arXiv subjects

Wanquan Liu

Publications and source records attributed to Wanquan Liu.

At least 37 records · Page 2Linked to original sources

arXiv2025

STAR-Net: An Interpretable Model-Aided Network for Remote Sensing Image Denoising

Remote sensing image (RSI) denoising is an important topic in the field of remote sensing. Despite the impressive denoising performance of RSI denoising methods, most current deep learning-based approaches function as black boxes and lack integration with physical information models, leading to limited interpretability. Additionally, many methods may struggle with insufficient attention to non-local self-similarity in RSI and require tedious tuning of regularization parameters to achieve optimal performance, particularly in conventional iterative optimization approaches. In this paper, we first propose a novel RSI denoising method named sparse tensor-aided representation network (STAR-Net), which leverages a low-rank prior to effectively capture the non-local self-similarity within RSI. Furthermore, we extend STAR-Net to a sparse variant called STAR-Net-S to deal with the interference caused by non-Gaussian noise in original RSI for the purpose of improving robustness. Different from conventional iterative optimization, we develop an alternating direction method of multipliers (ADMM)-guided deep unrolling network, in which all regularization parameters can be automatically learned, thus inheriting the advantages of both model-based and deep learning-based approaches and successfully addressing the above-mentioned shortcomings. Comprehensive experiments on synthetic and real-world datasets demonstrate that STAR-Net and STAR-Net-S outperform state-of-the-art RSI denoising methods.

cs.CV↗

arXiv2025

Robust Sparse Phase Retrieval: Statistical Guarantee, Optimality Theory and Convergent Algorithm

Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a novel robust sparse PR method that covers both real- and complex-valued cases. The core is to leverage the Huber function to measure the loss and adopt the $\ell_{1/2}$-norm regularization to realize feature selection, thereby improving the robustness of PR. In theory, we establish statistical guarantees for such robustness and derive necessary optimality conditions for global minimizers. Particularly, for the complex-valued case, we provide a fixed point inclusion property inspired by Wirtinger derivatives. Furthermore, we develop an efficient optimization algorithm by integrating the gradient descent method into a majorization-minimization (MM) framework. It is rigorously proved that the whole generated sequence is convergent and also has a linear convergence rate under mild conditions, which has not been investigated before. Numerical examples under different types of noise validate the robustness and effectiveness of our proposed method.

math.OC↗

arXiv2025

Bi-Level Unsupervised Feature Selection

Unsupervised feature selection (UFS) is an important task in data engineering. However, most UFS methods construct models from a single perspective and often fail to simultaneously evaluate feature importance and preserve their inherent data structure, thus limiting their performance. To address this challenge, we propose a novel bi-level unsupervised feature selection (BLUFS) method, including a clustering level and a feature level. Specifically, at the clustering level, spectral clustering is used to generate pseudo-labels for representing the data structure, while a continuous linear regression model is developed to learn the projection matrix. At the feature level, the $\ell_{2,0}$-norm constraint is imposed on the projection matrix for more effectively selecting features. To the best of our knowledge, this is the first work to combine a bi-level framework with the $\ell_{2,0}$-norm. To solve the proposed bi-level model, we design an efficient proximal alternating minimization (PAM) algorithm, whose subproblems either have explicit solutions or can be computed by fast solvers. Furthermore, we establish the convergence result and computational complexity. Finally, extensive experiments on two synthetic datasets and eight real datasets demonstrate the superiority of BLUFS in clustering and classification tasks.

cs.LG↗

arXiv2025

A Newton Interior-Point Method for $\ell_0$ Factor Analysis

Factor Analysis is an effective way of dimensionality reduction achieved by revealing the low-rank plus sparse structure of the data covariance matrix. The corresponding model identification task is often formulated as an optimization problem with suitable regularizations. In particular, we use the nonconvex discontinuous $\ell_0$ norm in order to induce the sparsity of the covariance matrix of the idiosyncratic noise. This paper shows that such a challenging optimization problem can be approached via an interior-point method with inner-loop Newton iterations. To this end, we first characterize the solutions to the unconstrained $\ell_0$ regularized optimization problem through the $\ell_0$ proximal operator, and demonstrate that local optimality is equivalent to the solution of a stationary-point equation. The latter equation can then be solved using standard Newton's method, and the procedure is integrated into an interior-point algorithm so that inequality constraints of positive semidefiniteness can be handled. Finally, numerical examples validate the effectiveness of our algorithm.

math.OC↗

arXiv2025

MATCNN: Infrared and Visible Image Fusion Method Based on Multi-scale CNN with Attention Transformer

While attention-based approaches have shown considerable progress in enhancing image fusion and addressing the challenges posed by long-range feature dependencies, their efficacy in capturing local features is compromised by the lack of diverse receptive field extraction techniques. To overcome the shortcomings of existing fusion methods in extracting multi-scale local features and preserving global features, this paper proposes a novel cross-modal image fusion approach based on a multi-scale convolutional neural network with attention Transformer (MATCNN). MATCNN utilizes the multi-scale fusion module (MSFM) to extract local features at different scales and employs the global feature extraction module (GFEM) to extract global features. Combining the two reduces the loss of detail features and improves the ability of global feature representation. Simultaneously, an information mask is used to label pertinent details within the images, aiming to enhance the proportion of preserving significant information in infrared images and background textures in visible images in fused images. Subsequently, a novel optimization algorithm is developed, leveraging the mask to guide feature extraction through the integration of content, structural similarity index measurement, and global feature loss. Quantitative and qualitative evaluations are conducted across various datasets, revealing that MATCNN effectively highlights infrared salient targets, preserves additional details in visible images, and achieves better fusion results for cross-modal images. The code of MATCNN will be available at https://github.com/zhang3849/MATCNN.git.

cs.CV↗

arXiv2025

$\ell_0$ Factor Analysis: A P-Stationary Point Theory

Factor Analysis is a widely used modeling technique for stationary time series which achieves dimensionality reduction by revealing a hidden low-rank plus sparse structure of the covariance matrix. Such an idea of parsimonious modeling has also been important in the field of systems and control. In this article, a nonconvex nonsmooth optimization problem involving the $\ell_0$ norm is constructed in order to achieve the low-rank and sparse additive decomposition of the sample covariance matrix. We establish the existence of an optimal solution and characterize these solutions via the concept of proximal stationary points. Furthermore, an ADMM algorithm is designed to solve the $\ell_0$ optimization problem, and a subsequence convergence result is proved under reasonable assumptions. Finally, numerical experiments demonstrate the effectiveness of our method in comparison with some alternatives in the literature.

math.OC↗

arXiv2025

Enhancing Unsupervised Feature Selection via Double Sparsity Constrained Optimization

Unsupervised feature selection (UFS) is widely applied in machine learning and pattern recognition. However, most of the existing methods only consider a single sparsity, which makes it difficult to select valuable and discriminative feature subsets from the original high-dimensional feature set. In this paper, we propose a new UFS method called DSCOFS via embedding double sparsity constrained optimization into the classical principal component analysis (PCA) framework. Double sparsity refers to using $\ell_{2,0}$-norm and $\ell_0$-norm to simultaneously constrain variables, by adding the sparsity of different types, to achieve the purpose of improving the accuracy of identifying differential features. The core is that $\ell_{2,0}$-norm can remove irrelevant and redundant features, while $\ell_0$-norm can filter out irregular noisy features, thereby complementing $\ell_{2,0}$-norm to improve discrimination. An effective proximal alternating minimization method is proposed to solve the resulting nonconvex nonsmooth model. Theoretically, we rigorously prove that the sequence generated by our method globally converges to a stationary point. Numerical experiments on three synthetic datasets and eight real-world datasets demonstrate the effectiveness, stability, and convergence of the proposed method. In particular, the average clustering accuracy (ACC) and normalized mutual information (NMI) are improved by at least 3.34% and 3.02%, respectively, compared with the state-of-the-art methods. More importantly, two common statistical tests and a new feature similarity metric verify the advantages of double sparsity. All results suggest that our proposed DSCOFS provides a new perspective for feature selection.

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arXiv2024

A Point-Neighborhood Learning Framework for Nasal Endoscope Image Segmentation

Lesion segmentation on nasal endoscopic images is challenging due to its complex lesion features. Fully-supervised deep learning methods achieve promising performance with pixel-level annotations but impose a significant annotation burden on experts. Although weakly supervised or semi-supervised methods can reduce the labelling burden, their performance is still limited. Some weakly semi-supervised methods employ a novel annotation strategy that labels weak single-point annotations for the entire training set while providing pixel-level annotations for a small subset of the data. However, the relevant weakly semi-supervised methods only mine the limited information of the point itself, while ignoring its label property and surrounding reliable information. This paper proposes a simple yet efficient weakly semi-supervised method called the Point-Neighborhood Learning (PNL) framework. PNL incorporates the surrounding area of the point, referred to as the point-neighborhood, into the learning process. In PNL, we propose a point-neighborhood supervision loss and a pseudo-label scoring mechanism to explicitly guide the model's training. Meanwhile, we proposed a more reliable data augmentation scheme. The proposed method significantly improves performance without increasing the parameters of the segmentation neural network. Extensive experiments on the NPC-LES dataset demonstrate that PNL outperforms existing methods by a significant margin. Additional validation on colonoscopic polyp segmentation datasets confirms the generalizability of the proposed PNL.

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arXiv2024

$\ell_0$ factor analysis

Factor Analysis is about finding a low-rank plus sparse additive decomposition from a noisy estimate of the signal covariance matrix. In order to get such a decomposition, we formulate an optimization problem using the nuclear norm for the low-rank component, the $\ell_0$ norm for the sparse component, and the Kullback-Leibler divergence to control the residual in the sample covariance matrix. An alternating minimization algorithm is designed for the solution of the optimization problem. The effectiveness of the algorithm is verified via simulations on synthetic and real datasets.

math.OC↗

arXiv2024

Learning Interaction-aware 3D Gaussian Splatting for One-shot Hand Avatars

In this paper, we propose to create animatable avatars for interacting hands with 3D Gaussian Splatting (GS) and single-image inputs. Existing GS-based methods designed for single subjects often yield unsatisfactory results due to limited input views, various hand poses, and occlusions. To address these challenges, we introduce a novel two-stage interaction-aware GS framework that exploits cross-subject hand priors and refines 3D Gaussians in interacting areas. Particularly, to handle hand variations, we disentangle the 3D presentation of hands into optimization-based identity maps and learning-based latent geometric features and neural texture maps. Learning-based features are captured by trained networks to provide reliable priors for poses, shapes, and textures, while optimization-based identity maps enable efficient one-shot fitting of out-of-distribution hands. Furthermore, we devise an interaction-aware attention module and a self-adaptive Gaussian refinement module. These modules enhance image rendering quality in areas with intra- and inter-hand interactions, overcoming the limitations of existing GS-based methods. Our proposed method is validated via extensive experiments on the large-scale InterHand2.6M dataset, and it significantly improves the state-of-the-art performance in image quality. Project Page: \url{https://github.com/XuanHuang0/GuassianHand}.

cs.CV↗

arXiv2022

AFD Types Sparse Representations vs. the Karhunen-Loeve Expansion for Decomposing Stochastic Processes

This article introduces adaptive Fourier decomposition (AFD) type methods, emphasizing on those that can be applied to stochastic processes and random fields, mainly including stochastic adaptive Fourier decomposition and stochastic pre-orthogonal adaptive Fourier decomposition. We establish their algorithms based on the covariant function and prove that they enjoy the same convergence rate as the Karhunen-Loève (KL) decomposition. The AFD type methods are compared with the KL decomposition. In contrast with the latter, the AFD type methods do not need to compute eigenvalues and eigenfunctions of the kernel-integral operator induced by the covariance function, and thus considerably reduce the computation complexity and computer consumes. Various kinds of dictionaries offer AFD flexibility to solve problems of a great variety, including different types of deterministic and stochastic equations. The conducted experiments show, besides the numerical convenience and fast convergence, that the AFD type decompositions outperform the KL type in describing local details, in spite of the proven global optimality of the latter.

math.ST↗

arXiv2022

A Novel Exploration of Diffusion Process based on Multi-types Galton-Watson Forests

Diffusion is a commonly used technique for spreading information from point to point on a graph. The rationale behind diffusion is not clear. And the multi-types Galton-Watson forest is a random model of population growth without space or any other resource constraints. In this paper, we use the degenerated multi-types Galton-Watson forest (MGWF) to interpret the diffusion process and establish an equivalent relationship between them. With the two-phase setting of the MGWF, one can interpret the diffusion process and the Google PageRank system explicitly. It also improves the convergence behaviour of the iterative diffusion process and Google PageRank system. We validate the proposal by experiment while providing new research directions.

cs.SI↗

arXiv2022

Granule Description based on Compound Concepts

Concise granule descriptions for definable granules and approaching descriptions for indefinable granules are challenging and important issues in granular computing. The concept with only common attributes has been intensively studied. To investigate the granules with some special needs, we propose a novel type of compound concepts in this paper, i.e., common-and-necessary concept. Based on the definitions of concept-forming operations, the logical formulas are derived for each of the following types of concepts: formal concept, object-induced three-way concept, object oriented concept and common-and-necessary concept. Furthermore, by utilizing the logical relationship among various concepts, we have derived concise and unified equivalent conditions for definable granules and approaching descriptions for indefinable granules for all four kinds of concepts.

cs.AI↗

arXiv2021

A New Algorithm based on Extent Bit-array for Computing Formal Concepts

The emergence of Formal Concept Analysis (FCA) as a data analysis technique has increased the need for developing algorithms which can compute formal concepts quickly. The current efficient algorithms for FCA are variants of the Close-By-One (CbO) algorithm, such as In-Close2, In-Close3 and In-Close4, which are all based on horizontal storage of contexts. In this paper, based on algorithm In-Close4, a new algorithm based on the vertical storage of contexts, called In-Close5, is proposed, which can significantly reduce both the time complexity and space complexity of algorithm In-Close4. Technically, the new algorithm stores both context and extent of a concept as a vertical bit-array, while within In-Close4 algorithm the context is stored only as a horizontal bit-array, which is very slow in finding the intersection of two extent sets. Experimental results demonstrate that the proposed algorithm is much more effective than In-Close4 algorithm, and it also has a broader scope of applicability in computing formal concept in which one can solve the problems that cannot be solved by the In-Close4 algorithm.

cs.AI↗

arXiv2021

Concept and Attribute Reduction Based on Rectangle Theory of Formal Concept

Based on rectangle theory of formal concept and set covering theory, the concept reduction preserving binary relations is investigated in this paper. It is known that there are three types of formal concepts: core concepts, relative necessary concepts and unnecessary concepts. First, we present the new judgment results for relative necessary concepts and unnecessary concepts. Second, we derive the bounds for both the maximum number of relative necessary concepts and the maximum number of unnecessary concepts and it is a difficult problem as either in concept reduction preserving binary relations or attribute reduction of decision formal contexts, the computation of formal contexts from formal concepts is a challenging problem. Third, based on rectangle theory of formal concept, a fast algorithm for reducing attributes while preserving the extensions for a set of formal concepts is proposed using the extension bit-array technique, which allows multiple context cells to be processed by a single 32-bit or 64-bit operator. Technically, the new algorithm could store both formal context and extent of a concept as bit-arrays, and we can use bit-operations to process set operations "or" as well as "and". One more merit is that the new algorithm does not need to consider other concepts in the concept lattice, thus the algorithm is explicit to understand and fast. Experiments demonstrate that the new algorithm is effective in the computation of attribute reductions.

cs.AI↗

arXiv2021

Sleep Staging Based on Multi Scale Dual Attention Network

Sleep staging plays an important role on the diagnosis of sleep disorders. In general, experts classify sleep stages manually based on polysomnography (PSG), which is quite time-consuming. Meanwhile, the acquisition process of multiple signals is much complex, which can affect the subject's sleep. Therefore, the use of single-channel electroencephalogram (EEG) for automatic sleep staging has become a popular research topic. In the literature, a large number of sleep staging methods based on single-channel EEG have been proposed with promising results and achieve the preliminary automation of sleep staging. However, the performance for most of these methods in the N1 stage do not satisfy the needs of the diagnosis. In this paper, we propose a deep learning model multi scale dual attention network(MSDAN) based on raw EEG, which utilizes multi-scale convolution to extract features in different waveforms contained in the EEG signal, connects channel attention and spatial attention mechanisms in series to filter and highlight key information, and uses soft thresholding to remove redundant information. Experiments were conducted using two datasets with 5-fold cross-validation and hold-out validation method. The final average accuracy, overall accuracy, macro F1 score and Cohen's Kappa coefficient of the model reach 96.70%, 91.74%, 0.8231 and 0.8723 on the Sleep-EDF dataset, 96.14%, 90.35%, 0.7945 and 0.8284 on the Sleep-EDFx dataset. Significantly, our model performed superiorly in the N1 stage, with F1 scores of 54.41% and 52.79% on the two datasets respectively. The results show the superiority of our network over the existing methods, reaching a new state-of-the-art. In particular, the proposed method achieves excellent results in the N1 sleep stage compared to other methods.

cs.LG↗

arXiv2021

Using the Split Bregman Algorithm to Solve the Self-repelling Snake Model

Preserving contour topology during image segmentation is useful in many practical scenarios. By keeping the contours isomorphic, it is possible to prevent over-segmentation and under-segmentation, as well as to adhere to given topologies. The Self-repelling Snake model (SR) is a variational model that preserves contour topology by combining a non-local repulsion term with the geodesic active contour model (GAC). The SR is traditionally solved using the additive operator splitting (AOS) scheme. In our paper, we propose an alternative solution to the SR using the Split Bregman method. Our algorithm breaks the problem down into simpler sub-problems to use lower-order evolution equations and a simple projection scheme rather than re-initialization. The sub-problems can be solved via fast Fourier transform (FFT) or an approximate soft thresholding formula which maintains stability, shortening the convergence time, and reduces the memory requirement. The Split Bregman and AOS algorithms are compared theoretically and experimentally.

cs.CV↗

arXiv2020

iffDetector: Inference-aware Feature Filtering for Object Detection

Modern CNN-based object detectors focus on feature configuration during training but often ignore feature optimization during inference. In this paper, we propose a new feature optimization approach to enhance features and suppress background noise in both the training and inference stages. We introduce a generic Inference-aware Feature Filtering (IFF) module that can easily be combined with modern detectors, resulting in our iffDetector. Unlike conventional open-loop feature calculation approaches without feedback, the IFF module performs closed-loop optimization by leveraging high-level semantics to enhance the convolutional features. By applying Fourier transform analysis, we demonstrate that the IFF module acts as a negative feedback that theoretically guarantees the stability of feature learning. IFF can be fused with CNN-based object detectors in a plug-and-play manner with negligible computational cost overhead. Experiments on the PASCAL VOC and MS COCO datasets demonstrate that our iffDetector consistently outperforms state-of-the-art methods by significant margins\footnote{The test code and model are anonymously available in https://github.com/anonymous2020new/iffDetector }.

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