Hyperspectral images (HSIs) are often corrupted by a mixture of several types of noise during the acquisition process, e.g., Gaussian noise, impulse noise, dead lines, stripes, etc. Such complex noise could degrade the quality of the acquired HSIs, limiting the precision of the subsequent processing. In this paper, we present a novel tensor-based HSI restoration approach by fully identifying the intrinsic structures of the clean HSI part and the mixed noise part. Specifically, for the clean HSI part, we use tensor Tucker decomposition to describe the global correlation among all bands, and an anisotropic spatial–spectral total variation regularization to characterize the piecewise smooth structure in both spatial and spectral domains. For the mixed noise part, we adopt the $\ell _1$ norm regularization to detect the sparse noise, including stripes, impulse noise, and dead pixels. Despite that TV regularization has the ability of removing Gaussian noise, the Frobenius norm term is further used to model heavy Gaussian noise for some real-world scenarios. Then, we develop an efficient algorithm for solving the resulting optimization problem by using the augmented Lagrange multiplier method. Finally, extensive experiments on simulated and real-world noisy HSIs are carried out to demonstrate the superiority of the proposed method over the existing state-of-the-art ones.

Tensor recovery is a fundamental problem in tensor research field. It generally requires to explore intrinsic prior structures underlying tensor data, and formulate them as certain forms of regularization terms for guiding a sound estimate of the restored tensor. Recent researches have made significant progress by adopting two insightful tensor priors, i.e., global low-rankness (L) and local smoothness (S), which are always encoded as a sum of two separate regularizers into recovery models. However, unlike the primary theoretical developments on low-rank tensor recovery, these joint “L+S” models have no theoretical exact-recovery guarantees yet, making the methods lack reliability in real practice. To this crucial issue, in this work, we build a unique regularizer termed as tensor correlated total variation (t-CTV), which essentially encodes both L and S priors of a tensor simultaneously. Especially, by equipping t-CTV into the recovery models, we can rigorously prove the exact recovery guarantees for two typical tensor recovery tasks, i.e., tensor completion and tensor robust principal component analysis. To the best of our knowledge, this should be the first exact-recovery results among all related “L+S” methods for tensor recovery. We further propose ADMM algorithms with fine convergence to solve the proposed models. Significant recovery accuracy improvements are observed in extensive experiments. Typically, our method achieves a workable performance when the missing rate is extremely large, e.g., 99.5%, for the color image inpainting task, while all its peers totally fail in such a challenging case. Code is released at https://github.com/wanghailin97 .

Mining structural priors in data is a widely recognized technique for hyperspectral image (HSI) denoising tasks, whose typical ways include model-based methods and data-based methods. The model-based methods have good generalization ability, while the runtime can hardly meet the fast processing requirements of the practical situations due to the large size of an HSI X ϵ R ^MN×B . For the data-based methods, they perform relatively fast on new test data once they have been trained. However, their generalization ability is always insufficient. In this paper, we propose a fast model-based approach via a novel regularizer named the Representative Coefficient Total Variation (RCTV) to simultaneously characterize the low rank and local smooth properties. The RCTV regularizer is proposed based on the observation that the representative coefficient matrix U ϵ R ^MN×R ( R ≪ B ) obtained by orthogonally transforming the original HSI X can inherit the strong local-smooth prior of X. Since R/B is very small, the model based on the RCTV regularizer has lower time complexity. Additionally, we find that the representative coefficient matrix U is robust to noise, and thus the RCTV regularizer can somewhat promote the robustness of the HSI denoising model. Extensive experiments on mixed noise removal demonstrate that the proposed method realizes a perfect compromise between denoising performance and denoising speed as compared with other state-of-the-art methods. Remarkably, the denoising speed of our proposed method outperforms all competing model-based techniques and is comparable with the deep learning-based approaches. The code of our algorithm is released at https://github.com/andrew-pengjj/rctv.git.

It has recently been claimed that the outstanding performance of machine-learning scoring functions (SFs) is exclusively due to the presence of training complexes with highly similar proteins to those in the test set. Here, we revisit this question using 24 similarity-based training sets, a widely used test set, and four SFs. Three of these SFs employ machine learning instead of the classical linear regression approach of the fourth SF (X-Score which has the best test set performance out of 16 classical SFs). We have found that random forest (RF)-based RF-Score-v3 outperforms X-Score even when 68% of the most similar proteins are removed from the training set. In addition, unlike X-Score, RF-Score-v3 is able to keep learning with an increasing training set size, becoming substantially more predictive than X-Score when the full 1105 complexes are used for training. These results show that machine-learning SFs owe a substantial part of their performance to training on complexes with dissimilar proteins to those in the test set, against what has been previously concluded using the same data. Given that a growing amount of structural and interaction data will be available from academic and industrial sources, this performance gap between machine-learning SFs and classical SFs is expected to enlarge in the future.

In general, hyperspectral images (HSIs) are degraded by a mixture of complicated noise (i.e., mixture of Gaussian and sparse noise), and how to precisely model HSI noise plays a vital role in the task of HSI denoising. The most popular choices for encoding the noise distribution are Gaussian, Laplacian, and the mixture of Gaussians, but they are always incompatible with real-world HSI noise. By investigating histograms of the error map, we firstly explore that asymmetry is a typical and general feature of HSI noise. Inspired by this discovery, we find that a bandwise asymmetric Laplacian distribution can be finely employed to model this type of noise. Equipped with the low-rank matrix factorization (LRMF) framework, we formulate a novel model by the maximum likelihood estimation (MLE) principle, which can be efficiently solved by using the iterative optimization algorithm. Extensive experimental results on synthetic and real datasets demonstrate that the proposed model outperforms other counterparts. It is also found that scale and asymmetry parameters in the asymmetric Laplacian distribution can well interpret the pattern of real-world HSI noise.

In recent years, the imputation of spatiotemporal traffic data has emerged as a critical area of research within intelligent transportation systems. A commonly employed approach is low-rank matrix/tensor completion combined with additional spatiotemporal regularization techniques. However, many existing methods simply incorporate these regularizations into the low-rank model, resulting in models that are highly sensitive to trade-off parameters and yield mediocre results. Motivated by this problem, in this paper, we propose a method called Low-Rank Tensor Completion with 3D Spatiotemporal Transform (LRTC-3DST) for traffic data imputation, which effectively integrates low-rankness with three types of spatiotemporal characteristics in a fused manner and thus avoids trade-off parameters. We first design three specific transformations including graph Laplacian transform, fractional difference transform and periodic circulant transform for encoding the spatial local consistency, temporal local consistency and approximate periodicity of 3D traffic data, respectively. Then the LRTC-3DST model is proposed by using the truncated tensor nuclear norm on the three spatiotemporal feature tensors. The proposed model is optimized via the alternating direction multipliers method. Extensive experiments on a series of real traffic datasets demonstrate that our LRTC-3DST significantly outperforms numerous related methods, even when the missing rate is as high as $99\%$ . The code is available at https://github.com/HaoShu2000/LRTC-3DST.