Hyperspectral anomaly detection (HAD) aims at effectively separating the anomaly target from the background. The low-rank and sparse matrix decomposition (LRaSMD) technique has shown great potential in HAD tasks. However, some LRaSMD models need to convert the hyperspectral data into a two-dimensional matrix. This cannot well maintain the characteristics of the hyperspectral image (his) in each dimension, thus degenerating its representation capacity. In this context, this article proposes a tensor-based Go decomposition (GODEC) model, called TGODEC. The TGODEC model supports the idea of GODEC, representing the HSI data as a combination of background tensor, anomaly tensor, and noise tensor. In detail, the background tensor is solved by the tensor singular value hard thresholding decomposition. The anomaly tensor is solved by a mapping matrix using the corresponding sparse cardinality. Interestingly, the obtained background and anomaly tensors can also be developed for HAD, thus a TGODEC-based anomaly detector is established, called TGODEC-AD. Specifically, the TGODEC-AD method combines the typical RX-AD and R-AD with the above decomposition result of the TGODEC model and constructs different modal operator detectors. Experimental results on multiple real hyperspectral datasets verify the effectiveness of the TGODEC and TGODEC-AD methods. It means that the proposed TGODEC model can effectively characterize the spatial structural features of HSI. As a result, the pure decomposed components can be obtained, contributing to detecting the anomaly target and suppressing the background better in HAD tasks.

In the classic sparse representation (SR)-based models and their improved versions with the spatial consistency, such as joint representation (JR)-based frameworks, the sparse coefficient is generally considered with the dictionary together for representation. In fact, there is latent significance and property under the sparse coefficient which can be further exploited for classification. In this paper, we first introduce two important definitions. One is the activity degree (AD) into the coefficient vector, and the other one is the neighborhood activity degree (NAD) into the coefficient matrix. Through the estimation of AD, we establish a simplified and equivalent model to the classic SR-based classifier (SRC), called AD-driven representation-based classifier (ADRC). Based on the evaluation of NAD, we propose a novel classifier as an extension to ADRC, named NAD-driven representation-based classifier (NADRC), including the spatial coherence. The proposed methods take advantages of the sparse idea for effective and concise utilization of individual and overall sparsity. Experimental results on three real hyperspectral data sets demonstrate their efficiency and improvements over the SR-based models and their spatial variants.

Sparse representation (SR)-based models have been widely applied for hyperspectral image classification. In our previously established constraint representation (CR) model, we exploited the underlying significance of the sparse coefficient and proposed the participation degree (PD) to represent the contribution of the training sample in representing the testing pixel. However, the spatial variants of the original residual error-driven frameworks often suffer the obstacles to optimization due to the strong constraints. In this paper, based on the object-based image classification (OBIC) framework, we firstly propose a spectral–spatial classification method, called superpixel-level constraint representation (SPCR). Firstly, it uses the PD in respect to the sparse coefficient from CR model. Then, transforming the individual PD to a united activity degree (UAD)-driven mechanism via a spatial constraint generated by the superpixel segmentation algorithm. The final classification is determined based on the UAD-driven mechanism. Considering that the SPCR is susceptible to the segmentation scale, an improved multiscale superpixel-level constraint representation (MSPCR) is further proposed through the decision fusion process of SPCR at different scales. The SPCR method is firstly performed at each scale, and the final category of the testing pixel is determined by the maximum number of the predicated labels among the classification results at each scale. Experimental results on four real hyperspectral datasets including a GF-5 satellite data verified the efficiency and practicability of the two proposed methods.

The low-rank and sparse matrix decomposition (LSMD) approach effectively separates background components from anomalies in hyperspectral anomaly detection (HAD), suppressing background interference and enhancing target saliency. However, the high dimensionality, spectral redundancy, and massive data volume pose significant challenges for processing hyperspectral images (HSI). To address these issues, selecting efficient dimensionality reduction strategies for concise and effective extraction of background and anomaly information is crucial for robust anomaly detection. In this paper, we use compressed sensing technology to reduce the dimensionality of HSI data and establish a go decomposition-based iterative multiple random compressed sampling anomaly detection method (IMRCSGD). The IMRCSGD applies the low-rank and sparse matrix decomposition in compressed sampling band domains, and performs RX and RAD anomaly detection in a compressed composite subspace. Specifically, IMRCSGD employs multiple compressive sampling processes to preserve as much significant spectral-spatial information as possible. In addition, a novel iteration mechanism is introduced to reduce the random characteristic and improve the detection performance by incorporating feedback from the texture and content of the newly generated detection results. The effectiveness of the IMRCSGD is validated by experimental results obtained from six real hyperspectral datasets.