In recent years, fusing high-resolution multispectral images (HR-MSIs) and low-resolution hyperspectral images (LR-HSIs) has become a widely used approach for hyperspectral image super-resolution (HSI-SR). The deep unfolding framework has attracted significant attention thanks to its ability to formulate the problem into a data module and a prior module. However, there are still two critical issues that hinder the performance enhancement of the existing methods: 1) Parameters in the data module are fixed (though learnable) at each iteration, i.e., lacking the adaptivity to comprehensive data; 2) The Transformer in the prior module cannot effectively capture high-frequency information. To resolve these issues, we propose a Content-Adaptive Unfolding Wavelet Transformer (CAUWT) for HSI-SR, where the parameters are adaptively learned based on the reconstructed HSI at each iteration. Moreover, we propose a novel Wavelet-Assisted Transformer (WAT), by integrating the Discrete Wavelet Transform (DWT) and the Hybrid Spectral-Spatial Attention Block (HSSAB) to further upgrade the high-frequency information quality of HSI at no cost of extra branch structures, where the former is for multi-scale and multi-frequency details and the latter is for correlations between and within sub-band components. Extensive experiments performed on both simulated and real datasets well demonstrate the effectiveness of the proposed method. In comparison with mainstream HSI-SR methods, our method exhibits superior performance and lower computational overhead.

Multi-view tensor clustering (MVTC) has gained much attention for its effectiveness in capturing global high-order correlations across views. However, current MVTC methods suffer from two limitations: 1) adopting a two-stage process to learn the latent features for clustering, and 2) either ignoring local similarities within views or treating local similarities and global high-order correlations equally. In this paper, we propose a smooth low-rank MVTC (SLR-MVTC) method, which aims to extract latent features that are smooth within each view and low-rank across views, enhancing clustering performance. Specifically, we first learn latent features from each view using orthogonal projection and then construct the latent feature tensor by concatenation and rotation. Then, we introduce a new smooth tensor nuclear norm to depict the low-rank components of the low-frequency parts in the feature tensor. Benefiting from the fast Fourier transform along the sample dimension, the obtained low-frequency components effectively capture local smoothness within views, while their low-rank parts further explore global correlations across views. Experimental results on six multi-view datasets demonstrate that SLR-MVTC outperforms state-of-the-art algorithms in terms of clustering performance and CPU time.

Line segments are fundamental elements in computer vision. However, aside from a few computationally expensive deep learning-based methods, most existing approaches treat their detection and description as independent tasks, leading to redundant computations and suboptimal performance. This paper introduces a Unified approach for Line Segment Detection and Description (ULSD2), designed for real-time vision tasks with minimal computational overhead. The core insight is to unify line segment detection and description by analyzing dedicated level lines and their differences, derived from gradients, which effectively capture the intrinsic characteristics of line segments. Furthermore, instead of the traditional scalar-based description, the use of level lines and their differences in local patches across multiple granularities enables a vectorized representation that encodes line segments from coarse to fine. Experiments demonstrate that ULSD2 outperforms other non-deep learning-based methods and competes with state-of-the-art deep learning-based methods while significantly improving efficiency. The code is available at https://github.com/roylin1229/ULSD2.

Hybrid models that combine convolution and self attention are popular for efficient local feature extraction and capturing long-range dependencies. However, these models often:1) only explore local and global features; 2) flatten high-order features at the output layer, which limit feature hierarchy exploration and the feature utility in the output layer. To address these issues, this paper introduces Tensor Ring Regression with Local-to-Global Features (TRR-LGF), a simple and effective classification network. It uses a local-to-global learning framework to capture diverse features at multiple scales. Additionally, a tensor ring regression layer replaces the linear output layer, preserving high-order feature structure and reducing parameters. Experimental results show that TRR-LGF outperforms existing state-of-the-art methods on various datasets, especially in noisy and sample-imbalanced settings. Furthermore, the model utilizes 7.6M parameters, reducing computational requirements by about 50% compared to the multilayer perceptron output layer. The code is available at https://github.com/Calcium-Oxide/TRR-LGF.

Anchor-based multi-view clustering has garnered much attention for its effectiveness in handling massive datasets. However, current methods either fail to consider intra-view similarity or require ($\mathcal {O}(N^{3})$O(N3)) for exploring intra-view similarity, making efficient large-scale multi-view clustering difficult. This paper introduces a novel tensor low-frequency component (TLFC) operator, which achieves smooth representation among samples. Furthermore, this TLFC operator, which explores intra-view similarity, incorporates tensor nuclear norm (TNN) operator and consensus regularization that explore inter-view correlations, resulting in the development of tensor low-rank and low-frequency for scalable multi-view clustering (TLRLF4MVC). Iteratively, as intra-view sample similarity and complementary information across views achieve balance, the learned embedding features are mapped into a smooth and compact subspace, ultimately leading to outstanding clustering performance. Extensive experiments on six large-scale multi-view datasets demonstrate that TLRLF4MVC not only significantly outperforms state-of-the-art methods in terms of clustering accuracy but also achieves remarkable computational efficiency, particularly when handling massive data.

Anchor-based large-scale multi-view clustering has attracted considerable attention for its effectiveness in handling massive datasets. However, current methods mainly seek the consensus embedding feature for clustering by exploring global correlations between anchor graphs or projection matrices. In this paper, we propose a simple yet efficient scalable multi-view tensor clustering (S2MVTC) approach, where our focus is on learning correlations of embedding features within and across views. Specifically, we first construct the embedding feature tensor by stacking the embedding features of different views into a tensor and rotating it. Additionally, we build a novel tensor low-frequency approximation (TLFA) operator, which incorporates graph similarity into embedding feature learning, efficiently achieving smooth representation of embedding features within different views. Furthermore, consensus constraints are applied to embedding features to ensure inter-view semantic consistency. Experimental results on six large-scale multi-view datasets demonstrate that S2MVTC significantly outperforms state-of-the-art algorithms in terms of clustering performance and CPU execution time, especially when handling massive data. The code of S2MVTC is publicly available at https://github.com/longzhen520/S2MVTC.

Despite the significant progress made by deep clustering models in high-dimensional data processing, they remain vulnerable to adversarial examples. However, research on adversarial attacks against deep clustering algorithms appears to be relatively underexplored. To fill this gap, we propose a query-efficient black-box attack on deep clustering models, which leverages the transferability between different deep clustering models. Initially, we train a generator using a substitute deep clustering model, reducing the number of queries to the target model. Subsequently, when targeting an unknown deep clustering model, we employ the target query information to update both the substitute deep clustering model and the generator. Experimental evaluations on four state-of-the-art deep clustering models across three datasets demonstrate the efficacy of our method in disrupting clustering performance. The results indicate that our approach surpasses the performance of existing methods.

In recent years, fusing high spatial resolution multispectral images (HR-MSIs) and low spatial resolution hyperspectral images (LR-HSIs) has become a widely used approach for hyperspectral image super-resolution (HSI-SR). Various unsupervised HSI-SR methods based on deep image prior (DIP) have gained wide popularity thanks to no pre-training requirement. However, DIP-based methods often demonstrate mediocre performance in extracting latent information from the data. To resolve this performance deficiency, we propose a coupled spatial and spectral deep image priors (CS2DIPs) method for the fusion of an HR-MSI and an LR-HSI into an HR-HSI. Specifically, we integrate the nonnegative matrix-vector tensor factorization (NMVTF) into the DIP framework to jointly learn the abundance tensor and spectral feature matrix. The two coupled DIPs are designed to capture essential spatial and spectral features in parallel from the observed HR-MSI and LR-HSI, respectively, which are then used to guide the generation of the abundance tensor and spectral signature matrix for the fusion of the HSI-SR by mode-3 tensor product, meanwhile taking some inherent physical constraints into account. Free from any training data, the proposed CS2DIPs can effectively capture rich spatial and spectral information. As a result, it exhibits much superior performance and convergence speed over most existing DIP-based methods. Extensive experiments are provided to demonstrate its state-of-the-art overall performance including comparison with benchmark peer methods.

Multi-view subspace clustering employs learned self-representation from multiple tensor decompositions to exploit the low-rank information. However, the data structures embedded with self-representation tensors may vary in different multi-view datasets. Therefore, a pre-defined decomposition may not fully exploit low-rank information from various data, resulting in sub-optimal multi-view clustering performance. To alleviate this, we proposed the adaptively topological tensor network (ATTN). ATTN can learn a suitable decomposition structure that can represent the low-rank structure and high-order correlation of the self-representation tensors better in a data-driven way, which can capture the intra-view and inter-view information better. Firstly, instead of connecting the tensor network blindly, ATTN utilizes the correlation between adjacent factors to prune redundant connections from the fully connected tensor networks, making the tensor network more expressive. Furthermore, a greedy adaptive rank-increasing strategy is applied to optimize the pruned tensor network structure, which improves the capacity of capturing low-rank structure. We apply ATTN on a multi-view subspace clustering task and utilize the alternating direction method of multipliers(ADMM) method to optimize it. Experiments show that multi-view subspace clustering based on ATTN has better performance on nine multi-view datasets.

T-SVD based incomplete multi-view clustering (IMVC) has received wide attention due to its ability to capture high-order correlations. However, t-SVD suffers from rotation sensitivity, failing to fully explore both inter- and intra-view consistencies. Besides, current methods mainly consider inter- or intra-view correlations, ignoring the low-rank information of sample features within views. To address these weaknesses, we first propose a feature space recovery based IMVC (FSR-IMVC) method, where low-rank feature space recovery and low-rank tensor ring based consistency learning are considered into a unified framework. Furthermore, we extend FSR-IMVC by incorporating anchor learning on the latent feature space, resulting in a scalable FSR-IMVC (sFSR-IMVC) approach that is well-suited to large-scale data. In an iterative way, the learned inter- and intra-view correlations will guide the recovery of missing features, while the explored low-rank information from feature spaces will in turn facilitate consistency exploration, eventually achieving outstanding clustering performance. Experimental results show that FSR-IMVC provides a significant improvement over known state-of-the-art algorithms in terms of ACC, NMI and Purity. Compared with FSR-IMVC, sFSR-IMVC performs slightly worse in clustering accuracy, but offers a notable advantage in computational efficiency, particularly for large-scale datasets. The codes of FSR-IMVC and sFSR-IMVC are publicly available athttps://github.com/longzhen520/sFSR-IMVC.

Tensor-based multi-view subspace clustering (MSC) can capture high-order correlation in the self-representation tensor. Current tensor decompositions for MSC suffer from highly unbalanced unfolding matrices or rotation sensitivity, failing to fully explore inter/intra-view information. Using the advanced tensor network, namely, multi-scale entanglement renormalization ansatz (MERA), we propose a low-rank MERA based MSC (MERA-MSC) algorithm, where MERA factorizes a tensor into contractions of one top core factor and the rest orthogonal/semi-orthogonal factors. Benefiting from multiple interactions among orthogonal/semi-orthogonal (low-rank) factors, the low-rank MERA has a strong representation power to capture the complex inter/intra-view information in the self-representation tensor. The alternating direction method of multipliers is adopted to solve the optimization model. Experimental results on five multi-view datasets demonstrate MERA-MSC has superiority against the compared algorithms on six evaluation metrics. Furthermore, we extend MERA-MSC by incorporating anchor learning and develop a scalable low-rank MERA based multi-view clustering method (sMREA-MVC). To our knowledge, this is the first work to introduce MERA to the multi-view clustering topic. The effectiveness and efficiency of sMERA-MVC have been validated on three large-scale multi-view datasets.

Incomplete multi-view clustering (IMVC), based on imputation and clustering unification, has received wide attention due to its ability to exploit hidden information from missing views. However, current methods mainly consider inter/intra-view correlations, ignoring the structural information of sample features within views. In this paper, we propose a feature space recovery based IMVC method, where low-rank feature space recovery and consensus representation learning of inter/intra-views are considered into a unified framework. Moreover, low-rank tensor ring approximation is used to capture the correlations of self-representation tensor. In an iterative way, the learned inter/intra-view correlations will guide the recovery of missing features, while the explored low-rank information from feature spaces will in turn facilitate self-representation learning, eventually achieving out-standing clustering performance. Experimental results show our method has a very significant improvement over known state-of-the-art algorithms in terms of ACC, NMI and Purity.

Tensor completion is a powerful technique for recovering missing entries from partial observations. Tensor tree network, with a hierarchical structure, has gained widespread attention for its ability to balance and effectively explore the correlations in high-order data. However, the performance of tensor trees is influenced by the order of modes, leading to variations in their effectiveness. To address this, we propose to minimize the loss of entanglement entropy to determine the optimal mode order within the tensor tree network, thereby optimizing its representation performance. We correspondingly construct an optimal low-rank tensor tree completion model, where the optimal low-rank tensor tree network captures global structures and total variation investigates local structures. The alternating direction method of multipliers is employed to solve the optimization problem. Experimental results on color images and light field images demonstrate that our method outperforms state-of-the-art algorithms in terms of recovery performance.

Low-rank tensor completion aims to recover the missing entries of multi-way data, which has become popular and vital in many fields such as signal processing and computer vision. It varies with different tensor decomposition frameworks. Compared with matrix SVD, recently emerging transform t-SVD can better characterize the low-rank structure of order-3 data. However, it suffers from rotation sensitivity, and dimensional limitation (i.e., only effective for order-3 tensors). To alleviate these deficiencies, we develop a novel multiplex transformed tensor decomposition (MTTD) framework, which can characterize the global low-rank structure along all modes for any order- N tensor. Based on MTTD, we propose a related multi-dimensional square model for low-rank tensor completion. Besides, a total variation term is also introduced to utilize the local piecewise smoothness of the tensor data. The classic alternating direction method of multipliers is used to solve the convex optimization problems. For performance testing, we choose three linear invertible transforms including FFT, DCT, and a group of unitary transform matrices for our proposed methods. The simulated and real-data experiments demonstrate the superior recovery accuracy and computational efficiency of our method compared with state-of-the-art ones.

Low rank tensor ring based data recovery can recover missing image entries in signal acquisition and transformation. The recently proposed tensor ring (TR) based completion algorithms generally solve the low rank optimization problem by alternating least squares method with predefined ranks, which may easily lead to overfitting when the unknown ranks are set too large and only a few measurements are available. In this article, we present a Bayesian low rank tensor ring completion method for image recovery by automatically learning the low-rank structure of data. A multiplicative interaction model is developed for low rank tensor ring approximation, where sparsity-inducing hierarchical prior is placed over horizontal and frontal slices of core factors. Compared with most of the existing methods, the proposed one is free of parameter-tuning, and the TR ranks can be obtained by Bayesian inference. Numerical experiments, including synthetic data, real-world color images and YaleFace dataset, show that the proposed method outperforms state-of-the-art ones, especially in terms of recovery accuracy.

Tensor completion recovers missing components of multi-way data. The existing methods use either the Tucker rank or the CANDECOMP/PARAFAC (CP) rank in low-rank tensor optimization for data completion. In fact, these two kinds of tensor ranks represent different high-dimensional data structures. In this paper, we propose to exploit the two kinds of data structures simultaneously for image recovery through jointly minimizing the CP rank and Tucker rank in the low-rank tensor approximation. We use the alternating direction method of multipliers (ADMM) to reformulate the optimization model with two tensor ranks into its two sub-problems, and each has only one tensor rank optimization. For the two main sub-problems in the ADMM, we apply rank-one tensor updating and weighted sum of matrix nuclear norms minimization methods to solve them, respectively. The numerical experiments on some image and video completion applications demonstrate that the proposed method is superior to the state-of-the-art methods.

Tensor completion recovers missing entries of multiway data. Most of the current methods exploit the low-rank tensor structure for image completion applications. In this paper, we simultaneously exploit the globally multidimensional structure and locally piecewise smoothness to further enhance the performance. In the proposed optimization model, the low tensor tree rank minimization is used for the global data structure, and the total variation minimization is used for the local structure. Two kinds of total variation functions are discussed. The optimization problem is transformed into several subproblems by alternating direction method of multipliers. The subproblem on low tensor tree rank minimization is solved by singular value thresholding, and the subproblem on total variation minimization can be solved by soft thresholding. Numerical experiments on color images and light field images demonstrate that the proposed method outperforms most of the state-of-the-art methods in terms of recovery accuracy and computational complexity.