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Nowadays, some tensor-based hyperspectral anomaly detection (HAD) approaches are still insufficient in utilizing the spatial–spectral structure information of hyperspectral images (HSIs), resulting in the inability to isolate the background and abnormal targets well. In this letter, an enhanced tensor low-rank representation (ETLR) learning model is proposed for HAD. Specifically, the original 3-D HSI data is first decomposed into a structural background component, an anomaly component, and a noise component. Among them, with the help of multisubspace learning technology, the structural background component is reformulated by the t-product of the background dictionary tensor and the corresponding coefficient tensor. Then, the tensor nuclear norm (TNN) is adopted to preserve the global low-rank property of the background component in both spatial and spectral dimensions. For the abnormal component, an $\ell _{2,1,1}$ -norm is designed to enhance the group sparsity of abnormal pixels. For the noise component, a tensor $F$ -norm constraint is imposed to suppress the confusion of noise and anomalies. Meanwhile, a robust dictionary tensor that can adequately characterize the background is constructed by using tensor robust principal component analysis (TRPCA). Furthermore, to reduce the interference of redundant information on detection accuracy, the optimal clustering framework (OCF) method is utilized for band selection. Finally, extensive experiments on one simulated and three real HSI datasets confirm that our algorithm is superior to current HAD algorithms. [ABSTRACT FROM AUTHOR]

Autoencoder is an efficient technique for unsupervised feature learning, which can be applied to hyperspectral unmixing. In this letter, we present an autoencoder network with adaptive abundance smoothing (AAS) to solve the challenges of previous techniques. Specifically, the proposed method uses a multilayer encoder to obtain the abundance and a single-layer decoder to reconstruct the image. The AAS algorithm tackles the outliers by exploiting the spatial–contextual information and can be adaptive for each pixel. Moreover, the softmax function is used as the encoder output function with the help of L1/2 regularization to produce sparse output. Experimental results of the synthetic and real data reveal the superior performance of the proposed method against other competitors. [ABSTRACT FROM AUTHOR]

In recent years, low-rank representation (LRR) has attracted considerable attention in the field of hyperspectral anomaly detection. The main objective of LRR-based methods is to extract anomalies from the complex background. However, the presence of anomalies in the background dictionary can lower the detection performance. In this letter, a novel method is proposed for hyperspectral anomaly detection based on the LRR model. This method facilitates the discrimination between the anomalous targets and background by utilizing a novel dictionary and an adaptive filter based on the local outlier factor (LOF). In order to exclude the potential anomalies from the dictionary, the ranking of LOF scores for each pixel is adapted to select the potential background pixels as dictionary atoms. A filter that explores the intrinsic spatial structure is designed to enhance the differences between the anomalies and the background pixels. The experimental results that conducted on three real-world data sets demonstrate that the proposed method achieves a better performance than several state-of-the-art hyperspectral anomaly detection methods. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing (HU) is a crucial technique for exploiting remotely sensed hyperspectral data, which aims at estimating a set of spectral signatures, called endmembers and their corresponding proportions, called abundances. The performance of HU is often seriously degraded by various kinds of noise existing in hyperspectral images (HSIs). Most of existing robust HU methods are based on the assumption that noise or outlier only exists in one kind of formulation, e.g., band noise or pixel noise. However, in real-world applications, HSIs are unavoidably corrupted by noisy bands and noisy pixels simultaneously, which require robust HU in both the spatial dimension and spectral dimension. Meanwhile, the sparsity of abundances is an inherent property of HSIs and different regions in an HSI may possess various sparsity levels across locations. This article proposes a correntropy-based spatial-spectral robust sparsity-regularized unmixing model to achieve 2-D robustness and adaptive weighted sparsity constraint for abundances simultaneously. The updated rules of the proposed model are efficient to be implemented and carried out by a half-quadratic technique. The experimental results obtained by both synthetic and real hyperspectral data demonstrate the superiority of the proposed method compared to the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

This letter presents a superpixel-based dual window RX (SPDWRX) anomaly detection (AD) algorithm that uses superpixel segmentation (SPS) to adaptively determine the dual window for local RX (LRX) detection, rather than using a fixed dual window. The main premise of SPDWRX is to first divide the hyperspectral image into multiple superpixels and then extend the minimum bounding rectangle to determine the background of each superpixel. Finally, LRX AD is conducted on each pixel in the same superpixel using the same background. Furthermore, a fine SPS method is proposed based on the entropy rate superpixel to quickly obtain uniform superpixels. The experimental results show that the proposed SPDWRX method can significantly improve the detection speed and slightly improve the detection performance, and the modified SPS can further improve the detection performance of SPDWRX. [ABSTRACT FROM AUTHOR]

The orthogonal-projection-based band selection (OPBS) algorithm is one of the newly proposed band selection methods. In this letter, we present a nonlinear version of the OPBS method, which is denoted as the Kernel-OPBS method. The OPBS method selects the desired bands one by one, and in each round of lookup, it chooses the band that has the maximum distance to the hyperplane spanned by the currently selected bands. Extending this algorithm to a feature space associated with the original input space through a certain nonlinear mapping function can provide a nonlinear version of the OPBS algorithm. Although it is basically intractable to compute the mapped bands due to the high dimensionality of the feature space produced by the nonlinear mapping function, the selection criterion of the Kernel-OPBS method is actually related to only the inner products of the mapped bands; thus, the kernel function can be applied and it is unnecessary to define the nonlinear mapping function. Experimental results on different data sets demonstrate that the selected bands obtained by the Kernel-OPBS method can achieve higher pixel classification performances than that by the OPBS method. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing (HU) is a crucial technique for exploiting remotely sensed hyperspectral data, which aims to estimate a set of spectral signatures, called endmembers and their corresponding proportions, called abundances. Nonnegative matrix factorization (NMF) and its various robust extensions have been widely applied to HU. Most existing robust NMF methods consider that noises only exist in one kind of formulation. However, the hyperspectral images (HSIs) are unavoidably corrupted by noisy bands and noisy pixels simultaneously in the real applications. This paper proposes a novel spectral–spatial robust NMF model by incorporating $\ell _{2,1}$ norm and $\ell _{1,2}$ norm, which achieves robustness to band noise and pixel noise simultaneously. The Huber’s M-estimator is integrated into the proposed model to achieve better assignations of weights for each pixel and band with various noise intensities, which avoids the singularity problem and effectively improves the unmixing performance. The elegant updating rules of the proposed spectral–spatial robust model are also efficiently learned and provided. Experiments are conducted on both synthetic and real hyperspectral data sets. The experimental results demonstrate the effectiveness of the proposed methods in unmixing performance. [ABSTRACT FROM AUTHOR]

Kernel nonnegative matrix factorization (KNMF) is an extension of NMF designed to capture nonlinear dependence features in data matrix through kernel functions. In KNMF, the size of the kernel matrices is closely associated with the input data matrix, of which the calculation consumes a large amount of memory and computing resource. When applied on large-scale hyperspectral data, KNMF often meets the bottleneck of memory and may cause the overflow of memory. And when dealing with dynamically acquired data, KNMF requires recomputation of the whole data set when newly acquired data arrived, which produces huge memory and computing resource requirements. To reduce the usage of memory and improve the computational efficiency when applying KNMF on large scale and dynamic hyperspectral data, we extend KNMF by introducing partition matrix theory and considering the relationships among dividing blocks. The decomposition results of hyperspectral data are derived from much smaller scale matrices containing the formerly achieved results and the newly data blocks incrementally. In this paper, we propose an incremental KNMF (IKNMF) to reduce the computing requirements for large-scale data in hyperspectral unmixing. An improved IKNMF (IIKNMF) is also proposed to further improve the abundance results of IKNMF. Experiments are conducted on both synthetic and real hyperspectral data sets. The experimental results demonstrate that the proposed methods can effectively save memory resources without degrading the unmixing performance and the proposed IIKNMF can achieve better abundance results than IKNMF and KNMF. [ABSTRACT FROM AUTHOR]

Band selection (BS) tries to find a few useful bands to represent the whole hyperspectral image cube. This letter proposes a novel unsupervised BS method based on the band correlation analysis (BCA). The BCA method tries to find a subset of bands that can well represent the whole image data set. To avoid the exhaustive search, the BCA method iteratively adds the band with the good representative ability and low redundancy into the selected band set, until the sufficient quantity of bands has been obtained. The redundancy and the representative ability of one band are computed by its correlation with the currently selected bands and the remaining unselected bands, respectively. Through constructing a correlation matrix of total bands, the BCA method can find the bands that with large amounts of information and low redundancy, which ensures that the selected bands are useful for the further applications like pixels classification. Experimental results on three different data sets demonstrate that the proposed method is very effective and can achieve the best performance among the competitors. [ABSTRACT FROM AUTHOR]

Band selection (BS) is a special case of the feature selection problem, and it tries to remove redundant bands and select a few informative and distinctive bands to represent the whole image cube. The maximum ellipsoid volume (MEV) method regards the band subset with the maximum volume as the optimal band combination. However, the MEV method cannot be directly applied for hyperspectral imagery due to the high dimensionality of the data sets. Therefore, we first combine MEV with the sequential forward search (SFS) and propose a new unsupervised BS method called MEV-SFS. Furthermore, a subtle relationship between the ellipsoid volume of the band set and the orthogonal projections (OPs) of the candidate bands is observed. Based on this relationship, we propose another equivalent method, namely, the OP-based BS (OPBS) method. OPBS is the fast version of MEV-SFS, and it has a better computational efficiency and the potential to determine the number of bands to be selected. We specifically explain the rationality of the MEV-based methods (MEV-SFS and OPBS) and illustrate their theoretical significance and physical meaning from different aspects. Theoretical analysis also demonstrates that OPBS can be regarded as a model or framework for BS, and thus, we further propose a third novel BS method named the OPBS-information divergence (OPBS-ID) method, which is a variant of OPBS. OPBS-ID can achieve a better classification performance than OPBS in many cases. Experimental results on different hyperspectral data sets demonstrate that the proposed methods have high computational efficiency, and the selected bands can achieve satisfactory classification performances. [ABSTRACT FROM AUTHOR]

Nonlinear unmixing, which has attracted considerable interest from researchers and developers, has been successfully applied in many real-world hyperspectral imaging scenarios. Hopfield neural network (HNN) machine learning has already proven successful in solving the linear mixture model; this study utilized an HNN machine learning approach to solve the generalized bilinear model (GBM) optimization problem. Two HNNs were constructed in a successive manner to solve respective seminonnegative matrix factorization problems intended for abundance and nonlinear coefficient estimation. In the proposed HNN-based GBM unmixing method, both HNNs evolve to stable states after a number of iterations to obtain unmixing results related to the states of neurons. In experiments on synthetic data, the proposed method showed more efficient performance in regard to abundance estimation accuracy than other GBM optimization algorithms, especially when given reliable endmember spectra. The proposed method was also applied to real hyperspectral data and still demonstrated notable advantages despite the obvious increase in unmixing difficulty. [ABSTRACT FROM PUBLISHER]

Nonlinear spectral mixture analysis is important when the light suffers multiple interactions among distinct materials. Few attempts have been conducted to incorporate spatial information to improve the performance of nonlinear unmixing algorithms. In this letter, local windows are adopted in the preliminary classification map to search the relevant endmembers for each pixel. Virtual endmembers, resulting from the relevant endmembers, represent the multiple-scattering effects in each pixel, and the corresponding abundances are estimated based on a modified bilinear model. Experiments on simulated and real hyperspectral images demonstrate that the proposed method provides a competitive or even better performance over some existing algorithms. [ABSTRACT FROM PUBLISHER]

Endmember extraction is an important and challenging step to solve the spectral unmixing problem. Most existing endmember extraction algorithms (EEAs) usually find image pixels as endmembers assuming the presence of pure pixels in an image scene or generate virtual endmembers without pure-pixel assumption. When some prevalent materials have pure-pixel representation and pure pixels of other less prevalent materials are absent in the image, it would be more appropriate to extract the endmembers of both prevalent and less prevalent materials, respectively. Therefore, a novel two-stage EEA is presented in this paper. In the first stage, conventional pure-pixel-based EEAs are applied to generate a candidate pixel set, and then spatial information of the candidate pixels is exploited to determine the endmembers of prevalent materials. In the second stage, given known endmembers of prevalent materials, a modified algorithm based on nonnegative matrix factorization is performed to generate the endmembers of less prevalent materials. The validity of the proposed algorithm is demonstrated by experiments based on synthetic mixtures and a real image scene. [ABSTRACT FROM AUTHOR]