Ting‐Zhu Huang

Xian-Ming Gu, Bruno Carpentieri, Ting-Zhu Huang et al.

In the present study, we establish two new block variants of the Conjugate Orthogonal Conjugate Gradient (COCG) and the Conjugate A-Orthogonal Conjugate Residual (COCR) Krylov subspace methods for solving complex symmetric linear systems with multiple right hand sides. The proposed Block iterative solvers can fully exploit the complex symmetry property of coefficient matrix of the linear system. We report on extensive numerical experiments to show the favourable convergence properties of our newly developed Block algorithms for solving realistic electromagnetic simulations.

B. Carpentieri, Y. -F. Jing, T. -Z. Huang et al.

We present economical iterative algorithms built on the Biconjugate $A$-Orthonormalization Procedure for real unsymmetric and complex non-Hermitian systems. The principal characteristics of the developed solvers is that they are fast convergent and cheap in memory. We report on a large combination of numerical experiments to demonstrate that the proposed family of methods is highly competitive and often superior to other popular algorithms built upon the Arnoldi method and the biconjugate Lanczos procedures for unsymmetric linear sytems.

Ting Huang, Zeyu Zhang, Ruicheng Zhang et al.

3D scene understanding plays a fundamental role in vision applications such as robotics, autonomous driving, and augmented reality. However, advancing learning-based 3D scene understanding remains challenging due to two key limitations: (1) the large scale and complexity of 3D scenes lead to higher computational costs and slower training compared to 2D counterparts; and (2) high-quality annotated 3D datasets are significantly scarcer than those available for 2D vision. These challenges underscore the need for more efficient learning paradigms. In this work, we propose DC-Scene, a data-centric framework tailored for 3D scene understanding, which emphasizes enhancing data quality and training efficiency. Specifically, we introduce a CLIP-driven dual-indicator quality (DIQ) filter, combining vision-language alignment scores with caption-loss perplexity, along with a curriculum scheduler that progressively expands the training pool from the top 25% to 75% of scene-caption pairs. This strategy filters out noisy samples and significantly reduces dependence on large-scale labeled 3D data. Extensive experiments on ScanRefer and Nr3D demonstrate that DC-Scene achieves state-of-the-art performance (86.1 CIDEr with the top-75% subset vs. 85.4 with the full dataset) while reducing training cost by approximately two-thirds, confirming that a compact set of high-quality samples can outperform exhaustive training. Code will be available at https://github.com/AIGeeksGroup/DC-Scene.

Tai-Xiang Jiang, Ting-Zhu Huang, Xi-Le Zhao et al.

Rain streak removal is an important issue in outdoor vision systems and has recently been investigated extensively. In this paper, we propose a novel video rain streak removal approach FastDeRain, which fully considers the discriminative characteristics of rain streaks and the clean video in the gradient domain. Specifically, on the one hand, rain streaks are sparse and smooth along the direction of the raindrops, whereas on the other hand, clean videos exhibit piecewise smoothness along the rain-perpendicular direction and continuity along the temporal direction. Theses smoothness and continuity results in the sparse distribution in the different directional gradient domain, respectively. Thus, we minimize 1) the $\ell_1$ norm to enhance the sparsity of the underlying rain streaks, 2) two $\ell_1$ norm of unidirectional Total Variation (TV) regularizers to guarantee the anisotropic spatial smoothness, and 3) an $\ell_1$ norm of the time-directional difference operator to characterize the temporal continuity. A split augmented Lagrangian shrinkage algorithm (SALSA) based algorithm is designed to solve the proposed minimization model. Experiments conducted on synthetic and real data demonstrate the effectiveness and efficiency of the proposed method. According to comprehensive quantitative performance measures, our approach outperforms other state-of-the-art methods especially on account of the running time. The code of FastDeRain can be downloaded at https://github.com/TaiXiangJiang/FastDeRain.

Yu-Bang Zheng, Xi-Le Zhao, Junhua Zeng et al.

Tensor network (TN) representation is a powerful technique for computer vision and machine learning. TN structure search (TN-SS) aims to search for a customized structure to achieve a compact representation, which is a challenging NP-hard problem. Recent "sampling-evaluation"-based methods require sampling an extensive collection of structures and evaluating them one by one, resulting in prohibitively high computational costs. To address this issue, we propose a novel TN paradigm, named SVD-inspired TN decomposition (SVDinsTN), which allows us to efficiently solve the TN-SS problem from a regularized modeling perspective, eliminating the repeated structure evaluations. To be specific, by inserting a diagonal factor for each edge of the fully-connected TN, SVDinsTN allows us to calculate TN cores and diagonal factors simultaneously, with the factor sparsity revealing a compact TN structure. In theory, we prove a convergence guarantee for the proposed method. Experimental results demonstrate that the proposed method achieves approximately 100 to 1000 times acceleration compared to the state-of-the-art TN-SS methods while maintaining a comparable level of representation ability.

Tian-Jing Zhang, Liang-Jian Deng, Ting-Zhu Huang et al.

Pansharpening refers to the fusion of a panchromatic image with a high spatial resolution and a multispectral image with a low spatial resolution, aiming to obtain a high spatial resolution multispectral image. In this paper, we propose a novel deep neural network architecture with level-domain based loss function for pansharpening by taking into account the following double-type structures, \emph{i.e.,} double-level, double-branch, and double-direction, called as triple-double network (TDNet). By using the structure of TDNet, the spatial details of the panchromatic image can be fully exploited and utilized to progressively inject into the low spatial resolution multispectral image, thus yielding the high spatial resolution output. The specific network design is motivated by the physical formula of the traditional multi-resolution analysis (MRA) methods. Hence, an effective MRA fusion module is also integrated into the TDNet. Besides, we adopt a few ResNet blocks and some multi-scale convolution kernels to deepen and widen the network to effectively enhance the feature extraction and the robustness of the proposed TDNet. Extensive experiments on reduced- and full-resolution datasets acquired by WorldView-3, QuickBird, and GaoFen-2 sensors demonstrate the superiority of the proposed TDNet compared with some recent state-of-the-art pansharpening approaches. An ablation study has also corroborated the effectiveness of the proposed approach.

Ben-Zheng Li, Xi-Le Zhao, Teng-Yu Ji et al.

The linear transform-based tensor nuclear norm (TNN) methods have recently obtained promising results for tensor completion. The main idea of this type of methods is exploiting the low-rank structure of frontal slices of the targeted tensor under the linear transform along the third mode. However, the low-rankness of frontal slices is not significant under linear transforms family. To better pursue the low-rank approximation, we propose a nonlinear transform-based TNN (NTTNN). More concretely, the proposed nonlinear transform is a composite transform consisting of the linear semi-orthogonal transform along the third mode and the element-wise nonlinear transform on frontal slices of the tensor under the linear semi-orthogonal transform, which are indispensable and complementary in the composite transform to fully exploit the underlying low-rankness. Based on the suggested low-rankness metric, i.e., NTTNN, we propose a low-rank tensor completion (LRTC) model. To tackle the resulting nonlinear and nonconvex optimization model, we elaborately design the proximal alternating minimization (PAM) algorithm and establish the theoretical convergence guarantee of the PAM algorithm. Extensive experimental results on hyperspectral images, multispectral images, and videos show that the our method outperforms linear transform-based state-of-the-art LRTC methods qualitatively and quantitatively.

Yun-Yang Liu, Xi-Le Zhao, Guang-Jing Song et al.

The robust tensor completion (RTC) problem, which aims to reconstruct a low-rank tensor from partially observed tensor contaminated by a sparse tensor, has received increasing attention. In this paper, by leveraging the superior expression of the fully-connected tensor network (FCTN) decomposition, we propose a $\textbf{FCTN}$-based $\textbf{r}$obust $\textbf{c}$onvex optimization model (RC-FCTN) for the RTC problem. Then, we rigorously establish the exact recovery guarantee for the RC-FCTN. For solving the constrained optimization model RC-FCTN, we develop an alternating direction method of multipliers (ADMM)-based algorithm, which enjoys the global convergence guarantee. Moreover, we suggest a $\textbf{FCTN}$-based $\textbf{r}$obust $\textbf{n}$on$\textbf{c}$onvex optimization model (RNC-FCTN) for the RTC problem. A proximal alternating minimization (PAM)-based algorithm is developed to solve the proposed RNC-FCTN. Meanwhile, we theoretically derive the convergence of the PAM-based algorithm. Comprehensive numerical experiments in several applications, such as video completion and video background subtraction, demonstrate that proposed methods are superior to several state-of-the-art methods.

Jin-Fan Hu, Ting-Zhu Huang, Liang-Jian Deng et al.

Hyperspectral images are of crucial importance in order to better understand features of different materials. To reach this goal, they leverage on a high number of spectral bands. However, this interesting characteristic is often paid by a reduced spatial resolution compared with traditional multispectral image systems. In order to alleviate this issue, in this work, we propose a simple and efficient architecture for deep convolutional neural networks to fuse a low-resolution hyperspectral image (LR-HSI) and a high-resolution multispectral image (HR-MSI), yielding a high-resolution hyperspectral image (HR-HSI). The network is designed to preserve both spatial and spectral information thanks to an architecture from two folds: one is to utilize the HR-HSI at a different scale to get an output with a satisfied spectral preservation; another one is to apply concepts of multi-resolution analysis to extract high-frequency information, aiming to output high quality spatial details. Finally, a plain mean squared error loss function is used to measure the performance during the training. Extensive experiments demonstrate that the proposed network architecture achieves best performance (both qualitatively and quantitatively) compared with recent state-of-the-art hyperspectral image super-resolution approaches. Moreover, other significant advantages can be pointed out by the use of the proposed approach, such as, a better network generalization ability, a limited computational burden, and a robustness with respect to the number of training samples.

Meng Ding, Ting-Zhu Huang, Xi-Le Zhao et al.

In recent studies, the tensor ring (TR) rank has shown high effectiveness in tensor completion due to its ability of capturing the intrinsic structure within high-order tensors. A recently proposed TR rank minimization method is based on the convex relaxation by penalizing the weighted sum of nuclear norm of TR unfolding matrices. However, this method treats each singular value equally and neglects their physical meanings, which usually leads to suboptimal solutions in practice. In this paper, we propose to use the logdet-based function as a nonconvex smooth relaxation of the TR rank for tensor completion, which can more accurately approximate the TR rank and better promote the low-rankness of the solution. To solve the proposed nonconvex model efficiently, we develop an alternating direction method of multipliers algorithm and theoretically prove that, under some mild assumptions, our algorithm converges to a stationary point. Extensive experiments on color images, multispectral images, and color videos demonstrate that the proposed method outperforms several state-of-the-art competitors in both visual and quantitative comparison. Key words: nonconvex optimization, tensor ring rank, logdet function, tensor completion, alternating direction method of multipliers.

Meng Ding, Ting-Zhu Huang, Xi-Le Zhao et al.

The tensor train (TT) rank has received increasing attention in tensor completion due to its ability to capture the global correlation of high-order tensors ($\textrm{order} >3$). For third order visual data, direct TT rank minimization has not exploited the potential of TT rank for high-order tensors. The TT rank minimization accompany with \emph{ket augmentation}, which transforms a lower-order tensor (e.g., visual data) into a higher-order tensor, suffers from serious block-artifacts. To tackle this issue, we suggest the TT rank minimization with nonlocal self-similarity for tensor completion by simultaneously exploring the spatial, temporal/spectral, and nonlocal redundancy in visual data. More precisely, the TT rank minimization is performed on a formed higher-order tensor called group by stacking similar cubes, which naturally and fully takes advantage of the ability of TT rank for high-order tensors. Moreover, the perturbation analysis for the TT low-rankness of each group is established. We develop the alternating direction method of multipliers tailored for the specific structure to solve the proposed model. Extensive experiments demonstrate that the proposed method is superior to several existing state-of-the-art methods in terms of both qualitative and quantitative measures.

Yu-Bang Zheng, Ting-Zhu Huang, Xi-Le Zhao et al.

As low-rank modeling has achieved great success in tensor recovery, many research efforts devote to defining the tensor rank. Among them, the recent popular tensor tubal rank, defined based on the tensor singular value decomposition (t-SVD), obtains promising results. However, the framework of the t-SVD and the tensor tubal rank are applicable only to three-way tensors and lack of flexibility to handle different correlations along different modes. To tackle these two issues, we define a new tensor unfolding operator, named mode-$k_1k_2$ tensor unfolding, as the process of lexicographically stacking the mode-$k_1k_2$ slices of an $N$-way tensor into a three-way tensor, which is a three-way extension of the well-known mode-$k$ tensor matricization. Based on it, we define a novel tensor rank, the tensor $N$-tubal rank, as a vector whose elements contain the tubal rank of all mode-$k_1k_2$ unfolding tensors, to depict the correlations along different modes. To efficiently minimize the proposed $N$-tubal rank, we establish its convex relaxation: the weighted sum of tensor nuclear norm (WSTNN). Then, we apply WSTNN to low-rank tensor completion (LRTC) and tensor robust principal component analysis (TRPCA). The corresponding WSTNN-based LRTC and TRPCA models are proposed, and two efficient alternating direction method of multipliers (ADMM)-based algorithms are developed to solve the proposed models. Numerical experiments demonstrate that the proposed models significantly outperform the compared ones.

Ye-Tao Wang, Xi-Le Zhao, Tai-Xiang Jiang et al.

Rain streak removal is an important issue and has recently been investigated extensively. Existing methods, especially the newly emerged deep learning methods, could remove the rain streaks well in many cases. However the essential factor in the generative procedure of the rain streaks, i.e., the motion blur, which leads to the line pattern appearances, were neglected by the deep learning rain streaks approaches and this resulted in over-derain or under-derain results. In this paper, we propose a novel rain streak removal approach using a kernel guided convolutional neural network (KGCNN), achieving the state-of-the-art performance with simple network architectures. We first model the rain streak interference with its motion blur mechanism. Then, our framework starts with learning the motion blur kernel, which is determined by two factors including angle and length, by a plain neural network, denoted as parameter net, from a patch of the texture component. Then, after a dimensionality stretching operation, the learned motion blur kernel is stretched into a degradation map with the same spatial size as the rainy patch. The stretched degradation map together with the texture patch is subsequently input into a derain convolutional network, which is a typical ResNet architecture and trained to output the rain streaks with the guidance of the learned motion blur kernel. Experiments conducted on extensive synthetic and real data demonstrate the effectiveness of the proposed method, which preserves the texture and the contrast while removing the rain streaks.

Xian-Ming Gu, Ting-Zhu Huang, Guojian Yin et al.

It is known that the restarted full orthogonalization method (FOM) outperforms the restarted generalized minimum residual (GMRES) method in several circumstances for solving shifted linear systems when the shifts are handled simultaneously. Many variants of them have been proposed to enhance their performance. We show that another restarted method, the restarted Hessenberg method [M. Heyouni, Méthode de Hessenberg Généralisée et Applications, Ph.D. Thesis, Université des Sciences et Technologies de Lille, France, 1996] based on Hessenberg procedure, can effectively be employed, which can provide accelerating convergence rate with respect to the number of restarts. Theoretical analysis shows that the new residual of shifted restarted Hessenberg method is still collinear with each other. In these cases where the proposed algorithm needs less enough CPU time elapsed to converge than the earlier established restarted shifted FOM, weighted restarted shifted FOM, and some other popular shifted iterative solvers based on the short-term vector recurrence, as shown via extensive numerical experiments involving the recent popular applications of handling the time fractional differential equations.

Yaru Fan, Yilun Wang, Tingzhu Huang

Joint sparsity has attracted considerable attention in recent years in many fields including sparse signal recovery in compressed sensing (CS), statistics, and machine learning. Traditional convex models suffer from the suboptimal performance though enjoying tractable computation. In this paper, we propose a new non-convex joint sparsity model, and develop a corresponding multi-stage adaptive convex relaxation algorithm. This method extends the idea of iterative support detection (ISD) from the single vector estimation to the multi-vector estimation by considering the joint sparsity prior. We provide some preliminary theoretical analysis including convergence analysis and a sufficient recovery condition. Numerical experiments from both compressive sensing and feature learning show the better performance of the proposed method in comparison with several state-of-the-art alternatives. Moreover, we demonstrate that the extension of ISD from the single vector to multi-vector estimation is not trivial. In particular, while ISD does not work well for reconstructing the signal channel sparse Bernoulli signal, it does achieve significantly improved performance when recovering the multi-channel sparse Bernoulli signal thanks to its ability of natural incorporation of the joint sparsity structure.

Yiming Bu, Bruno Carpentieri, Zhaoli Shen et al.

In this paper we introduce an algebraic recursive multilevel incomplete factorization preconditioner, based on a distributed Schur complement formulation, for solving general linear systems. The novelty of the proposed method is to combine factorization techniques of both implicit and explicit type, recursive combinatorial algorithms, multilevel mechanisms and overlapping strategies to maximize sparsity in the inverse factors and consequently reduce the factorization costs. Numerical experiments demonstrate the good potential of the proposed solver to precondition effectively general linear systems, also against other state-of-the-art iterative solvers of both implicit and explicit form.

Liang-Jian Deng, Weihong Guo, Ting-Zhu Huang

Image super-resolution is a process to enhance image resolution. It is widely used in medical imaging, satellite imaging, target recognition, etc. In this paper, we conduct continuous modeling and assume that the unknown image intensity function is defined on a continuous domain and belongs to a space with a redundant basis. We propose a new iterative model for single image super-resolution based on an observation: an image is consisted of smooth components and non-smooth components, and we use two classes of approximated Heaviside functions (AHFs) to represent them respectively. Due to sparsity of the non-smooth components, a $L_{1}$ model is employed. In addition, we apply the proposed iterative model to image patches to reduce computation and storage. Comparisons with some existing competitive methods show the effectiveness of the proposed method.

Gang Liu, Ting-Zhu Huang, Xiao-Guang Lv et al.

The least-square regression problems or inverse problems have been widely studied in many fields such as compressive sensing, signal processing, and image processing. To solve this kind of ill-posed problems, a regularization term (i.e., regularizer) should be introduced, under the assumption that the solutions have some specific properties, such as sparsity and group sparsity. Widely used regularizers include the $\ell_1$ norm, total variation (TV) semi-norm, and so on. Recently, a new regularization term with overlapping group sparsity has been considered. Majorization minimization iteration method or variable duplication methods are often applied to solve them. However, there have been no direct methods for solve the relevant problems because of the difficulty of overlapping. In this paper, we proposed new explicit shrinkage formulas for one class of these relevant problems, whose regularization terms have translation invariant overlapping groups. Moreover, we apply our results in TV deblurring and denoising with overlapping group sparsity. We use alternating direction method of multipliers to iterate solve it. Numerical results also verify the validity and effectiveness of our new explicit shrinkage formulas.

Jun Liu, Ting-Zhu Huang, Ivan W. Selesnick et al.

Image restoration is one of the most fundamental issues in imaging science. Total variation (TV) regularization is widely used in image restoration problems for its capability to preserve edges. In the literature, however, it is also well known for producing staircase-like artifacts. Usually, the high-order total variation (HTV) regularizer is an good option except its over-smoothing property. In this work, we study a minimization problem where the objective includes an usual $l_2$ data-fidelity term and an overlapping group sparsity total variation regularizer which can avoid staircase effect and allow edges preserving in the restored image. We also proposed a fast algorithm for solving the corresponding minimization problem and compare our method with the state-of-the-art TV based methods and HTV based method. The numerical experiments illustrate the efficiency and effectiveness of the proposed method in terms of PSNR, relative error and computing time.