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A hyperspectral anomaly detection (AD) task is a typical binary classification problem, and utilizing background prior knowledge is a key technique to solving such problems. The two most commonly used priors for hyperspectral images (HSIs) are low-rank and local-smooth properties. Most traditional matrix-based methods use two regularizations to model these two types of priors and integrate them into one model, which makes these two regularizations unable to maximize their effectiveness. In addition, the matrix method also destroys the structure of the HSIs. To address these issues, this study identified a unique sparsity property in the gradient tensor of HSI. Specifically, the core tensor resulting from the Tucker decomposition of the gradient tensor was observed to exhibit sparsity. This sparsity property, referred to as the sparsity on the core tensor of the gradient map (GCS), effectively captures the structural information of HSI and improves detection performance. The GCS regularization offers the following advantages: 1) GCS regularization uses one term to simultaneously capture both low rankness and local smoothness, the size of the core tensor represents the low rank prior to the background, and the $\ell _{1}$ norm describes the sparsity of gradient map, i.e., the local smoothness of the original data and 2) GCS is a constrained regularization, allowing for the full utilization of information from different dimensions of the HSI when updating the core tensor, i.e., utilizing the spatial and spectral information carried by three-factor matrices of the Tucker decomposition. Finally, extensive experiments validate the superiority of our proposed methods.

Monitoring vegetation growth, phenology, and health in agriculture requires very high spatial and spectral resolution sensors. Sentinel-2 is among the spaceborne sensors that tried to meet these requirements. However, due to physical constraints, few visible bands are present with relatively large spectral responses, which limits the leaf pigment content estimation. In this work, we propose to fuse Sentinel-2 bands with a Sentinel-3 image, which has a lower spatial resolution but contains several spectral narrower bands in both the visible and near-infrared (NIR) domains. The fusion procedure consists in sharpening the Sentinel-3 bands to match the Sentinel-2 spatial resolution leading to a higher spatial resolution Sentinel-3 image. The proposed fusion technique follows a physics-based approach based on the use of a radiative transfer model (RTM) for establishing a correspondence between Sentinel-2 and Sentinel-3 images. In greater details, the main spectrally pure constituent of each high-resolution Sentinel-2 pixel is identified for each pixel, and it is then related to the corresponding low-resolution Sentinel-3 pixel. Pure materials are the barycenters of clusters obtained by an unsupervised classification of the Sentinel-2 image. Sentinel-3 signatures are obtained using coarse resolution pixel matching with the Sentinel-2 image. The latter result is then corrected using radiative transfer modeling allowing the production of more realistic signatures. Validation was done using real Sentinel-2/Sentinel-3 images taken with a delay of only one day or less and by comparing the sharpened Sentinel-3 bands Oa04, Oa06, Oa08, and Oa17 with the corresponding Sentinel-2 bands B2, B3, B4, and B8A, as they are, respectively, spectrally close. For all the bands, the rms is lower than 0.007, and compared with the state-of-the-art techniques, it shows competitive results and robustness against scene heterogeneity. Besides, our findings prove that the retrieved Sentinel-3 signatures at full resolution (FR) are physically consistent and in good agreement with the Sentinel-2 data.

Hyperspectral unmixing allows representing mixed pixels as a set of pure materials weighted by their abundances. Spectral features alone are often insufficient, so it is common to rely on other features of the scene. Matrix models become insufficient when the hyperspectral image (HSI) is represented as a high-order tensor with additional features in a multimodal, multifeature framework. Tensor models such as canonical polyadic decomposition allow for this kind of unmixing but lack a general framework and interpretability of the results. In this article, we propose an interpretable methodological framework for low-rank multifeature hyperspectral unmixing based on tensor decomposition (MultiHU-TD) that incorporates the abundance sum-to-one constraint in the alternating optimization alternating direction method of multipliers (ADMM) algorithm and provide in-depth mathematical, physical, and graphical interpretation and connections with the extended linear mixing model. As additional features, we propose to incorporate mathematical morphology and reframe a previous work on neighborhood patches within MultiHU-TD. Experiments on real HSIs showcase the interpretability of the model and the analysis of the results. Python and MATLAB implementations are made available on GitHub.

The detection of deformation in Global Navigation Satellite System (GNSS) time series associated with (a)seismic events down to a low magnitude is still a challenging issue. The presence of a considerable amount of noise in the data makes it difficult to reveal patterns of small ground deformation. Traditional analyses and methodologies are able to effectively retrieve the deformation associated with medium to large magnitude events. However, the automatic detection and characterization of such events is still a complex task, because traditionally employed methods often separate the time series analysis from the source characterization. Here we propose a first end‐to‐end framework to characterize seismic sources using geodetic data by means of deep learning, which can be an efficient alternative to the traditional workflow, possibly overcoming its performance. We exploit three different geodetic data representations in order to leverage the intrinsic spatio‐temporal structure of the GNSS noise and the target signal associated with (slow) earthquake deformation. We employ time series, images, and image time series to account for the temporal, spatial, and spatio‐temporal domain, respectively. Thereafter, we design and develop a specific deep learning model for each dataset. We analyze the performance of the tested models both on synthetic and real data from North Japan, showing that image time series of geodetic deformation can be an effective data representation to embed the spatio‐temporal evolution, with the associated deep learning method outperforming the other two. Therefore, jointly accounting for the spatial and temporal evolution may be the key to effectively detect and characterize fast or slow earthquakes. The continuous monitoring of ground displacement with Global Navigation Satellite System allowed, at the beginning of the 2000s, the discovery of slow earthquakes—a transient slow slippage of tectonic faults that releases stress without generating seismic waves. Nevertheless, the detection of small events is still a challenge, because they are hidden in the noise. Most of the methods which are traditionally employed are able to extract the deformation down to a certain signal‐to‐noise level. However, one can ask if deep learning can be a more efficient and powerful alternative. To this end, we address the problem by using deep learning, as it stands as a powerful way to automatize and possibly overcome traditional methods. We use and compare three data representations, that is time series, images, and image time series of deformation, which account for the temporal, spatial, and spatio‐temporal variability, respectively. We train our methods on synthetic data, since real datasets are still not enough to be effectively employed with deep learning, and we test on synthetic and real data as well, claiming that image time series and its associated deep learning model may be more effective toward the study of the slow deformation. We develop deep learning approaches on synthetics mimicking the spatio‐temporal structure of static deformation and realistic Global Navigation Satellite System (GNSS) noiseWe design three deep learning models and we train and test them against three GNSS data representationsTransformers and image time series of deformation can effectively characterize small deformation patterns associated with the seismic source We develop deep learning approaches on synthetics mimicking the spatio‐temporal structure of static deformation and realistic Global Navigation Satellite System (GNSS) noise We design three deep learning models and we train and test them against three GNSS data representations Transformers and image time series of deformation can effectively characterize small deformation patterns associated with the seismic source