to approach the classification task by learning a new similarity measure of pixel pairs under a two-branch neural network. Specifically, a binary classification dataset with same-class and different-class pixel pairs is first constructed, which can significantly increase the number of training samples. Then, the DSN utilizes two sub-networks to extract deep features from the pixel pairs, and computes the similarity between the extracted deep features by a fusion sub-network. Finally, the output of the DSN is used to measure the similarity to each class and the similarity determines the class label. To make full use of the spatial information, the extended multi-attribute profile is incorporated to the DSN. Moreover, a joint loss function is proposed to enhance the discrimination and alleviate the challenge caused by the spatial variability of spectral signatures. Experiments on real HSI datasets verify the superiority of the DSN over several state-of-the-art methods in HSI classification. For instance, the overall accuracy of the DSN on Houston2013 dataset is 89.07%, which achieves a marked improvement of at least 4.2% over all compared methods like convolutional neural network, deep learning with attribute profiles and so on.

Hyperspectral 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.

Hyperspectral unmixing (HU) has been one of the most significant tasks in hyperspectral image (HSI) processing. In recent years, nonnegative matrix factorization (NMF) has received great attention in the HU due to its simultaneous estimation, flexible modeling, and little requirement on prior information. However, several common NMF algorithms still suffer from high computational complexity, instability, and low convergence rate. Motivated by the matrix manifold theory, this article proposes a new sparse oblique-manifold ( $\mathcal {OB}$ ) NMF method from the perspective of matrix manifold. The critical idea of the proposed method is to regard the abundance matrix as locating on the oblique manifold, which eliminates its constraint of nonnegativity and sum-to-one and incorporates its intrinsic Riemannian geometry. Meanwhile, the $L_{1/2}$ -norm on the Euclidean space can be transformed equivalently into the $L_{1}$ -norm on oblique manifold. Then, via solving this sparse $\mathcal {OB}$ NMF by the Riemannian conjugated gradient (RCG) algorithm and the multiplicative iterative rule, the proposed method not only ensures improvement in the solution accuracy but also leads to a much faster convergence rate. Experimental results from the synthetic and real-world datasets illustrate the effectiveness and efficiency of the proposed method compared with the state-of-the-art NMF methods in HU.

The deep network has shown its superiority to extract discriminative features for hyperspectral image (HSI) classification. However, most existing methods only exploit label information of land classes to supervise the learning of deep features, and the learning process is totally automatic. Considering the complex spectral–spatial characteristic in real HSI, it is reasonable to utilize the manifold structure of input data to provide complementary information for precise classification. This article proposes a structure-preserving spectral–spatial network (SPSSN) to exploit the manifold structure information during the feature learning process, which can extract discriminative deep structure-preserving spectral–spatial features. Specifically, a basic spectral–spatial network (SSN), comprising a spectral module and a spatial module connected in series, is first built to learn spectral–spatial features from HSI cubes. Second, a novel structure-preserving constraint is introduced to transfer the intrinsic manifold structure of the input data into the learned deep spectral–spatial features, so as to enhance the discrimination. Furthermore, a feasible algorithm of imposing the constraint is designed to make it compatible with the deep learning framework, which results in a structure-preserving loss. Finally, the SSN is combined with the structure-preserving loss to obtain the SPSSN. Experiments on real HSI datasets verify the effectiveness and superiority of the SPSSN compared with several state-of-the-art methods in HSI classification.