Recently, low-rank representation (LRR) methods have been widely applied for hyperspectral anomaly detection, due to their potentials in separating the backgrounds and anomalies. However, existing LRR models generally convert 3-D hyperspectral images (HSIs) into 2-D matrices, inevitably leading to the destruction of intrinsic 3-D structure properties in HSIs. To this end, we propose a novel tensor low-rank and sparse representation (TLRSR) method for hyperspectral anomaly detection. A 3-D TLR model is expanded to separate the LR background part represented by a tensorial background dictionary and corresponding coefficients. This representation characterizes the multiple subspace property of the complex LR background. Based on the weighted tensor nuclear norm and the $L_{F,1}$ sparse norm, a dictionary is designed to make its atoms more relevant to the background. Moreover, a principal component analysis (PCA) method can be assigned as one preprocessing step to exact a subset of HSI bands, retaining enough the HSI object information and reducing computational time of the postprocessing tensorial operations. The proposed model is efficiently solved by the well-designed alternating direction method of multipliers (ADMMs). A comparison with the existing algorithms via experiments establishes the competitiveness of the proposed method with the state-of-the-art competitors in the hyperspectral anomaly detection task.

Owing to the rapid development of sensor technology, hyperspectral (HS) remote sensing (RS) imaging has provided a significant amount of spatial and spectral information for the observation and analysis of Earth’s surface at a distance of data acquisition devices. The recent advancement and even revolution of HS RS techniques offer opportunities to realize the potential of various applications while confronting new challenges for efficiently processing and analyzing the enormous HS acquisition data. Due to the maintenance of the 3D HS inherent structure, tensor decomposition has aroused widespread concern and spurred research in HS data processing tasks over the past decades. In this article, we aim to present a comprehensive overview of tensor decomposition, specifically contextualizing the five broad topics in HS data processing: HS restoration, compressive sensing (CS), anomaly detection (AD), HS–multispectral (MS) fusion, and spectral unmixing (SU). For each topic, we elaborate on the remarkable achievements of tensor decomposition models for HS RS, with a pivotal description of the existing methodologies and a representative exhibition of experimental results. As a result, the remaining challenges of the follow-up research directions are outlined and discussed from the perspective of actual HS RS practices and tensor decomposition merged with advanced priors and even deep neural networks. This article summarizes different tensor decomposition-based HS data processing methods and categorizes them into different classes, from simple adoptions to complex combinations with other priors for algorithm beginners. We expect that this survey provides new investigations and development trends for experienced researchers to some extent.

The total variation (TV) regularization has been widely used in various applications related to hyperspectral (HS) signal and image processing due to its potential in modeling the underlying smoothness of HS data. However, most existing TV norms usually tend to generate spatial oversmoothing or artifacts. To this end, we propose a novel l ₀ - l ₁ hybrid TV ( l ₀ - l ₁ HTV) regularization with the applications to HS mixed noise removal and compressed sensing (CS). More specifically, l ₀ - l ₁ HTV can be regarded as a globally and locally integrated TV regularizer, where the l ₀ gradient constraint is incorporate into the l ₁ spatial-spectral TV ( l ₁ -SSTV). l ₁ -SSTV is capable of exploiting the local structure information across both spatial and spectral domains, while the l ₀ gradient can promote a globally spectral-spatial smoothness by directly controlling the number of nonzero gradients of HS images. This efficient combination considers more comprehensive prior knowledge of HS images, yielding sharper edge preservation and resolving the above drawbacks of existing pure TV norms. More significantly, l ₀ - l ₁ HTV can be easily injected into HS-related processing models, and an effective algorithm based on the alternating direction method of multipliers (ADMM) is developed to solve the optimization problems. Extensive experiments conducted on several HS data sets substantiate the superiority and effectiveness of the proposed method in comparison with many state-of-the-art methods.

Remote sensing images (RSIs) are characterized by complex spatial layouts and ground object structures. ViT can be a good choice for scene classification owing to the ability to capture long-range interactive information between patches of input images. However, due to the lack of some inductive biases inherent to CNNs, such as locality and translation equivariance, ViT cannot generalize well when trained on insufficient amounts of data. Compared with training ViT from scratch, transferring a large-scale pre-trained one is more cost-efficient with better performance even when the target data is small-scale. In addition, In addition, the cross-entropy (CE) loss is frequently utilized in scene classification yet has low robustness to noise labels and poor generalization performances for different scenes. In this paper, a ViT-based model in combination with supervised contrastive learning (CL) is proposed, named ViT-CL. For CL, Supervised contrastive (SupCon) loss which is developed by extending the self-supervised contrastive approach to the fully-supervised setting, can explore the label information of RSIs in embedding space and improve the robustness to common image corruption. In ViT-CL, a joint loss function that combines CE loss and SupCon loss is developed to prompt the model to learn more discriminative features. Also, a two-stage optimization framework is introduced to enhance the controllability of the optimization process of the ViT-CL model. Extensive experiments on the AID, NWPU-RESISC45, and UCM datasets verified the superior performance of ViT-CL, with the highest accuracies of 97.42%, 94.54%, and 99.76% among all competing methods, respectively.

Several methods based on Total Variation (TV) have been proposed for Hyperspectral Image (HSI) denoising. However, the TV terms of these methods just use various l ₁ norms and penalize image gradient magnitudes, having a negative influence on the preprocessing of HSI denoising and further HSI classification task. In this paper, a novel l ₀ Total Variation (l ₀ TV) is first introduced and analyzed for the HSI noise removal framework to preserve more information for classification. We propose a novel Tensor low-rank constraint and l ₀ Total Variation (TLR-l ₀ TV) model in this paper. l ₀ TV directly controls the number of non-zero gradients and focuses on recovering the sharp image edges. The spectral-spatial information among all bands is exploited uniformly for removing mixed noise, which facilitates the subsequent classification after denoising. Including the Weighted Sum of Weighted Nuclear Norm (WSWNN) and the Weighted Sum of Weighted Tensor Nuclear Norm (WSWTNN), we propose two TLR-l ₀ TV-based algorithms, namely WSWNN-l ₀ TV and WSWTNN-l ₀ TV. The Alternating Direction Method of Multipliers (ADMM) and the Augmented Lagrange Multiplier (ALM) are employed to solve the l ₀ TV model and TLR-l ₀ TV model, respectively. In both simulated and real data, the proposed models achieve superior performances in mixed noise removal of HSI. Especially, HSI classification accuracy is improved more effectively after denoising by the proposed TLR-l ₀ TV method.

Conventional low-rank (LR)-based hyperspectral image (HSI) denoising models generally convert high-dimensional data into 2-D matrices or just treat this type of data as 3-D tensors. However, these pure LR or tensor low-rank (TLR)-based methods lack flexibility for considering different correlation information from different HSI directions, which leads to the loss of comprehensive structure information and inherent spatial-spectral relationship. To overcome these shortcomings, we propose a novel multidirectional LR modeling and spatial-spectral total variation (MLR-SSTV) model for removing HSI mixed noise. By incorporating the weighted nuclear norm, we obtain the weighted sum of weighted nuclear norm minimization (WSWNNM) and the weighted sum of weighted tensor nuclear norm minimization (WSWTNNM) to estimate the more accurate LR tensor, especially, to remove the dead-line noise better. Gaussian noise is further denoised and the local spatial-spectral smoothness is preserved effectively by SSTV regularization. We develop an efficient algorithm for solving the derived optimization based on the alternating direction method of multipliers (ADMM). Extensive experiments on both synthetic data and real data demonstrate the superior performance of the proposed MLR-SSTV model for HSI mixed noise removal.