Leveraging intrinsic data priors is critical for effective data recovery. However, existing approaches often struggle to achieve theoretical guarantees, strong performance, and computational efficiency simultaneously. In this paper, we introduce a novel Representative Coefficient Correlated Total Variation (RCCTV) regularizer that captures the recently observed low-rank and local smoothness properties of the representative coefficient tensor derived from a low-rank decomposition. RCCTV regularizer offers three key advantages: (1) it operates on a compact representative coefficient image significantly smaller than the original data, enabling highly efficient optimization; (2) it jointly enforces low-rankness and spatial smoothness through a single regularizer, eliminating the need for trade-off parameters; and (3) when integrated into a robust PCA framework (i.e., RCCTV-RPCA model), it admits provable exact recovery under mild conditions. To solve the resulting model, we develop an efficient ADMM-based algorithm accelerated via fast Fourier transform. Extensive experiments on both synthetic and real-world datasets demonstrate that the RCCTV-RPCA model achieves state-of-the-art accuracy while running significantly faster. Our code and Supplementary Material are available at https://github.com/mendy-2013/RCCTV.

Hyperspectral images (HSIs) are frequently noisy and of low resolution due to the constraints of imaging devices. Recently launched satellites can concurrently acquire HSIs and panchromatic (PAN) images, enabling the restoration of HSIs to generate clean and high-resolution imagery through fusing PAN images for denoising and super-resolution. However, previous studies treated these two tasks as independent processes, resulting in accumulated errors. This paper introduces \textbf{H}yperspectral \textbf{I}mage Joint \textbf{Pand}enoising \textbf{a}nd Pan\textbf{s}harpening (Hipandas), a novel learning paradigm that reconstructs HRHS images from noisy low-resolution HSIs (LRHS) and high-resolution PAN images. The proposed zero-shot Hipandas framework consists of a guided denoising network, a guided super-resolution network, and a PAN reconstruction network, utilizing an HSI low-rank prior and a newly introduced detail-oriented low-rank prior. The interconnection of these networks complicates the training process, necessitating a two-stage training strategy to ensure effective training. Experimental results on both simulated and real-world datasets indicate that the proposed method surpasses state-of-the-art algorithms, yielding more accurate and visually pleasing HRHS images.

The nuclear norm (NN) has been widely explored in matrix recovery problems, such as Robust PCA and matrix completion, leveraging the inherent global low-rank structure of the data. In this study, we introduce a new modified nuclear norm (MNN) framework, where the MNN family norms are defined by adopting suitable transformations and performing the NN on the transformed matrix. The MNN framework offers two main advantages: (1) it jointly captures both local information and global low-rankness without requiring trade-off parameter tuning; (2) under mild assumptions on the transformation, we provide theoretical recovery guarantees for both Robust PCA and MC tasks—an achievement not shared by existing methods that combine local and global information. Thanks to its general and flexible design, MNN can accommodate various proven transformations, enabling a unified and effective approach to structured low-rank recovery. Extensive experiments demonstrate the effectiveness of our method. Code and supplementary material are available at https://github.com/andrew-pengjj/modified_nuclear_norm.

Real-world datasets like multi-spectral images and videos are naturally represented as tensors. However, limitations in data acquisition often lead to corrupted or incomplete tensor data, making tensor recovery a critical challenge. Solving this problem requires exploiting inherent structural patterns, with the low-rank property being particularly vital. An important category of existing low-rank tensor recovery methods relies on the tensor nuclear norms. However, these methods struggle with either computational inefficiency or weak theoretical guarantees for large-scale data. To address these issues, we propose a fast guaranteed tensor recovery framework based on a new tensor nuclear norm. Our approach adaptively extracts a column-orthogonal matrix from the data, reducing a large-scale tensor into a smaller subspace for efficient processing. This dimensionality reduction enhances speed without compromising accuracy. The recovery theories of two typical models are established by introducing an adjusted incoherence condition. Extensive experiments demonstrate the effectiveness of the proposed method, showing improved accuracy and speed over existing approaches. Our code and supplementary material are available at https://github.com/andrew-pengjj/adaptive_tensor_nuclear_norm.

Seismic data denoising is essential for subsequent inversion and interpretation tasks. However, most existing methods rely on loss functions that assume seismic noise follows an independent and identically distributed (i.i.d.) Gaussian distribution, which does not align with the characteristics of actual seismic noise. In this paper, we first analyze the principle of the L2norm loss function in suppressing i.i.d. Gaussian noise from the maximum a posteriori (MAP) perspective, and then introduce the Mixture of Gaussians (MoG) model to handle non-i.i.d. noise suppression. Additionally, we optimize the MoG model using the Expectation-Maximization (EM) algorithm for improved performance. We propose a novel approach, DIP-MoG, which integrates the Deep Image Prior (DIP) with the MoG model for enhanced denoising. To validate the performance of DIP-MoG, we conduct experiments on two synthetic datasets contaminated with a mixture of Gaussian noise and field noise, as well as a field seismic dataset. The results from both synthetic and field data demonstrate the superior denoising performance of DIP-MoG.

For infrared small target detection tasks, deep unfolding techniques have demonstrated effectiveness and practical value. However, existing methods generally emphasize the low-rankness of background and the sparsity of targets within the robust principal component analysis (RPCA) framework, which may overlook the intrinsic gradient prior information existed in background. To address the challenges of complex background estimation and accurate small target detection, we propose a gradient prior-guided deep unfolding network, termed the correlated total variation network (CTVNet). First, we introduce a correlated total variation regularization to simultaneously characterize the low-rankness and local smoothness of the background, and transform it into the estimation of gradient maps. Subsequently, we employ a multi-scale feature fusion network to thoroughly extract gradient priors, replacing the complex and limited analytical computation of gradient correlations. Finally, we unfold the designed iterative algorithm using alternating direction method of multipliers (ADMM) into a learnable network, where each module corresponds to a specific operator within the iterative process, and all parameters are learnable. By training the network end-to-end, the learnable modules can be automatically optimized to better separate the background and the target. Extensive experimental results demonstrate that our proposed method achieves competitive performance compared to several state-of-the-art algorithms while exhibiting superior performance and generalization capabilities on both in-distribution and out-of-distribution data. Our code is available at https://github.com/AuroraPei/CTVNet.

Seismic data inevitably suffers from random noise due to environmental contributors, which seriously affects subsequent processing and analysis. Deep learning has been a successful tool for seismic data random noise attenuation. Due to the scarcity of clean labels in real scenarios, researchers have attached more attention to self-supervised methods without paired training data. However, most self-supervised methods are costly in computations and thus are inefficient for practical large data volume implementation. In this paper, we propose a novel self-supervised method for seismic random noise attenuation by designing a Kolmogorov-Arnold network (KAN)-empowered neural low-rank representation (NLRR) method. Specifically, the proposed method adopts a compact tensor factorization parameterized by implicit neural representations to efficiently encode both low-rank and smooth priors of seismic data into the model. Moreover, we introduce generalized KANs by using multiple sinusoidal activation functions with different frequencies, serving as factor functions of NLRR to empower its representation ability. Extensive experiments on synthetic and field seismic data demonstrate the clear superiority of our method in terms of efficiency and efficacy over several traditional and deep learning-based methods for random noise attenuation. Specifically, our method reduces over 90% execution time against existing self-supervised methods while still achieving evidently better denoising results.

Remote sensing image restoration, which aims to reconstruct corrupted or missing regions, heavily relies on low-rank models. A recent trend in this field is to jointly model low-rank and local smoothness priors using a single regularization term, in order to better recover fine textures. However, due to the entanglement of low- and high-frequency components in an image, existing methods often struggle to simultaneously capture both coarse-grained structures and fine-grained textures, while also suffering from high computational complexity. To address these issues, this paper proposes a novel regularization, the Haar Nuclear Norm (HNN), for efficient and effective remote sensing image restoration. HNN transforms images into wavelet coefficients that separate low-frequency (coarse-grained) and high-frequency (fine-grained) components, and enforces low-rankness via nuclear norms on the mode-3 unfolding matrices of these wavelet coefficients. Experimental evaluations conducted on hyperspectral image inpainting, multi-temporal image cloud removal, and hyperspectral image denoising have revealed the HNN's potential. Typically, HNN achieves a performance improvement of 1-4 dB and a speedup of 10-28x compared to some state-of-the-art methods (e.g., tensor correlated total variation, and fully-connected tensor network) for inpainting tasks. The code is available at https://github.com/isyuchang/HNN.

Abstract. Recently, the CTV-RPCA model proposed the first recoverable theory for separating low-rank and local-smooth matrices and sparse matrices based on the correlated total variation (CTV) regularizer. However, the CTV-RPCA model ignores the influence of noise, which makes the model unable to effectively extract low-rank and local-smooth principal components under noisy circumstances. To alleviate this issue, this article extends the CTV-RPCA model by considering the influence of noise and proposes two robust models with parameter adaptive adjustment, i.e., Stable Principal Component Pursuit based on CTV (CTV-SPCP) and Square Root Principal Component Pursuit based on CTV (CTV-[Formula: see text]). Furthermore, we present a statistical recoverable error bound for the proposed models, which allows us to know the relationship between the solution of the proposed models and the ground-truth. It is worth mentioning that, in the absence of noise, our theory degenerates back to the exact recoverable theory of the CTV-RPCA model. Finally, we develop the effective algorithms with the strict convergence guarantees. Extensive experiments adequately validate the theoretical assertions and also demonstrate the superiority of the proposed models over many state-of-the-art methods on various typical applications, including video foreground extraction, multispectral image denoising, and hyperspectral image denoising. The source code is released at https://github.com/andrew-pengjj/CTV-SPCP .

Infrared small target detection (ISTD) is a challenging task in the computer vision field due to factors such as target scale variations and strong clutter. The existing infrared patch tensor (IPT) models achieve good detection performance but still have several limitations, such as inaccurate background modeling results and poor robustness against noise. To alleviate these issues, in this article, we propose a new IPT model (dubbed as IPT-TCTV) by fully exploiting prior background knowledge. We construct an improved spatial-temporal (STT) model by sliding a 3-D window, which could better preserve the spatial correlation and temporal continuity of multiframe infrared images in the constructed tensor. Specifically, a joint low-rank and local smoothness regularization, i.e., tensor correlated total variation (TCTV), is utilized to characterize the background since the background exhibits not only the low-rank property but also the local smoothness property, without introducing additional trade-off parameters. Furthermore, considering the effect of edge structures, the${l} _{2,1}$norm is adopted as a noise constraint to eliminate strong residuals, which can help to extract real targets from the background with more precision. Finally, we design an efficient alternating direction method of multipliers (ADMMs) approach to solve the proposed model. Experimental results on some benchmark datasets illustrate that our IPT-TCTV model can achieve better detection performance than other state-of-the-art (SOTA) methods in various real scenes. The source code is released athttps://github.com/AuroraPei/IPT-TCTV.

Fully characterizing the spatial-spectral priors of hyperspectral images (HSI) is crucial for HSI denoising tasks. Recently, HSI denoising models based on representative coefficient images (RCIs) under the spectral low-rank decomposition framework have garnered significant attention due to their clever utilization of spatial-spectral information in HSI at a low cost. However, current methods either employ handcrafted classical denoisers or off-the-shelf deep denoisers to denoise RCIs, failing to fully capture the structural information of RCIs. In this paper, we propose a specific optimization framework for learning an RCI denoiser under the low-rank decomposition framework for the first time. Since low-rank decomposition can characterize the global low-rank property of HSI, our RCI denoiser only needs to learn the spatial prior of RCIs. Consequently, our optimization framework is inclined to learn a more powerful RCI denoiser. However, learning an RCI denoiser is not an easy task, primarily due to the lack of paired clean-noisy RCI data. To address this issue, we employ parametric techniques to represent the to-be-restored HSI as a function of RCI denoiser network parameters. In this way, the parameters of the RCI denoiser can thus be updated using noisy-clean HSI pairs. Furthermore, we adopt residual learning and Gaussian whitening techniques to enhance the RCI denoiser’s denoising ability for HSIs with various noise levels and different rank settings. Extensive experiments demonstrate that our method can achieve significant improvements in both denoising effectiveness and speed compared to state-of-the-art methods. The code of our algorithm is released at https://github.com/andrew-pengjj/RCILD.git.

Hyperspectral image (HSI) denoising is an essential preprocessing step for downstream applications. Fully characterizing the spatial-spectral priors of HSI is crucial for HSI denoising tasks. In recent years, denoising methods based on low-rank subspaces have garnered attention. Within the low-rank decomposition framework (LRDF), the restoration of HSIs can be formulated as a problem of restoring two subspace factors. Since the rank of the HSI data has been predetermined by LRDF, subspace-based methods have already characterized the spectral low-rankness information. Next, subspace-based methods only need to encode spatial priors for HSIs. Existing subspace-based methods either rely on a manual-designed regularization or a pre-trained deep neural network. The former fails to fully capture the intrinsic priors of the HSI, while the latter may encounter generalization issues. Inspired by the unsupervised deep image prior (DIP) technique, this article proposes a double subspace deep prior (DSDP) model to track the mentioned issues. In this model, the two subspace factors are parallelly represented by two deep neural networks. By incorporating popular attention modules into classical convolutional neural networks, the well-designed subspace factor neural network can effectively capture the deep prior of the two subspace factors separately from each HSI in an unsupervised manner. Additionally, the total variation (TV) regularizer is added to constrain the generation of the subspace factor neural network, and further to ensure the effectiveness and robustness of the parameter learning process. Extensive experiments demonstrate that our method outperforms a series of competing methods.

This article introduces a novel paradigm for hyperspectral image (HSI) denoising, which is termed pan-denoising. In a given scene, panchromatic (PAN) images capture similar structures and textures to HSIs but with less noise. This enables the utilization of PAN images to guide the HSI denoising process. Consequently, pan-denoising, which incorporates an additional prior, has the potential to uncover underlying structures and details beyond the internal information modeling of traditional HSI denoising methods. However, the proper modeling of this additional prior poses a significant challenge. To alleviate this issue, the article proposes a novel regularization term, panchromatic weighted representation coefficient total variation (PWRCTV). It employs the gradient maps of PAN images to automatically assign different weights of total variation (TV) regularization for each pixel, resulting in larger weights for smooth areas and smaller weights for edges. This regularization forms the basis of a pan-denoising model, which is solved using the alternating direction method of multipliers (ADMM). Extensive experiments on synthetic and real-world datasets demonstrate that PWRCTV outperforms several state-of-the-art methods in terms of metrics and visual quality. Furthermore, an HSI classification experiment confirms that PWRCTV, as a preprocessing method, can enhance the performance of downstream classification tasks. The code and data are available athttps://github.com/shuangxu96/PWRCTV.

In the field of remote sensing (RS) imaging, the occurrence of adverse meteorological conditions or sensor malfunctions can lead to missing data, posing a substantial impediment. Low-rank tensor decomposition has emerged as a promising strategy for resolving this issue, as it enables the integration of diverse data priors within a unified framework. Although various decomposition techniques, such as Tucker decomposition and tensor ring decomposition (TRD), have been developed based on multilinear products, they may not adequately capture the complex structure of RS imagery. Therefore, there is a need for tensor decompositions that incorporate nonlinear operations. To alleviate this challenge, a multi-nonlinear product is defined, which enables the construction of a nonlinear Tucker decomposition (NTD) model. To enhance the model’s capability, a stacked Tucker decomposition (STD) model is formulated, by representing a tensor as the product of a core tensor and a collection of factor matrices along each mode, utilizing the multi-nonlinear product, which potentially regulates the distribution of singular values, thereby achieving a more accurate characterization of textures. The proposed model, integrated with total variation regularization, is subsequently applied to the task of RS imagery inpainting. Extensive experimental results demonstrate the superiority of the proposed model over state-of-the-art (SOTA) methods across various tasks. This validates its effectiveness and adaptability in mitigating the challenges associated with RS imagery inpainting. The code is available athttps://github.com/shuangxu96/STDTV.

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 athttps://github.com/HaoShu2000/LRTC-3DST.

A plethora of previous studies indicates that making full use of multifarious intrinsic properties of primordial data is a valid pathway to recover original images from their degraded observations. Typically, both low-rankness and local-smoothness broadly exist in real-world tensor data such as hyperspectral images and videos. Modeling based on both properties has received a great deal of attention, whereas most studies concentrate on experimental performance, and theoretical investigations are still lacking. In this paper, we study the tensor compressive sensing problem based on the tensor correlated total variation, which is a new regularizer used to simultaneously capture both properties existing in the same dataset. The new regularizer has the outstanding advantage of not using a trade-off parameter to balance the two properties. The obtained theories provide a robust recovery guarantee, where the error bound shows that our model certainly benefits from both properties in ground-truth data adaptively. Moreover, based on the ADMM update procedure, we design an algorithm with a global convergence guarantee to solve this model. At last, we carry out experiments to apply our model to hyperspectral image and video restoration problems. The experimental results show that our method is prominently better than many other competing ones. Our code and Supplementary Material are available at https://github.com/fsliuxl/cs-tctv.

Low-rank matrix factorization (LRMF) is a canonical problem in non-convex optimization, the objective function to be minimized is non-convex and even non-smooth, which makes the global convergence guarantee of gradient-based algorithm quite challenging. Recent work made a breakthrough on proving that standard gradient descent converges to the $\varepsilon$-global minima after $O( \frac{d \kappa^2}{\tau^2} {\rm ln} \frac{d \sigma_d}{\tau} + \frac{d \kappa^2}{\tau^2} {\rm ln} \frac{\sigma_d}{\varepsilon})$ iterations from small initialization with a very small learning rate (both are related to the small constant $\tau$). While the dependence of the convergence on the \textit{condition number} $\kappa$ and \textit{small learning rate} makes it not practical especially for ill-conditioned LRMF problem. In this paper, we show that precondition helps in accelerating the convergence and prove that the scaled gradient descent (ScaledGD) and its variant, alternating scaled gradient descent (AltScaledGD) converge to an $\varepsilon$-global minima after $O( {\rm ln} \frac{d}{\delta} + {\rm ln} \frac{d}{\varepsilon})$ iterations from general random initialization. Meanwhile, for small initialization as in gradient descent, both ScaledGD and AltScaledGD converge to $\varepsilon$-global minima after only $O({\rm ln} \frac{d}{\varepsilon})$ iterations. Furthermore, we prove that as a proximity to the alternating minimization, AltScaledGD converges faster than ScaledGD, its global convergence does not rely on small learning rate and small initialization, which certificates the advantages of AltScaledGD in LRMF.

It is known that the decomposition in low-rank and sparse matrices (L+S for short) can be achieved by several Robust PCA techniques. Besides the low rankness, the local smoothness (LSS) is a vitally essential prior for many real-world matrix data such as hyperspectral images and surveillance videos, which makes such matrices have low-rankness and local smoothness property at the same time. This poses an interesting question: Can we make a matrix decomposition in terms of L&LSS +S form exactly? To address this issue, we propose in this paper a new RPCA model based on three-dimensional correlated total variation regularization (3DCTV-RPCA for short) by fully exploiting and encoding the prior expression underlying such joint low-rank and local smoothness matrices. Specifically, using a modification of Golfing scheme, we prove that under some mild assumptions, the proposed 3DCTV-RPCA model can decompose both components exactly, which should be the first theoretical guarantee among all such related methods combining low rankness and local smoothness. In addition, by utilizing Fast Fourier Transform (FFT), we propose an efficient ADMM algorithm with a solid convergence guarantee for solving the resulting optimization problem. Finally, a series of experiments on both simulations and real applications are carried out to demonstrate the general validity of the proposed 3DCTV-RPCA model.

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.

The total variation (TV) regularizer is a widely used technique in image processing tasks to model an image’s local smoothness property. Intrinsically, the TV regularizer imposes sparsity constraints on the gradient maps of the image, which inevitably weakens the image texture structure and thus affects the quality of image restoration. To alleviate this issue, we propose a novel texture-preserved total variation (TPTV) regularizer for hyperspectral image (HSI) by introducing a weighting scheme. Specifically, the weights are assigned to the gradient maps of HSI, which help slack the sparsity constraint for the pixels with large variations, thus preserving the texture structure. Additionally, we elaborate an empirical method to learn the weights adaptively from observed HSI. Then, we propose an HSI denoising method based on the TPTV regularizer. Experimental results on synthetic and real HSI illustrate the superiority of our proposed method over other state-of-the-art methods. In addition, the proposed weighting scheme can be finely embedded into other TV regularizers and protect the image texture. The experiment results also demonstrate that the denoising performance of the original method is significantly improved after embedding the weighting scheme.

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 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 hyperspectral images (HSI). 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 GCS (the sparsity on the core tensor of the gradient map), 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 ℓ1norm describes the sparsity of gradient map, i.e., the local smoothness of the original data; 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.

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${\mathbf {X}}\in \mathbb {R}^{\textrm {MN}\times B}$. 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 article, 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${\mathbf {U}}\in \mathbb {R}^{\textrm {MN}\times R} (R\ll B)$obtained by orthogonally transforming the original HSI${\mathbf {X}}$can inherit the strong local-smooth prior of${\mathbf {X}}$. Since$R/B$is very small, the model based on the RCTV regularizer has lower time complexity. In addition, we find that the representative coefficient matrix${\mathbf {U}}$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 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 athttps://github.com/andrew-pengjj/rctv.git.

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 first explore that asymmetry is a typical and general feature of HSI noise. Inspired by this discovery, we find that a bandwise asymmetric Laplacian (AL) distribution can be finely used 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 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 AL distribution can well interpret the pattern of real-world HSI noise.

The total variation (TV) is a powerful regularization term encoding the local smoothness prior structure underlying images. By combining the TV regularization term with low rank prior, the 3D total variation (3DTV) regularizer has achieved advanced performance in general hyperspectral image (HSI) processing tasks. Intrinsically, 3DTV assumes i.i.d. sparsity structures on all bands of the gradient maps calculated along the spectrum and space of an HSI. This, however, largely deviates from the real-world cases, where the gradient maps generally have different while correlated gradient map structures across all bands. To alleviate this issue, we propose an enhanced 3DTV (E-3DTV) regularization term beyond the conventional. Instead of imposing sparsity on gradient maps themselves, the new term calculates sparsity on the subspace bases on gradient maps along all bands of an HSI, which naturally encodes the correlation and difference among all these bands, and thus more faithfully reflects the insightful configurations of an HSI. The E-3DTV term can easily replace the conventional 3DTV term and be embedded into an HSI processing model to ameliorate its performance. We made such attempts on two typical related tasks: HSI denoising and compressed sensing. The superiority of our proposed method is substantiated by extensive experiments on synthetic and real HSI data, visually and quantitatively on both tasks, as compared with current state-of-the-arts. The code of our algorithm is released athttps://github.com/andrew-pengjj/Enhanced-3DTV.git.

MOTIVATION: Studies have shown that the accuracy of random forest (RF)-based scoring functions (SFs), such as RF-Score-v3, increases with more training samples, whereas that of classical SFs, such as X-Score, does not. Nevertheless, the impact of the similarity between training and test samples on this matter has not been studied in a systematic manner. It is therefore unclear how these SFs would perform when only trained on protein-ligand complexes that are highly dissimilar or highly similar to the test set. It is also unclear whether SFs based on machine learning algorithms other than RF can also improve accuracy with increasing training set size and to what extent they learn from dissimilar or similar training complexes. RESULTS: We present a systematic study to investigate how the accuracy of classical and machine-learning SFs varies with protein-ligand complex similarities between training and test sets. We considered three types of similarity metrics, based on the comparison of either protein structures, protein sequences or ligand structures. Regardless of the similarity metric, we found that incorporating a larger proportion of similar complexes to the training set did not make classical SFs more accurate. In contrast, RF-Score-v3 was able to outperform X-Score even when trained on just 32% of the most dissimilar complexes, showing that its superior performance owes considerably to learning from dissimilar training complexes to those in the test set. In addition, we generated the first SF employing Extreme Gradient Boosting (XGBoost), XGB-Score, and observed that it also improves with training set size while outperforming the rest of SFs. Given the continuous growth of training datasets, the development of machine-learning SFs has become very appealing. AVAILABILITY AND IMPLEMENTATION: https://github.com/HongjianLi/MLSF. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Cerebrovascular diseases, i.e., acute stroke, are a common cause of serious long-term disability. Cerebral perfusion computed tomography (CPCT) can provide rapid, high-resolution, quantitative hemodynamic maps to assess and stratify perfusion in patients with acute stroke symptoms. However, CPCT imaging typically involves a substantial radiation dose due to its repeated scanning protocol. Therefore, in this paper, we present a low-dose CPCT image reconstruction method to yield high-quality CPCT images and high-precision hemodynamic maps by utilizing the great similarity information among the repeated scanned CPCT images. Specifically, a newly developed low-rank tensor decomposition with spatial-temporal total variation (LRTD-STTV) regularization is incorporated into the reconstruction model. In the LRTD-STTV regularization, the tensor Tucker decomposition is used to describe global spatial-temporal correlations hidden in the sequential CPCT images, and it is superior to the matricization model (i.e., low-rank model) that fails to fully investigate the prior knowledge of the intrinsic structures of the CPCT images after vectorizing the CPCT images. Moreover, the spatial-temporal TV regularization is used to characterize the local piecewise smooth structure in the spatial domain and the pixels' similarity with the adjacent frames in the temporal domain, because the intensity at each pixel in CPCT images is similar to its neighbors. Therefore, the presented LRTD-STTV model can efficiently deliver faithful underlying information of the CPCT images and preserve the spatial structures. An efficient alternating direction method of multipliers algorithm is also developed to solve the presented LRTD-STTV model. Extensive experimental results on numerical phantom and patient data are clearly demonstrated that the presented model can significantly improve the quality of CPCT images and provide accurate diagnostic features in hemodynamic maps for low-dose cases compared with the existing popular algorithms.