arXiv subjects

Ting-Zhu Huang

Publications and source records attributed to Ting-Zhu Huang.

At least 19 recordsLinked to original sources

arXiv2026

Pre-Trained Low-Rank Tensor Decomposition for Multi-Dimensional Image Recovery

Recently, tensor decompositions are prevalent for multi-dimensional image representation, which learn the instance-specific structure of each image from scratch. However, tensor decompositions neglect the common structure across different images, leading to limited semantic modeling capability, high computational cost, and a large number of learnable parameters. To address this challenge, we suggest the first pre-trained low-rank tensor decomposition (PLTD) framework, which organically integrates the pre-trained large vision model into the classical tensor decomposition framework. Beyond the shallow and untrained deep tensor decomposition, the suggested PLTD achieves an unprecedented balance among higher recovery fidelity, fewer learnable parameters, and smaller carbon footprint. Specifically, PLTD factorizes the target tensor into a latent tensor and a learnable transform that maps the latent tensor back to the original data domain. The latent tensor consists of two indispensable and complementary terms, i.e., a fixed pre-trained latent tensor and a learnable low-rank latent tensor. The fixed pre-trained latent tensor is distilled from a pre-trained large vision model (i.e., DINOv3) to capture the common structure of the target tensor, while the learnable low-rank latent tensor characterizes the instance-specific structure of the target tensor. To examine the potential of PLTD, we develop the corresponding multi-dimensional image recovery model and theoretically justify the advantages of this framework. Additionally, we discuss the connections between PLTD and classical tensor decomposition frameworks. Extensive experiments on multi-dimensional image recovery demonstrate that PLTD consistently achieves superior performance compared with state-of-the-art methods.

cs.CV↗

arXiv2026

Neural Approximation and Its Applications

Multivariate function approximation is a fundamental problem in machine learning. Classic multivariate function approximations rely on hand-crafted basis functions (e.g., polynomial basis and Fourier basis), which limits their approximation ability and data adaptation ability, resulting in unsatisfactory performance. To address these challenges, we introduce the neural basis function by leveraging an untrained neural network as the basis function. Equipped with the proposed neural basis function, we suggest the neural approximation (NeuApprox) paradigm for multivariate function approximation. Specifically, the underlying multivariate function behind the multi-dimensional data is decomposed into a sum of block terms. The clear physically-interpreted block term is the product of expressive neural basis functions and their corresponding learnable coefficients, which allows us to faithfully capture distinct components of the underlying data and also flexibly adapt to new data by readily fine-tuning the neural basis functions. Attributed to the elaborately designed block terms, the suggested NeuApprox enjoys strong approximation ability and flexible data adaptation ability over the hand-crafted basis function-based methods. We also theoretically prove that NeuApprox can approximate any multivariate continuous function to arbitrary accuracy. Extensive experiments on diverse multi-dimensional datasets (including multispectral images, light field data, videos, traffic data, and point cloud data) demonstrate the promising performance of NeuApprox in terms of both approximation capability and adaptability.

cs.LG↗

arXiv2026

SelfAI: A self-directed framework for long-horizon scientific discovery

Scientific discovery increasingly entails long-horizon exploration of complex hypothesis spaces, yet most existing approaches emphasize final performance while offering limited insight into how scientific exploration unfolds over time, particularly balancing efficiency-diversity trade-offs and supporting reproducible, human-in-the-loop discovery workflows. We introduce SelfAI, a self-directed, multi-agent-enabled discovery system that automates scientific exploration as a strategic, trajectory-driven decision-making process. SelfAI translates high-level research intent into executable experiments, reasons over accumulated experimental trajectories to guide subsequent exploration, and applies adaptive stopping decisions to terminate unproductive search paths within a closed-loop workflow governed by explicit efficiency-diversity trade-offs. Evaluated using real-world experiments spanning domains from machine learning to drug discovery, SelfAI consistently discovers high-quality solutions with substantially fewer redundant trials than classical optimization and recent LLM-based baselines. The proposed methods establish a general framework for organizing long-horizon scientific discovery and adaptive decision-making in complex scientific and engineering systems.

cs.LG↗

arXiv2025

A Knowledge-driven Adaptive Collaboration of LLMs for Enhancing Medical Decision-making

Medical decision-making often involves integrating knowledge from multiple clinical specialties, typically achieved through multidisciplinary teams. Inspired by this collaborative process, recent work has leveraged large language models (LLMs) in multi-agent collaboration frameworks to emulate expert teamwork. While these approaches improve reasoning through agent interaction, they are limited by static, pre-assigned roles, which hinder adaptability and dynamic knowledge integration. To address these limitations, we propose KAMAC, a Knowledge-driven Adaptive Multi-Agent Collaboration framework that enables LLM agents to dynamically form and expand expert teams based on the evolving diagnostic context. KAMAC begins with one or more expert agents and then conducts a knowledge-driven discussion to identify and fill knowledge gaps by recruiting additional specialists as needed. This supports flexible, scalable collaboration in complex clinical scenarios, with decisions finalized through reviewing updated agent comments. Experiments on two real-world medical benchmarks demonstrate that KAMAC significantly outperforms both single-agent and advanced multi-agent methods, particularly in complex clinical scenarios (i.e., cancer prognosis) requiring dynamic, cross-specialty expertise. Our code is publicly available at: https://github.com/XiaoXiao-Woo/KAMAC.

cs.AI↗

arXiv2024

SVDinsTN: A Tensor Network Paradigm for Efficient Structure Search from Regularized Modeling Perspective

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.

cs.LG↗

arXiv2023

CD-GAN: a robust fusion-based generative adversarial network for unsupervised remote sensing change detection with heterogeneous sensors

In the context of Earth observation, change detection boils down to comparing images acquired at different times by sensors of possibly different spatial and/or spectral resolutions or different modalities (e.g., optical or radar). Even when considering only optical images, this task has proven to be challenging as soon as the sensors differ by their spatial and/or spectral resolutions. This paper proposes a novel unsupervised change detection method dedicated to images acquired by such so-called heterogeneous optical sensors. It capitalizes on recent advances which formulate the change detection task into a robust fusion framework. Adopting this formulation, the work reported in this paper shows that any off-the-shelf network trained beforehand to fuse optical images of different spatial and/or spectral resolutions can be easily complemented with a network of the same architecture and embedded into an adversarial framework to perform change detection. A comparison with state-of-the-art change detection methods demonstrates the versatility and the effectiveness of the proposed approach.

eess.IV↗

arXiv2021

A Triple-Double Convolutional Neural Network for Panchromatic Sharpening

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.

cs.CV↗

arXiv2021

Fully-Connected Tensor Network Decomposition for Robust Tensor Completion Problem

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.

cs.CV↗

arXiv2021

Nonlinear Transform Induced Tensor Nuclear Norm for Tensor Completion

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.

cs.CV↗

arXiv2021

Fusformer: A Transformer-based Fusion Approach for Hyperspectral Image Super-resolution

Hyperspectral image has become increasingly crucial due to its abundant spectral information. However, It has poor spatial resolution with the limitation of the current imaging mechanism. Nowadays, many convolutional neural networks have been proposed for the hyperspectral image super-resolution problem. However, convolutional neural network (CNN) based methods only consider the local information instead of the global one with the limited kernel size of receptive field in the convolution operation. In this paper, we design a network based on the transformer for fusing the low-resolution hyperspectral images and high-resolution multispectral images to obtain the high-resolution hyperspectral images. Thanks to the representing ability of the transformer, our approach is able to explore the intrinsic relationships of features globally. Furthermore, considering the LR-HSIs hold the main spectral structure, the network focuses on the spatial detail estimation releasing from the burden of reconstructing the whole data. It reduces the mapping space of the proposed network, which enhances the final performance. Various experiments and quality indexes show our approach's superiority compared with other state-of-the-art methods.

cs.CV↗

arXiv2020

Hyperspectral Super-Resolution via Interpretable Block-Term Tensor Modeling

This work revisits coupled tensor decomposition (CTD)-based hyperspectral super-resolution (HSR). HSR aims at fusing a pair of hyperspectral and multispectral images to recover a super-resolution image (SRI). The vast majority of the HSR approaches take a low-rank matrix recovery perspective. The challenge is that theoretical guarantees for recovering the SRI using low-rank matrix models are either elusive or derived under stringent conditions. A couple of recent CTD-based methods ensure recoverability for the SRI under relatively mild conditions, leveraging on algebraic properties of the canonical polyadic decomposition (CPD) and the Tucker decomposition models, respectively. However, the latent factors of both the CPD and Tucker models have no physical interpretations in the context of spectral image analysis, which makes incorporating prior information challenging---but using priors is often essential for enhancing performance in noisy environments. This work employs an idea that models spectral images as tensors following the block-term decomposition model with multilinear rank-$(L_r, L_r, 1)$ terms (i.e., the LL1 model) and formulates the HSR problem as a coupled LL1 tensor decomposition problem. Similar to the existing CTD approaches, recoverability of the SRI is shown under mild conditions. More importantly, the latent factors of the LL1 model can be interpreted as the key constituents of spectral images, i.e., the endmembers' spectral signatures and abundance maps. This connection allows us to easily incorporate prior information for performance enhancement. A flexible algorithmic framework that can work with a series of structural information is proposed to take advantage of the model interpretability. The effectiveness is showcased using simulated and real data.

eess.SP↗

arXiv2020

Hyperspectral Image Super-resolution via Deep Spatio-spectral Convolutional Neural Networks

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.

eess.IV↗

arXiv2020

Fast second-order implicit difference schemes for time distributed-order and Riesz space fractional diffusion-wave equations

In this paper, fast numerical methods are established for solving a class of time distributed-order and Riesz space fractional diffusion-wave equations. We derive new difference schemes by the weighted and shifted Gr$\ddot{\rm{u}}$nwald formula in time and the fractional centered difference formula in space. The unconditional stability and second-order convergence in time, space and distributed-order of the difference schemes are analyzed. In the one-dimensional case, the Gohberg-Semencul formula utilizing the preconditioned Krylov subspace method is developed to solve the symmetric positive definite Toeplitz linear systems derived from the proposed difference scheme. In the two-dimensional case, we also design a global preconditioned conjugate gradient method with a truncated preconditioner to solve the discretized Sylvester matrix equations. We prove that the spectrums of the preconditioned matrices in both cases are clustered around one, such that the proposed numerical methods with preconditioners converge very quickly. Some numerical experiments are carried out to demonstrate the effectiveness of the proposed difference schemes and show that the performances of the proposed fast solution algorithms are better than other numerical methods.

math.NA↗

arXiv2020

Tensor completion via nonconvex tensor ring rank minimization with guaranteed convergence

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.

cs.CV↗

arXiv2020

Tensor train rank minimization with nonlocal self-similarity for tensor completion

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.

cs.CV↗

arXiv2020

A fast implicit difference scheme for solving the generalized time-space fractional diffusion equations with variable coefficients

In this paper, we first propose an unconditionally stable implicit difference scheme for solving generalized time-space fractional diffusion equations (GTSFDEs) with variable coefficients. The numerical scheme utilizes the $L1$-type formula for the generalized Caputo fractional derivative in time discretization and the second-order weighted and shifted Grünwald difference (WSGD) formula in spatial discretization, respectively. Theoretical results and numerical tests are conducted to verify the $(2 - γ)$-order and 2-order of temporal and spatial convergence with $γ\in(0,1)$ the order of Caputo fractional derivative, respectively. The fast sum-of-exponential approximation of the generalized Caputo fractional derivative and Toeplitz-like coefficient matrices are also developed to accelerate the proposed implicit difference scheme. Numerical experiments show the effectiveness of the proposed numerical scheme and its good potential for large-scale simulation of GTSFDEs.

math.NA↗

arXiv2020

Framelet Representation of Tensor Nuclear Norm for Third-Order Tensor Completion

The main aim of this paper is to develop a framelet representation of the tensor nuclear norm for third-order tensor completion. In the literature, the tensor nuclear norm can be computed by using tensor singular value decomposition based on the discrete Fourier transform matrix, and tensor completion can be performed by the minimization of the tensor nuclear norm which is the relaxation of the sum of matrix ranks from all Fourier transformed matrix frontal slices. These Fourier transformed matrix frontal slices are obtained by applying the discrete Fourier transform on the tubes of the original tensor. In this paper, we propose to employ the framelet representation of each tube so that a framelet transformed tensor can be constructed. Because of framelet basis redundancy, the representation of each tube is sparsely represented. When the matrix slices of the original tensor are highly correlated, we expect the corresponding sum of matrix ranks from all framelet transformed matrix frontal slices would be small, and the resulting tensor completion can be performed much better. The proposed minimization model is convex and global minimizers can be obtained. Numerical results on several types of multi-dimensional data (videos, multispectral images, and magnetic resonance imaging data) have tested and shown that the proposed method outperformed the other testing methods.

eess.IV↗

arXiv2020

Multi-dimensional imaging data recovery via minimizing the partial sum of tubal nuclear norm

In this paper, we investigate tensor recovery problems within the tensor singular value decomposition (t-SVD) framework. We propose the partial sum of the tubal nuclear norm (PSTNN) of a tensor. The PSTNN is a surrogate of the tensor tubal multi-rank. We build two PSTNN-based minimization models for two typical tensor recovery problems, i.e., the tensor completion and the tensor principal component analysis. We give two algorithms based on the alternating direction method of multipliers (ADMM) to solve proposed PSTNN-based tensor recovery models. Experimental results on the synthetic data and real-world data reveal the superior of the proposed PSTNN.

math.NA↗