The problem of robust matrix completion-the recovery of a low-rank matrix and a sparse matrix from a sampling of their superposition-has been addressed extensively in prior literature. Yet, much of this work has focused exclusively on the case in which the matrix sampling is done at random, as this scenario is amenable to theoretical analysis. In contrast, sampling with an arbitrary deterministic pattern is often more accommodating to hardware implementation; consequently, the problem of robust matrix completion under deterministic sampling is considered. To this end, a restricted approximate isometry property is proposed and used, along with a modified golfing scheme and a slightly strengthened incoherence condition, to prove that the latent low-rank and sparse matrices are uniquely recoverable via convex optimization with asymptotically high probability, providing the first exact-recovery theory for robust matrix completion with arbitrary deterministic sampling. A corresponding convex-optimization algorithm, driven by a traditional nuclear norm, is developed and then subsequently generalized by substituting a convolutional nuclear norm in order to cover a broader range of application scenarios. Empirical experiments on synthetic data verify the proposed theory while a battery of results on real-world images demonstrate the practical efficacy of the generalized algorithm for robust matrix recovery.

Hyperspectral super-resolution is commonly accomplished by the fusing of a hyperspectral imaging of low spatial resolution with a multispectral image of high spatial resolution, and many tensor-based approaches to this task have been recently proposed. Yet, it is assumed in such tensor-based methods that the spatial-blurring operation that creates the observed hyperspectral image from the desired super-resolved image is separable into independent horizontal and vertical blurring. Recent work has argued that such separable spatial degradation is ill-equipped to model the operation of real sensors which may exhibit, for example, anisotropic blurring. To accommodate this fact, a generalized tensor formulation based on a Kronecker decomposition is proposed to handle any general spatial-degradation matrix, including those that are not separable as previously assumed. Analysis of the generalized formulation reveals conditions under which exact recovery of the desired super-resolved image is guaranteed, and a practical algorithm for such recovery, driven by a blockwise-group-sparsity regularization, is proposed. Extensive experimental results demonstrate that the proposed generalized tensor approach outperforms not only traditional matrix-based techniques but also state-of-the-art tensor-based methods; the gains with respect to the latter are especially significant in cases of anisotropic spatial blurring.

Hyperspectral imaging is endowed with outstanding discriminability between different land types by its comprehensive sensing of the spectrum, thus favored applying to anomaly detection. However, blurring effect, as a critical cause for quality deterioration of hyperspectral imaging, has been omitted by previous hyperspectral anomaly detection models. On one hand, given that anomalies are sparsely distributed in nature, such blurring effect entangling neighboring pixels severely weighs those detection models down. On the other hand, abnormal objects jeopardize the low-dimensional structure of the image, thus deblurring those images with anomalies is more challenging than normal ones. Hence, it is of much significance to investigate anomaly detection using blurred hyperspectral images. To this end, this paper proposes a generalized non-convex surrogated tensor framework that is able to perform anomaly detection robustly to blurring effects on hyperspectral images. The proposed framework is featured to be a unified paradigm which guarantees convergence for a broad class of non-convex surrogates. Through treating the spatial and spectral low-rankness adaptively via Block Term Decomposition, the unevenness in the multi-linear low-rankness of hyperspectral image is comprehensively considered, which together with the non-convex surrogates results in a tighter modeling of the low-dimensional prior of hyperspectral images. Extensive experiments demonstrate the superiority of the proposed method compared with the state-of-the-art methods on both hyperspectral image deblurring and anomaly detection.

Fusion with corresponding finer-resolution images has been a promising way to enhance hyperspectral images (HSIs) spatially. Recently, low-rank tensor-based methods have shown advantages compared with other kind of ones. However, these current methods either relent to blind manual selection of latent tensor rank, whereas the prior knowledge about tensor rank is surprisingly limited, or resort to regularization to make the role of low rankness without exploration on the underlying low-dimensional factors, both of which are leaving the computational burden of parameter tuning. To address that, a novel Bayesian sparse learning-based tensor ring (TR) fusion model is proposed, named as FuBay. Through specifying hierarchical sprasity-inducing prior distribution, the proposed method becomes the first fully Bayesian probabilistic tensor framework for hyperspectral fusion. With the relationship between component sparseness and the corresponding hyperprior parameter being well studied, a component pruning part is established to asymptotically approaching true latent rank. Furthermore, a variational inference (VI)-based algorithm is derived to learn the posterior of TR factors, circumventing nonconvex optimization that bothers the most tensor decomposition-based fusion methods. As a Bayesian learning methods, our model is characterized to be parameter tuning-free. Finally, extensive experiments demonstrate its superior performance when compared with state-of-the-art methods.

Deep-learning-based methods are widely used in multisource remote-sensing image classification, and the improvement in their performance confirms the effectiveness of deep learning for classification tasks. However, the inherent underlying problems of deep-learning models still hinder the further improvement of classification accuracy. For example, after multiple rounds of optimization learning, representation bias and classifier bias are accumulated, which prevents the further optimization of network performance. In addition, the imbalance of fusion information among multisource images also leads to insufficient information interaction throughout the fusion process, thus making it difficult to fully utilize the complementary information of multisource data. To address these issues, a Representation-enhanced Status Replay Network (RSRNet) is proposed. First, a dual augmentation including modal augmentation and semantic augmentation is proposed to enhance the transferability and discreteness of feature representation, to reduce the impact of representation bias in the feature extractor. Then, to alleviate the classifier bias and maintain the stability of the decision boundary, a status replay strategy (SRS) is built to regulate the learning and optimization of the classifier. Finally, aiming to improve the interactivity of modal fusion, a novel cross-modal interactive fusion (CMIF) method is employed to jointly optimize the parameters of different branches by combining multisource information. Quantitative and qualitative results on three datasets demonstrate the superiority of RSRNet in multisource remote-sensing image classification, and its outperformance compared with other state-of-the-art methods.

Although spatio-spectral and spatio-temporal fusion has been well explored, few efforts are made on integrating spatio-spectral-temporal features. As an intrinsic prior, low tensor-rank has been successfully taken into effect by current fusion models, most of which, however, resort to establishing an overall low-rank norm without performing factorization techniques thus have trouble capturing the latent high-order structure of hyperspectral data cube. To address that, a novel Anisotropicly Sparse (AS) tensor norm is developed to make the rank minimization a learnable process under Tucker decomposition. The AS norm enables the model to minimize the multi-linear tensor ranks if imposed on the core tensor after factorization, hence it significantly improves the model’s fusion performance. In the temporal domain, a Hadamard-product based variability descriptor is incorporated into the fusion model to map the former information to current time. Additionally, piece-wise smooth prior of the Tucker factors is employed by extra regularizers as supplement to the loss spatial information. With the Proximal Differential Matrix being developed for optimization, the proposed method reaches state-of-the-art results on both spatio-spectral and spatio-spectral-temporal fusion at low computational cost.

Spectral quality is one of the most critical issues that has to be considered in real hyperspectral image (HSI) application. Denoising, destriping, inpainting, deblurring and super-resolution are common techniques to improve the quality of HSIs from different aspects. These techniques have attracted much attention that a diversity of methods, algorithms, tools have been well developed to facilitate the development of HSI restoration. Although effectively improving the quality of HSIs, these technologies mainly focus on recovering an HSI captured in the normal sunlight. It is acknowledged that HSIs are captured via passive imaging mechanisms covering the spectral bands from visible& near-infrared to shortwave infrared spectral range (i.e., around 400nm to 2500nm). The imaging condition limits HSI spectrometers to capture HSIs without sunlight (e.g., in dark environments or night time). In this work, a low-light HSI restoration method is proposed, where we borrow idea of intrinsic decomposition based on Retinex theory in natural image low-light enhancement. Additionally, camera response function that describe the spectral degradation of RGB image and relationship between irradiance and pixel values are employed, respectively. The experimental results validate the effectiveness of the proposed method.