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Sparse unmixing (SU) algorithms use the existing spectral library as prior knowledge to analyze the endmembers and estimate abundance maps. The majority of SU algorithms use loss functions based on the $L_{2,1}$ -norm or $F$ -norm to minimize reconstruction error. They have different advantages and shortcomings. In short, $F$ -norm has a differentiable characteristic, and it is easy to minimize as a loss function. However, it is very sensitive to heavy noise and outliers. While the $L_{2,1}$ -norm emphasizes the reconstruction error on each band and is robust to noise with different intensities in different bands. But the $L_{2,1}$ -norm is nondifferentiable at zero-point. This article introduces an adaptive loss function based on the $\sigma $ -norm for SU, which combines the advantages of the $L_{2,1}$ -norm and $F$ -norm. The adaptive loss function is related to a nonnegative parameter $\sigma $. By adjusting the parameter $\sigma $ , the adaptive loss function can approach the $F$ -norm or $L_{2,1}$ -norm. To the best of our knowledge, it is the first time to apply an adaptive loss function to SU. Moreover, the adaptive loss function is globally differentiable, and we propose an optimization algorithm for the adaptive loss function and verify its convergence. Experiments on real-world and synthetic HSIs show that the adaptive loss function effectively enhances the performance of the SU algorithms. [ABSTRACT FROM AUTHOR]

Sparse unmixing (SU) is a semisupervised learning problem, which performs abundance estimation when a spectral library is given. In this way, the essence of SU is to select the most suitable subset from the spectral library for representing all mixed pixels. Many SU methods adopt joint-sparse and low-rank constraints to guide the abundance estimation. However, the spatial correlation learning in these algorithms is not accurate enough, which seriously affects the unmixing performance. Besides, most pruning-based unmixing methods suffer from complicated pruning strategies and ignore the relationship between the spectral library and mixed pixels. This article proposes a reweighted low-rank and joint-sparse unmixing approach, which combines an effective pruning strategy (RLSU-LP). The RLSU-LP approach consists of rough unmixing stage, library pruning, and fine-tuning unmixing stage. First, the proposed method utilizes image segmentation to obtain different homogeneous regions, i.e., superpixels. A confidence index is introduced to describe the superpixel homogeneity, which is conducive to learning the meticulous spatial correlation. The RLSU-LP method reasonably relaxes or tightens the sparse and low-rank constraints of the abundance matrix by using the confidence index. Furthermore, a supervised library pruning strategy is proposed, which aims to eliminate the inactive endmembers by considering the contribution of representing mixed pixels. Experiments on the synthesized dataset and authentic hyperspectral images verify the effectiveness of our proposed algorithm. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing is an essential research topic for spectral data analysis due to the existence of mixed pixels. Recently, many methods based on sparse nonnegative matrix factorization (NMF) have been widely used for unmixing by incorporating similarity preserving. However, most of them conduct the similarity learning and unmixing by using two separate steps, which may lead to the case that the learned similarity matrix is not the optimal one for unmixing. Thus, the performance of unmixing would be influenced and become undesirable. To alleviate this problem, we propose an adaptive relationship preserving-based sparse NMF (ARP-NMF) for hyperspectral unmixing. Typically, we regard similarity learning and unmixing as an alternative optimization process. During this process, the learned similarity weights and unmixing results can be mutually improved. Thus, our proposed method can learn the optimal similarity weights for unmixing and obtain better generalization ability for different hyperspectral images than traditional methods. Moreover, by using the spectral and spatial local structure, our ARP-NMF method effectively preserves structure consistency between pixels and abundances. Experimental results both on the synthetic data and the real data reveal that our proposed method outperforms several representative sparse NMF-based methods. [ABSTRACT FROM AUTHOR]

Semisupervised band selection (BS) technique plays an important role in processing hyperspectral images (HSIs) because of its superiority of using the limited labeled data and plentiful unlabeled data to select the discriminative and informative feature, which copes with the problem of high-dimensional and scare labeled samples of HSIs. Among semisupervised BS models, graph-based methods are superior to others in many situations and have received more and more attention. However, traditional graph-based models construct a similarity matrix and select valuable bands independently. The similarity matrix remains constant, which will damage the local manifold structure and lead to a suboptimal result. To solve this problem, we propose a semisupervised band selection with an optimal graph (BSOG) approach, which performs BS and local structure learning simultaneously. Instead of fixing the input similarity matrix, the similarity matrix is updated constantly to learn a better local structure. Besides, the learned similarity matrix is adaptive. Then, the optimal band subset can be selected by analyzing the obtained projection matrix $\boldsymbol W$. An efficient and simple optimization algorithm is proposed to solve this model. Experiments on four real HSIs data validate the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Hyperspectral image super-resolution (SR) methods based on deep learning have achieved significant progress recently. However, previous methods lack the joint analysis between spectrum and horizontal or vertical direction. Besides, when both 2D and 3D convolution are in the network, the existing models cannot effectively combine the two. To address these issues, in this article, we propose a novel hyperspectral image SR method by exploring the relationship between 2D/3D convolution (ERCSR). Our method alternately employs 2D and 3D units to solve the problem of structural redundancy by sharing spatial information during reconstruction for existing model, which can enhance the learning ability of 2D spatial domain. Importantly, compared with the network using 3D units, i.e., 2D units are replaced by 3D units, it can not only reduce the size of the model but also improve the performance of the model. Furthermore, to exploit the spectrum fully, the split adjacent spatial and spectral convolution (SAEC) is designed to parallelly explore information between spectrum and horizontal or vertical direction in space. Experiments on widely used benchmark datasets demonstrate that the proposed approach outperforms state-of-the-art SR algorithms across different scales in terms of quantitative and qualitative analysis. [ABSTRACT FROM AUTHOR]

The fusion of a low-spatial-resolution hyperspectral image (HSI) (LR-HSI) with its corresponding high-spatial-resolution multispectral image (MSI) (HR-MSI) to reconstruct a high-spatial-resolution HSI (HR-HSI) has been a significant subject in recent years. Nevertheless, it is still difficult to achieve the cross-mode information fusion of spatial mode and spectral mode when reconstructing HR-HSI for the existing methods. In this article, based on a convolutional neural network (CNN), an interpretable spatial–spectral reconstruction network (SSR-NET) is proposed for more efficient HSI and MSI fusion. More specifically, the proposed SSR-NET is a physical straightforward model that consists of three components: 1) cross-mode message inserting (CMMI); this operation can produce the preliminary fused HR-HSI, preserving the most valuable information of LR-HSI and HR-MSI; 2) spatial reconstruction network (SpatRN); the SpatRN concentrates on reconstructing the lost spatial information of LR-HSI with the guidance of spatial edge loss (Lspat); and 3) spectral reconstruction network (SpecRN); the SpecRN pays attention to reconstruct the lost spectral information of HR-MSI under the constraint of spatial edge loss ({Lspec). Comparative experiments are conducted on six HSI data sets of Urban, Pavia University (PU), Pavia Center (PC), Botswana, Indian Pines (IP), and Washington DC Mall (WDCM), and the proposed SSR-NET achieves the superior or competitive results in comparison with seven state-of-the-art methods. The code of SSR-NET is available at https://github.com/hw2hwei/SSRNET. [ABSTRACT FROM AUTHOR]

Hyperspectral images can provide dozens to hundreds of continuous spectral bands, so the richness of information has been greatly improved. However, these bands lead to increasing complexity of data processing, and the redundancy of adjacent bands is large. Recently, although many band selection methods have been proposed, this task is rarely handled through the context information of the whole spectral bands. Moreover, the scholars mainly focus on the different numbers of selected bands to explain the influence by accuracy measures, neglecting how many bands to choose is appropriate. To tackle these issues, we propose a fast neighborhood grouping method for hyperspectral band selection (FNGBS). The hyperspectral image cube in space is partitioned into several groups using coarse-fine strategy. By doing so, it effectively mines the context information in a large spectrum range. Compared with most algorithms, the proposed method can obtain the most relevant and informative bands simultaneously as subset in accordance with two factors, such as local density and information entropy. In addition, our method can also automatically determine the minimum number of recommended bands by determinantal point process. Extensive experimental results on benchmark data sets demonstrate the proposed FNGBS achieves satisfactory performance against state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Over the past few years making use of deep networks, including convolutional neural networks (CNNs) and recurrent neural networks (RNNs), classifying hyperspectral images has progressed significantly and gained increasing attention. In spite of being successful, these networks need an adequate supply of labeled training instances for supervised learning, which, however, is quite costly to collect. On the other hand, unlabeled data can be accessed in almost arbitrary amounts. Hence it would be conceptually of great interest to explore networks that are able to exploit labeled and unlabeled data simultaneously for hyperspectral image classification. In this article, we propose a novel graph-based semisupervised network called nonlocal graph convolutional network (nonlocal GCN). Unlike existing CNNs and RNNs that receive pixels or patches of a hyperspectral image as inputs, this network takes the whole image (including both labeled and unlabeled data) in. More specifically, a nonlocal graph is first calculated. Given this graph representation, a couple of graph convolutional layers are used to extract features. Finally, the semisupervised learning of the network is done by using a cross-entropy error over all labeled instances. Note that the nonlocal GCN is end-to-end trainable. We demonstrate in extensive experiments that compared with state-of-the-art spectral classifiers and spectral–spatial classification networks, the nonlocal GCN is able to offer competitive results and high-quality classification maps (with fine boundaries and without noisy scattered points of misclassification). [ABSTRACT FROM AUTHOR]

Band selection is one of the most important technique in the reduction of hyperspectral image (HSI). Different from traditional feature selection problem, an important characteristic of it is that there is usually strong correlation between neighboring bands, that is, bands with close indexes. Aiming to fully exploit this prior information, a novel band selection method called optimal neighborhood reconstruction (ONR) is proposed. In ONR, band selection is considered as a combinatorial optimization problem. It evaluates a band combination by assessing its ability to reconstruct the original data, and applies a noise reducer to minimize the influence of noisy bands. Instead of using some approximate algorithms, ONR exploits a recurrence relation that underlies the optimization target to obtain the optimal solution in an efficient way. Besides, we develop a parameter selection approach to automatically determine the parameter of ONR, ensuring it is adaptable to different data sets. In experiments, ONR is compared with some state-of-the-art methods on six HSI data sets. The results demonstrate that ONR is more effective and robust than the others in most of the cases. [ABSTRACT FROM AUTHOR]

Hyperspectral anomaly detection (HAD) has drawn a significant attention of late due to its importance in many military and civilian applications. In this article, a fast hyperspectral anomaly detector that combines multiple features and isolation forest is proposed. This approach, which is based on the assumption that the anomalous pixels are more susceptible to isolation than the background pixels, consists of two main parts. First, the spectral, Gabor, extended morphological profile (EMP) and extended multiattribute profile (EMAP) features are extracted from the hyperspectral image (HSI). Next, the isolation forest of each feature is constructed using the subsampling strategy. This combination of multiple features can exploit both the spectral and spatial information of the HSI, thereby improving the anomaly detection performance significantly. Compared with eight state-of-the-art HAD methods, the experimental results on four real hyperspectral data sets demonstrate that the performance of our proposed approach is quite competitive in terms of detection accuracy and running time. [ABSTRACT FROM AUTHOR]

Sparse unmixing has become a popular tool for hyperspectral imagery interpretation. It refers to finding the optimal subset of a spectral library to reconstruct the image data and further estimate the proportions of different materials. Recently, multi-objective based sparse unmixing methods have presented promising performance because of their advantages in addressing combinatorial problems. A spectral and multi-objective based sparse unmixing (SMoSU) algorithm was proposed in our previous work, which solves the decision-making problem well. However, it does not show outstanding advantages in strong noise cases. To solve the problem, in this paper, SMoSU is improved based on the estimation of distribution algorithms (EDAs). The machine learning based EDAs have been a reliable approach in solving multi-objective problems. However, most of them are for special problems and relatively weak in theoretical foundations. Thus, it is unreliable to extend it directly to sparse unmixing. Here, we improve EDA on the basis of classification and propose a classification-based model for individual generating under the framework of SMoSU (CM-MoSU). In CM-MoSU, the whole population is divided to be positive and negative. Then, the macroinformation of positive individuals is used to guide the generation of new individuals. Therefore, the optimization task could pay more attention to the feasible space with high quality. Moreover, some theoretical analyses are presented to prove the reliability of CM-MoSU. In experiments, several state-of-the-art sparse unmixing algorithms are compared. Both synthetic and real-world experiments demonstrate the effectiveness of CM-MoSU. [ABSTRACT FROM AUTHOR]

Hyperspectral image (HSI) classification, which aims to assign an accurate label for hyperspectral pixels, has drawn great interest in recent years. Although low-rank representation (LRR) has been used to classify HSI, its ability to segment each class from the whole HSI data has not been exploited fully yet. LRR has a good capacity to capture the underlying low-dimensional subspaces embedded in original data. However, there are still two drawbacks for LRR. First, the LRR does not consider the local geometric structure within data, which makes the local correlation among neighboring data easily ignored. Second, the representation obtained by solving LRR is not discriminative enough to separate different data. In this paper, a novel locality- and structure-regularized LRR (LSLRR) model is proposed for HSI classification. To overcome the above-mentioned limitations, we present locality constraint criterion and structure preserving strategy to improve the classical LRR. Specifically, we introduce a new distance metric, which combines both spatial and spectral features, to explore the local similarity of pixels. Thus, the global and local structures of HSI data can be exploited sufficiently. In addition, we propose a structural constraint to make the representation have a near-block-diagonal structure. This helps to determine the final classification labels directly. Extensive experiments have been conducted on three popular HSI data sets. And the experimental results demonstrate that the proposed LSLRR outperforms other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Band selection, by choosing a set of representative bands in a hyperspectral image, is an effective method to reduce the redundant information without compromising the original contents. Recently, various unsupervised band selection methods have been proposed, but most of them are based on approximation algorithms which can only obtain suboptimal solutions toward a specific objective function. This paper focuses on clustering-based band selection and proposes a new framework to solve the above dilemma, claiming the following contributions: 1) an optimal clustering framework, which can obtain the optimal clustering result for a particular form of objective function under a reasonable constraint; 2) a rank on clusters strategy, which provides an effective criterion to select bands on existing clustering structure; and 3) an automatic method to determine the number of the required bands, which can better evaluate the distinctive information produced by certain number of bands. In experiments, the proposed algorithm is compared with some state-of-the-art competitors. According to the experimental results, the proposed algorithm is robust and significantly outperforms the other methods on various data sets. [ABSTRACT FROM AUTHOR]

Change detection is an important technique providing insights to urban planning, resources monitoring, and environmental studies. For multispectral images, most semi-supervised change detection methods focus on improving the contribution of training samples hard to be classified to the trained classifier. However, hard training samples will weaken the discrimination of the training model for multispectral change detection. Besides, these methods only use the spectral information, while the limited spectral information cannot represent objects very well. In this paper, a method named as coarse-to-fine semi-supervised change detection is proposed to solve the aforementioned problems. First, a novel multiscale feature is exploited by concatenating the spectral vector of the pixel to be detected and its adjacent pixels by different scales. Second, the enhanced metric learning is proposed to acquire more discriminant metric by strengthening the contribution of training samples easy to be classified and weakening the contribution of training samples hard to be classified to the trained model. Finally, a coarse-to-fine strategy is adopted to detect testing samples from the viewpoint of distance metric and label information of neighborhood in spatial space. The coarse detection result obtained from the enhanced metric learning is used to guide the final detection. The effectiveness of our proposed method is verified on two real-life operating scenarios, Taizhou and Kunshan data sets. Extensive experimental results demonstrate that our proposed algorithm has better performance than those of other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing is one of the most important techniques in analyzing hyperspectral images, which decomposes a mixed pixel into a collection of constituent materials weighted by their proportions. Recently, many sparse nonnegative matrix factorization (NMF) algorithms have achieved advanced performance for hyperspectral unmixing because they overcome the difficulty of absence of pure pixels and sufficiently utilize the sparse characteristic of the data. However, most existing sparse NMF algorithms for hyperspectral unmixing only consider the Euclidean structure of the hyperspectral data space. In fact, hyperspectral data are more likely to lie on a low-dimensional submanifold embedded in the high-dimensional ambient space. Thus, it is necessary to consider the intrinsic manifold structure for hyperspectral unmixing. In order to exploit the latent manifold structure of the data during the decomposition, manifold regularization is incorporated into sparsity-constrained NMF for unmixing in this paper. Since the additional manifold regularization term can keep the close link between the original image and the material abundance maps, the proposed approach leads to a more desired unmixing performance. The experimental results on synthetic and real hyperspectral data both illustrate the superiority of the proposed method compared with other state-of-the-art approaches. [ABSTRACT FROM PUBLISHER]