Hyperspectral images (HSIs) are usually corrupted by various noises during the image acquisition process, e.g., Gaussian noise, impulse noise, stripes, deadlines and many others. Such complex noise severely degrades the data quality, reduces the interpretation accuracy of HSIs, and restricts the subsequent HSI applications. In this paper, a spatial non-local and local rank-constrained low-rank regularized Plug-and-Play (NLRPnP) model is presented for mixed noise removal in HSIs. Specifically, we first divide HSIs into local overlapping patches. Local rank-constrained low-rank matrix recovery is adopted to effectively separate the low-rank clean HSI patches from the sparse noise and a part of Gaussian noise, and to significantly preserve local structure and detail information in HSIs. Then the spatial non-local based denoiser is introduced to promote the non-local self-similarity and obviously depress the Gaussian noise. Without increasing the difficulty of solving optimization problems, we combine the local and non-local based methods into the Plug-and-Play framework, and develop an efficient algorithm for solving the proposed NLRPnP model by using the alternating direction method of multipliers method. Finally, several experiments are conducted in both simulated and real data conditions to illustrate the better performance of the proposed NLRPnP model than the existing state-of-the-art denoising models.

In hyperspectral anomaly detection, tensor low-rankness is essential for effectively separating background and anomaly. However, most of the current low-rank-based methods do not use the spatial-spectral low-rankness and the nonlocal self-similarity simultaneously. To address this issue, we propose a tensor double nuclear norm based tensor approximation (TDNN-TA) model with all the priors in a unified convex framework, which can be efficiently handled through a well-organized alternating direction method of multipliers. Especially, to thoroughly model the background by tensor approximation, we propose a tensor double nuclear norm (TDNN), which achieves a more precise and flexible exploration of low-rankness and nonlocal self-similarity by applying different low-rank constraints to the global tensor and the group tensor. Moreover, to explore the intrinsic characteristics of different priors by various tensor ranks, we employ the Fourier transform-based three-directional tensor nuclear norm to approximate the nonlocal group tensor rank, and the framelet-based three-modal tensor nuclear norm to approximate the global tensor rank. Experimental results validated on several real hyperspectral datasets demonstrate that TDNN-TA is effective in detecting different sizes of anomalous targets and achieves competitive results for various scenes.

During the acquisition process, hyperspectral images (HSIs) are inevitably contaminated by mixed noise, which seriously affects the image quality. To improve the image quality, HSI denoising is a critical preprocessing step. In HSI denoising tasks, the method based on low-rank prior has achieved satisfying results. Among numerous denoising methods, the tensor nuclear norm (TNN), based on the tensor singular value decomposition (t-SVD), is employed to describe the low-rank prior approximately. Its calculation can be sped up by the fast Fourier transform (FFT). However, TNN is computed by the Fourier transform, which lacks the function of locating frequency. Besides, it only describes the low-rankness of the spectral correlations and ignores the spatial dimensions’ information. In this paper, to overcome the above deficiencies, we use the basis redundancy of the framelet and the low-rank characteristics of HSI in three modes. We propose the framelet-based tensor fibered rank as a new representation of the tensor rank, and the framelet-based three-modal tensor nuclear norm (F-3MTNN) as its convex relaxation. Meanwhile, the F-3MTNN is the new regularization of the denoising model. It can explore the low-rank characteristics of HSI along three modes that are more flexible and comprehensive. Moreover, we design an efficient algorithm via the alternating direction method of multipliers (ADMM). Finally, the numerical results of several experiments have shown the superior denoising performance of the proposed F-3MTNN model.

Depending on single target example under the influence of spectral variation, deep learning-based hyperspectral target detection (HTD) methods are challenged by the problem of insufficient target knowledge. Inspired by self-supervised learning, this paper proposes a novel HTD method based on macro-micro spectrum contrastive learning, which enhance detection knowledge by unsupervised intra-contrast learning and supervised inter-correction learning. Firstly, to address spectral variation, a multi-scale view transformation strategy is proposed to learn intrinsic features by contractive learning between macro and micro spectrum groups. Secondly, to distinguishing target knowledge, a multihead task-driven network is designed to learn discriminative features by integrating target spectrum into the band- wise correlation calculation. Lastly, to signalize the target and suppress the background, a composite loss is designed to maximize the average distance between the target and background in feature space. Experimental results on four benchmark datasets demonstrate the superior performance of the proposed method over existing state-of-the-art algorithms.

Hyperspectral target detection remains challenging due to complex nonlinear spectral mixing and insufficient in corporation of spatial context. Existing approaches often address these issues in isolation: bilinear models neglect spatial coherence, kernel-based methods require empirical selection of kernel types and parameters, and many spatial-contextual methods lack explicit modeling of material scattering effects. To address these limitations, we propose a spectral-spatial bilinear decomposition model (SSBDM) that explicitly models scattering-induced nonlinearity and exploits spatial contextual information to enhance target representation under nonlinear mixing. Specifically, a bilinear mixing model with second-order interaction terms is adopted to capture scattering effects beyond linear approximations, providing improved physical interpretability. Moreover, we introduce an adaptive multi-kernel automatic target generation strategy that dynamically fuses multiple kernels based on projection residuals, eliminating manual kernel selection while constructing a high-purity, scene-adaptive background dictionary. Furthermore, we propose dual spectral–spatial regularizations for coefficient estimation, consisting of a superpixel-based graph Laplacian to preserve local spatial homogeneity and mitigate spectral distortion, and a double reweighted sparsity constraint that down-weights low-contributing atoms (particularly second-order interaction atoms) to stabilize bilinear coefficient estimation. This dual design simultaneously enforces spatial coherence and selective sparsity, enhancing robustness and target–background separability under nonlinear mixing. Extensive experiments on four real-world datasets validate the effectiveness and robustness of SSBDM under spectral variability and limited supervision, outperforming state-of-the-art methods. Code will be available at https://github.com/shendb2022/SSBDM.