Low-Rank and Sparse Representation(LRSR)method has gained popularity in Hyperspectral Image(HSI)processing.However,existing LRSR models rarely exploited spectral-spatial classification of HSI.In this paper,we proposed...Low-Rank and Sparse Representation(LRSR)method has gained popularity in Hyperspectral Image(HSI)processing.However,existing LRSR models rarely exploited spectral-spatial classification of HSI.In this paper,we proposed a novel Low-Rank and Sparse Representation with Adaptive Neighborhood Regularization(LRSR-ANR)method for HSI classification.In the proposed method,we first represent the hyperspectral data via LRSR since it combines both sparsity and low-rankness to maintain global and local data structures simultaneously.The LRSR is optimized by using a mixed Gauss-Seidel and Jacobian Alternating Direction Method of Multipliers(M-ADMM),which converges faster than ADMM.Then to incorporate the spatial information,an ANR scheme is designed by combining Euclidean and Cosine distance metrics to reduce the mixed pixels within a neighborhood.Lastly,the predicted labels are determined by jointly considering the homogeneous pixels in the classification rule of the minimum reconstruction error.Experimental results based on three popular hyperspectral images demonstrate that the proposed method outperforms other related methods in terms of classification accuracy and generalization performance.展开更多
The task of dividing corrupted-data into their respective subspaces can be well illustrated,both theoretically and numerically,by recovering low-rank and sparse-column components of a given matrix.Generally,it can be ...The task of dividing corrupted-data into their respective subspaces can be well illustrated,both theoretically and numerically,by recovering low-rank and sparse-column components of a given matrix.Generally,it can be characterized as a matrix and a 2,1-norm involved convex minimization problem.However,solving the resulting problem is full of challenges due to the non-smoothness of the objective function.One of the earliest solvers is an 3-block alternating direction method of multipliers(ADMM)which updates each variable in a Gauss-Seidel manner.In this paper,we present three variants of ADMM for the 3-block separable minimization problem.More preciously,whenever one variable is derived,the resulting problems can be regarded as a convex minimization with 2 blocks,and can be solved immediately using the standard ADMM.If the inner iteration loops only once,the iterative scheme reduces to the ADMM with updates in a Gauss-Seidel manner.If the solution from the inner iteration is assumed to be exact,the convergence can be deduced easily in the literature.The performance comparisons with a couple of recently designed solvers illustrate that the proposed methods are effective and competitive.展开更多
This paper is concerned with the structured simultaneous low-rank and sparse recovery,which can be formulated as the rank and zero-norm regularized least squares problem with a hard constraint diag(■)=0.For this clas...This paper is concerned with the structured simultaneous low-rank and sparse recovery,which can be formulated as the rank and zero-norm regularized least squares problem with a hard constraint diag(■)=0.For this class of NP-hard problems,we propose a convex relaxation algorithm by applying the accelerated proximal gradient method to a convex relaxation model,which is yielded by the smoothed nuclear norm and the weighted l1-norm regularized least squares problem.A theoretical guarantee is provided by establishing the error bounds of the iterates to the true solution under mild restricted strong convexity conditions.To the best of our knowledge,this work is the first one to characterize the error bound of the iterates of the algorithm to the true solution.Finally,numerical results are reported for some random test problems and synthetic data in subspace clustering to verify the efficiency of the proposed convex relaxation algorithm.展开更多
Face recognition has attracted great interest due to its importance in many real-world applications. In this paper,we present a novel low-rank sparse representation-based classification(LRSRC) method for robust face r...Face recognition has attracted great interest due to its importance in many real-world applications. In this paper,we present a novel low-rank sparse representation-based classification(LRSRC) method for robust face recognition. Given a set of test samples, LRSRC seeks the lowest-rank and sparsest representation matrix over all training samples. Since low-rank model can reveal the subspace structures of data while sparsity helps to recognize the data class, the obtained test sample representations are both representative and discriminative. Using the representation vector of a test sample, LRSRC classifies the test sample into the class which generates minimal reconstruction error. Experimental results on several face image databases show the effectiveness and robustness of LRSRC in face image recognition.展开更多
Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Anal...Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Analysis (RPCA) addresses these limitations by decomposing data into a low-rank matrix capturing the underlying structure and a sparse matrix identifying outliers, enhancing robustness against noise and outliers. This paper introduces a novel RPCA variant, Robust PCA Integrating Sparse and Low-rank Priors (RPCA-SL). Each prior targets a specific aspect of the data’s underlying structure and their combination allows for a more nuanced and accurate separation of the main data components from outliers and noise. Then RPCA-SL is solved by employing a proximal gradient algorithm for improved anomaly detection and data decomposition. Experimental results on simulation and real data demonstrate significant advancements.展开更多
To realize effective co-phasing adjustment in large-aperture sparse-aperture telescopes,a multichannel stripe tracking approach is employed,allowing simultaneous interferometric measurements of multiple optical paths ...To realize effective co-phasing adjustment in large-aperture sparse-aperture telescopes,a multichannel stripe tracking approach is employed,allowing simultaneous interferometric measurements of multiple optical paths and circumventing the need for pairwise measurements along the mirror boundaries in traditional interferometric methods.This approach enhances detection efficiency and reduces system complexity.Here,the principles of the multibeam interference process and construction of a co-phasing detection module based on direct optical fiber connections were analyzed using wavefront optics theory.Error analysis was conducted on the system surface obtained through multipath interference.Potential applications of the interferometric method were explored.Finally,the principle was verified by experiment,an interferometric fringe contrast better than 0.4 is achieved through flat field calibration and incoherent digital synthesis.The dynamic range of the measurement exceeds 10 times of the center wavelength of the working band(1550 nm).Moreover,a resolution better than one-tenth of the working center wavelength(1550 nm)was achieved.Simultaneous three-beam interference can be achieved,leading to a 50%improvement in detection efficiency.This method can effectively enhance the efficiency of sparse aperture telescope co-phasing,meeting the requirements for observations of 8-10 m telescopes.This study provides a technological foundation for observing distant and faint celestial objects.展开更多
Background subtraction is a challenging problem in surveillance scenes. Although the low-rank and sparse decomposition(LRSD) methods offer an appropriate framework for background modeling, they fail to account for ima...Background subtraction is a challenging problem in surveillance scenes. Although the low-rank and sparse decomposition(LRSD) methods offer an appropriate framework for background modeling, they fail to account for image's local structure, which is favorable for this problem. Based on this, we propose a background subtraction method via low-rank and SILTP-based structured sparse decomposition, named LRSSD. In this method, a novel SILTP-inducing sparsity norm is introduced to enhance the structured presentation of the foreground region. As an assistance, saliency detection is employed to render a rough shape and location of foreground. The final refined foreground is decided jointly by sparse component and attention map. Experimental results on different datasets show its superiority over the competing methods, especially under noise and changing illumination scenarios.展开更多
This paper explores the recovery of block sparse signals in frame-based settings using the l_(2)/l_(q)-synthesis technique(0<q≤1).We propose a new null space property,referred to as block D-NSP_(q),which is based ...This paper explores the recovery of block sparse signals in frame-based settings using the l_(2)/l_(q)-synthesis technique(0<q≤1).We propose a new null space property,referred to as block D-NSP_(q),which is based on the dictionary D.We establish that matrices adhering to the block D-NSP_(q)condition are both necessary and sufficient for the exact recovery of block sparse signals via l_(2)/l_(q)-synthesis.Additionally,this condition is essential for the stable recovery of signals that are block-compressible with respect to D.This D-NSP_(q)property is identified as the first complete condition for successful signal recovery using l_(2)/l_(q)-synthesis.Furthermore,we assess the theoretical efficacy of the l2/lq-synthesis method under conditions of measurement noise.展开更多
LetΩbe homogeneous of degree zero,integrable on S^(d−1) and have vanishing moment of order one,a be a function on R^(d) such that ∇a∈L^(∞)(R^(d)).Let T*_(Ω,a) be the maximaloperator associated with the d-dimensional...LetΩbe homogeneous of degree zero,integrable on S^(d−1) and have vanishing moment of order one,a be a function on R^(d) such that ∇a∈L^(∞)(R^(d)).Let T*_(Ω,a) be the maximaloperator associated with the d-dimensional Calder´on commutator defined by T*_(Ωa)f(x):=sup_(ε>0)|∫_(|x-y|>ε)^Ω(x-y)/|x-y|^(d+1)(a(x)-a(y))f(y)dy.In this paper,the authors establish bilinear sparse domination for T*_(Ω,a) under the assumption Ω∈L∞(Sd−1).As applications,some quantitative weighted bounds for T*_(Ω,a) are obtained.展开更多
Multi-view Subspace Clustering (MVSC) emerges as an advanced clustering method, designed to integrate diverse views to uncover a common subspace, enhancing the accuracy and robustness of clustering results. The signif...Multi-view Subspace Clustering (MVSC) emerges as an advanced clustering method, designed to integrate diverse views to uncover a common subspace, enhancing the accuracy and robustness of clustering results. The significance of low-rank prior in MVSC is emphasized, highlighting its role in capturing the global data structure across views for improved performance. However, it faces challenges with outlier sensitivity due to its reliance on the Frobenius norm for error measurement. Addressing this, our paper proposes a Low-Rank Multi-view Subspace Clustering Based on Sparse Regularization (LMVSC- Sparse) approach. Sparse regularization helps in selecting the most relevant features or views for clustering while ignoring irrelevant or noisy ones. This leads to a more efficient and effective representation of the data, improving the clustering accuracy and robustness, especially in the presence of outliers or noisy data. By incorporating sparse regularization, LMVSC-Sparse can effectively handle outlier sensitivity, which is a common challenge in traditional MVSC methods relying solely on low-rank priors. Then Alternating Direction Method of Multipliers (ADMM) algorithm is employed to solve the proposed optimization problems. Our comprehensive experiments demonstrate the efficiency and effectiveness of LMVSC-Sparse, offering a robust alternative to traditional MVSC methods.展开更多
The method of recovering a low-rank matrix with an unknown fraction whose entries are arbitrarily corrupted is known as the robust principal component analysis （RPCA）. This RPCA problem, under some conditions, can b...The method of recovering a low-rank matrix with an unknown fraction whose entries are arbitrarily corrupted is known as the robust principal component analysis （RPCA）. This RPCA problem, under some conditions, can be exactly solved via convex optimization by minimizing a combination of the nuclear norm and the 11 norm. In this paper, an algorithm based on the Douglas-Rachford splitting method is proposed for solving the RPCA problem. First, the convex optimization problem is solved by canceling the constraint of the variables, and ~hen the proximity operators of the objective function are computed alternately. The new algorithm can exactly recover the low-rank and sparse components simultaneously, and it is proved to be convergent. Numerical simulations demonstrate the practical utility of the proposed algorithm.展开更多
In this paper,we focus on the recovery of piecewise sparse signals containing both fast-decaying and slow-decaying nonzero entries.In order to improve the performance of classic Orthogonal Matching Pursuit(OMP)and Gen...In this paper,we focus on the recovery of piecewise sparse signals containing both fast-decaying and slow-decaying nonzero entries.In order to improve the performance of classic Orthogonal Matching Pursuit(OMP)and Generalized Orthogonal Matching Pursuit(GOMP)algorithms for solving this problem,we propose the Piecewise Generalized Orthogonal Matching Pursuit(PGOMP)algorithm,by considering the mixed-decaying sparse signals as piecewise sparse signals with two components containing nonzero entries with different decay factors.The algorithm incorporates piecewise selection and deletion to retain the most significant entries according to the sparsity of each component.We provide a theoretical analysis based on the mutual coherence of the measurement matrix and the decay factors of the nonzero entries,establishing a sufficient condition for the PGOMP algorithm to select at least two correct indices in each iteration.Numerical simulations and an image decomposition experiment demonstrate that the proposed algorithm significantly improves the support recovery probability by effectively matching piecewise sparsity with decay factors.展开更多
Piezo actuators are widely used in ultra-precision fields because of their high response and nano-scale step length.However,their hysteresis characteristics seriously affect the accuracy and stability of piezo actuato...Piezo actuators are widely used in ultra-precision fields because of their high response and nano-scale step length.However,their hysteresis characteristics seriously affect the accuracy and stability of piezo actuators.Existing methods for fitting hysteresis loops include operator class,differential equation class,and machine learning class.The modeling cost of operator class and differential equation class methods is high,the model complexity is high,and the process of machine learning,such as neural network calculation,is opaque.The physical model framework cannot be directly extracted.Therefore,the sparse identification of nonlinear dynamics(SINDy)algorithm is proposed to fit hysteresis loops.Furthermore,the SINDy algorithm is improved.While the SINDy algorithm builds an orthogonal candidate database for modeling,the sparse regression model is simplified,and the Relay operator is introduced for piecewise fitting to solve the distortion problem of the SINDy algorithm fitting singularities.The Relay-SINDy algorithm proposed in this paper is applied to fitting hysteresis loops.Good performance is obtained with the experimental results of open and closed loops.Compared with the existing methods,the modeling cost and model complexity are reduced,and the modeling accuracy of the hysteresis loop is improved.展开更多
In this paper,a sparse graph neural network-aided(SGNN-aided)decoder is proposed for improving the decoding performance of polar codes under bursty interference.Firstly,a sparse factor graph is constructed using the e...In this paper,a sparse graph neural network-aided(SGNN-aided)decoder is proposed for improving the decoding performance of polar codes under bursty interference.Firstly,a sparse factor graph is constructed using the encoding characteristic to achieve high-throughput polar decoding.To further improve the decoding performance,a residual gated bipartite graph neural network is designed for updating embedding vectors of heterogeneous nodes based on a bidirectional message passing neural network.This framework exploits gated recurrent units and residual blocks to address the gradient disappearance in deep graph recurrent neural networks.Finally,predictions are generated by feeding the embedding vectors into a readout module.Simulation results show that the proposed decoder is more robust than the existing ones in the presence of bursty interference and exhibits high universality.展开更多
At present, although the human speech separation has achieved fruitful results, it is not ideal for the separation of singing and accompaniment. Based on low-rank and sparse optimization theory, in this paper, we prop...At present, although the human speech separation has achieved fruitful results, it is not ideal for the separation of singing and accompaniment. Based on low-rank and sparse optimization theory, in this paper, we propose a new singing voice separation algorithm called Low-rank, Sparse Representation with pre-learned dictionaries and side Information (LSRi). The algorithm incorporates both the vocal and instrumental spectrograms as sparse matrix and low-rank matrix, meanwhile combines pre-learning dictionary and the reconstructed voice spectrogram form the annotation. Evaluations on the iKala dataset show that the proposed methods are effective and efficient for singing voice separation.展开更多
Sparse identification of nonlinear dynamics(SINDy)has made significant progress in data-driven dynamics modeling.However,determining appropriate hyperparameters and addressing the time-consuming symbolic regression pr...Sparse identification of nonlinear dynamics(SINDy)has made significant progress in data-driven dynamics modeling.However,determining appropriate hyperparameters and addressing the time-consuming symbolic regression process remain substantial challenges.This study proposes the adaptive backward stepwise selection of fast SINDy(ABSS-FSINDy),which integrates statistical learning-based estimation and technical advancements to significantly reduce simulation time.This approach not only provides insights into the conditions under which SINDy performs optimally but also highlights potential failure points,particularly in the context of backward stepwise selection(BSS).By decoding predefined features into textual expressions,ABSS-FSINDy significantly reduces the simulation time compared with conventional symbolic regression methods.We validate the proposed method through a series of numerical experiments involving both planar/spatial dynamics and high-dimensional chaotic systems,including Lotka-Volterra,hyperchaotic Rossler,coupled Lorenz,and Lorenz 96 benchmark systems.The experimental results demonstrate that ABSS-FSINDy autonomously determines optimal hyperparameters within the SINDy framework,overcoming the curse of dimensionality in high-dimensional simulations.This improvement is substantial across both lowand high-dimensional systems,yielding efficiency gains of one to three orders of magnitude.For instance,in a 20D dynamical system,the simulation time is reduced from 107.63 s to just 0.093 s,resulting in a 3-order-of-magnitude improvement in simulation efficiency.This advancement broadens the applicability of SINDy for the identification and reconstruction of high-dimensional dynamical systems.展开更多
Deblending is a data processing procedure used to separate the source interferences of blended seismic data,which are obtained by simultaneous sources with random time delays to reduce the cost of seismic acquisition....Deblending is a data processing procedure used to separate the source interferences of blended seismic data,which are obtained by simultaneous sources with random time delays to reduce the cost of seismic acquisition.There are three types of deblending algorithms,i.e.,filtering-type noise suppression algorithm,inversion-based algorithm and deep-learning based algorithm.We review the merits of these techniques,and propose to use a sparse inversion method for seismic data deblending.Filtering-based deblending approach is applicable to blended data with a low blending fold and simple geometry.Otherwise,it can suffer from signal distortion and noise leakage.At present,the deep learning based deblending methods are still under development and field data applications are limited due to the lack of high-quality training labels.In contrast,the inversion-based deblending approaches have gained industrial acceptance.Our used inversion approach transforms the pseudo-deblended data into the frequency-wavenumber-wavenumher(FKK)domain,and a sparse constraint is imposed for the coherent signal estimation.The estimated signal is used to predict the interference noise for subtraction from the original pseudo-deblended data.Via minimizing the data misfit,the signal can be iteratively updated with a shrinking threshold until the signal and interference are fully separated.The used FKK sparse inversion algorithm is very accurate and efficient compared with other sparse inversion methods,and it is widely applied in field cases.Synthetic example shows that the deblending error is less than 1%in average amplitudes and less than-40 dB in amplitude spectra.We present three field data examples of land,marine OBN(Ocean Bottom Nodes)and streamer acquisitions to demonstrate its successful applications in separating the source interferences efficiently and accurately.展开更多
3D sparse convolution has emerged as a pivotal technique for efficient voxel-based perception in autonomous systems,enabling selective feature extraction from non-empty voxels while suppressing computational waste.Des...3D sparse convolution has emerged as a pivotal technique for efficient voxel-based perception in autonomous systems,enabling selective feature extraction from non-empty voxels while suppressing computational waste.Despite its theoretical efficiency advantages,practical implementations face under-explored limitations:the fixed geometric patterns of conventional sparse convolutional kernels inevitably process non-contributory positions during sliding-window operations,particularly in regions with uneven point cloud density.To address this,we propose Hierarchical Shape Pruning for 3D Sparse Convolution(HSP-S),which dynamically eliminates redundant kernel stripes through layer-adaptive thresholding.Unlike static soft pruning methods,HSP-S maintains trainable sparsity patterns by progressively adjusting pruning thresholds during optimization,enlarging original parameter search space while removing redundant operations.Extensive experiments validate effectiveness of HSP-S acrossmajor autonomous driving benchmarks.On KITTI’s 3D object detection task,our method reduces 93.47%redundant kernel computations whilemaintaining comparable accuracy(1.56%mAP drop).Remarkably,on themore complexNuScenes benchmark,HSP-S achieves simultaneous computation reduction(21.94%sparsity)and accuracy gains(1.02%mAP(mean Average Precision)and 0.47%NDS(nuScenes detection score)improvement),demonstrating its scalability to diverse perception scenarios.This work establishes the first learnable shape pruning framework that simultaneously enhances computational efficiency and preserves detection accuracy in 3D perception systems.展开更多
Efficient three-dimensional(3D)building reconstruction from drone imagery often faces data acquisition,storage,and computational challenges because of its reliance on dense point clouds.In this study,we introduced a n...Efficient three-dimensional(3D)building reconstruction from drone imagery often faces data acquisition,storage,and computational challenges because of its reliance on dense point clouds.In this study,we introduced a novel method for efficient and lightweight 3D building reconstruction from drone imagery using line clouds and sparse point clouds.Our approach eliminates the need to generate dense point clouds,and thus significantly reduces the computational burden by reconstructing 3D models directly from sparse data.We addressed the limitations of line clouds for plane detection and reconstruction by using a new algorithm.This algorithm projects 3D line clouds onto a 2D plane,clusters the projections to identify potential planes,and refines them using sparse point clouds to ensure an accurate and efficient model reconstruction.Extensive qualitative and quantitative experiments demonstrated the effectiveness of our method,demonstrating its superiority over existing techniques in terms of simplicity and efficiency.展开更多
基金National Natural Foundation of China(No.41971279)Fundamental Research Funds of the Central Universities(No.B200202012)。
文摘Low-Rank and Sparse Representation(LRSR)method has gained popularity in Hyperspectral Image(HSI)processing.However,existing LRSR models rarely exploited spectral-spatial classification of HSI.In this paper,we proposed a novel Low-Rank and Sparse Representation with Adaptive Neighborhood Regularization(LRSR-ANR)method for HSI classification.In the proposed method,we first represent the hyperspectral data via LRSR since it combines both sparsity and low-rankness to maintain global and local data structures simultaneously.The LRSR is optimized by using a mixed Gauss-Seidel and Jacobian Alternating Direction Method of Multipliers(M-ADMM),which converges faster than ADMM.Then to incorporate the spatial information,an ANR scheme is designed by combining Euclidean and Cosine distance metrics to reduce the mixed pixels within a neighborhood.Lastly,the predicted labels are determined by jointly considering the homogeneous pixels in the classification rule of the minimum reconstruction error.Experimental results based on three popular hyperspectral images demonstrate that the proposed method outperforms other related methods in terms of classification accuracy and generalization performance.
基金Supported by the National Natural Science Foundation of China(Grant No.11971149,11871381)Natural Science Foundation of Henan Province for Youth(Grant No.202300410146)。
文摘The task of dividing corrupted-data into their respective subspaces can be well illustrated,both theoretically and numerically,by recovering low-rank and sparse-column components of a given matrix.Generally,it can be characterized as a matrix and a 2,1-norm involved convex minimization problem.However,solving the resulting problem is full of challenges due to the non-smoothness of the objective function.One of the earliest solvers is an 3-block alternating direction method of multipliers(ADMM)which updates each variable in a Gauss-Seidel manner.In this paper,we present three variants of ADMM for the 3-block separable minimization problem.More preciously,whenever one variable is derived,the resulting problems can be regarded as a convex minimization with 2 blocks,and can be solved immediately using the standard ADMM.If the inner iteration loops only once,the iterative scheme reduces to the ADMM with updates in a Gauss-Seidel manner.If the solution from the inner iteration is assumed to be exact,the convergence can be deduced easily in the literature.The performance comparisons with a couple of recently designed solvers illustrate that the proposed methods are effective and competitive.
基金This work is supported by the National Natural Science Foundation of China(Nos.61402182 and 61273295).
文摘This paper is concerned with the structured simultaneous low-rank and sparse recovery,which can be formulated as the rank and zero-norm regularized least squares problem with a hard constraint diag(■)=0.For this class of NP-hard problems,we propose a convex relaxation algorithm by applying the accelerated proximal gradient method to a convex relaxation model,which is yielded by the smoothed nuclear norm and the weighted l1-norm regularized least squares problem.A theoretical guarantee is provided by establishing the error bounds of the iterates to the true solution under mild restricted strong convexity conditions.To the best of our knowledge,this work is the first one to characterize the error bound of the iterates of the algorithm to the true solution.Finally,numerical results are reported for some random test problems and synthetic data in subspace clustering to verify the efficiency of the proposed convex relaxation algorithm.
基金supported by National Natural Science Foundation of China(No.61374134)the key Scientific Research Project of Universities in Henan Province,China(No.15A413009)
文摘Face recognition has attracted great interest due to its importance in many real-world applications. In this paper,we present a novel low-rank sparse representation-based classification(LRSRC) method for robust face recognition. Given a set of test samples, LRSRC seeks the lowest-rank and sparsest representation matrix over all training samples. Since low-rank model can reveal the subspace structures of data while sparsity helps to recognize the data class, the obtained test sample representations are both representative and discriminative. Using the representation vector of a test sample, LRSRC classifies the test sample into the class which generates minimal reconstruction error. Experimental results on several face image databases show the effectiveness and robustness of LRSRC in face image recognition.
文摘Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Analysis (RPCA) addresses these limitations by decomposing data into a low-rank matrix capturing the underlying structure and a sparse matrix identifying outliers, enhancing robustness against noise and outliers. This paper introduces a novel RPCA variant, Robust PCA Integrating Sparse and Low-rank Priors (RPCA-SL). Each prior targets a specific aspect of the data’s underlying structure and their combination allows for a more nuanced and accurate separation of the main data components from outliers and noise. Then RPCA-SL is solved by employing a proximal gradient algorithm for improved anomaly detection and data decomposition. Experimental results on simulation and real data demonstrate significant advancements.
文摘To realize effective co-phasing adjustment in large-aperture sparse-aperture telescopes,a multichannel stripe tracking approach is employed,allowing simultaneous interferometric measurements of multiple optical paths and circumventing the need for pairwise measurements along the mirror boundaries in traditional interferometric methods.This approach enhances detection efficiency and reduces system complexity.Here,the principles of the multibeam interference process and construction of a co-phasing detection module based on direct optical fiber connections were analyzed using wavefront optics theory.Error analysis was conducted on the system surface obtained through multipath interference.Potential applications of the interferometric method were explored.Finally,the principle was verified by experiment,an interferometric fringe contrast better than 0.4 is achieved through flat field calibration and incoherent digital synthesis.The dynamic range of the measurement exceeds 10 times of the center wavelength of the working band(1550 nm).Moreover,a resolution better than one-tenth of the working center wavelength(1550 nm)was achieved.Simultaneous three-beam interference can be achieved,leading to a 50%improvement in detection efficiency.This method can effectively enhance the efficiency of sparse aperture telescope co-phasing,meeting the requirements for observations of 8-10 m telescopes.This study provides a technological foundation for observing distant and faint celestial objects.
基金supported in part by the EU FP7 QUICK project under Grant Agreement No.PIRSES-GA-2013-612652*National Nature Science Foundation of China(No.61671336,61502348,61231015,61671332,U1736206)+3 种基金Hubei Province Technological Innovation Major Project(No.2016AAA015,No.2017AAA123)the Fundamental Research Funds for the Central Universities(413000048)National High Technology Research and Development Program of China(863 Program)No.2015AA016306Applied Basic Research Program of Wuhan City(2016010101010025)
文摘Background subtraction is a challenging problem in surveillance scenes. Although the low-rank and sparse decomposition(LRSD) methods offer an appropriate framework for background modeling, they fail to account for image's local structure, which is favorable for this problem. Based on this, we propose a background subtraction method via low-rank and SILTP-based structured sparse decomposition, named LRSSD. In this method, a novel SILTP-inducing sparsity norm is introduced to enhance the structured presentation of the foreground region. As an assistance, saliency detection is employed to render a rough shape and location of foreground. The final refined foreground is decided jointly by sparse component and attention map. Experimental results on different datasets show its superiority over the competing methods, especially under noise and changing illumination scenarios.
基金Supported by The Featured Innovation Projects of the General University of Guangdong Province(2023KTSCX096)The Special Projects in Key Areas of Guangdong Province(ZDZX1088)Research Team Project of Guangdong University of Education(2024KYCXTD018)。
文摘This paper explores the recovery of block sparse signals in frame-based settings using the l_(2)/l_(q)-synthesis technique(0<q≤1).We propose a new null space property,referred to as block D-NSP_(q),which is based on the dictionary D.We establish that matrices adhering to the block D-NSP_(q)condition are both necessary and sufficient for the exact recovery of block sparse signals via l_(2)/l_(q)-synthesis.Additionally,this condition is essential for the stable recovery of signals that are block-compressible with respect to D.This D-NSP_(q)property is identified as the first complete condition for successful signal recovery using l_(2)/l_(q)-synthesis.Furthermore,we assess the theoretical efficacy of the l2/lq-synthesis method under conditions of measurement noise.
文摘LetΩbe homogeneous of degree zero,integrable on S^(d−1) and have vanishing moment of order one,a be a function on R^(d) such that ∇a∈L^(∞)(R^(d)).Let T*_(Ω,a) be the maximaloperator associated with the d-dimensional Calder´on commutator defined by T*_(Ωa)f(x):=sup_(ε>0)|∫_(|x-y|>ε)^Ω(x-y)/|x-y|^(d+1)(a(x)-a(y))f(y)dy.In this paper,the authors establish bilinear sparse domination for T*_(Ω,a) under the assumption Ω∈L∞(Sd−1).As applications,some quantitative weighted bounds for T*_(Ω,a) are obtained.
文摘Multi-view Subspace Clustering (MVSC) emerges as an advanced clustering method, designed to integrate diverse views to uncover a common subspace, enhancing the accuracy and robustness of clustering results. The significance of low-rank prior in MVSC is emphasized, highlighting its role in capturing the global data structure across views for improved performance. However, it faces challenges with outlier sensitivity due to its reliance on the Frobenius norm for error measurement. Addressing this, our paper proposes a Low-Rank Multi-view Subspace Clustering Based on Sparse Regularization (LMVSC- Sparse) approach. Sparse regularization helps in selecting the most relevant features or views for clustering while ignoring irrelevant or noisy ones. This leads to a more efficient and effective representation of the data, improving the clustering accuracy and robustness, especially in the presence of outliers or noisy data. By incorporating sparse regularization, LMVSC-Sparse can effectively handle outlier sensitivity, which is a common challenge in traditional MVSC methods relying solely on low-rank priors. Then Alternating Direction Method of Multipliers (ADMM) algorithm is employed to solve the proposed optimization problems. Our comprehensive experiments demonstrate the efficiency and effectiveness of LMVSC-Sparse, offering a robust alternative to traditional MVSC methods.
基金supported by the National Natural Science Foundation of China(No.61271014)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20124301110003)the Graduated Students Innovation Fund of Hunan Province(No.CX2012B238)
文摘The method of recovering a low-rank matrix with an unknown fraction whose entries are arbitrarily corrupted is known as the robust principal component analysis （RPCA）. This RPCA problem, under some conditions, can be exactly solved via convex optimization by minimizing a combination of the nuclear norm and the 11 norm. In this paper, an algorithm based on the Douglas-Rachford splitting method is proposed for solving the RPCA problem. First, the convex optimization problem is solved by canceling the constraint of the variables, and ~hen the proximity operators of the objective function are computed alternately. The new algorithm can exactly recover the low-rank and sparse components simultaneously, and it is proved to be convergent. Numerical simulations demonstrate the practical utility of the proposed algorithm.
基金Supported by the National Key R&D Program of China(Grant No.2023YFA1009200)the National Natural Science Foundation of China(Grant Nos.12271079+1 种基金12494552)the Fundamental Research Funds for the Central Universities of China(Grant No.DUT24LAB127)。
文摘In this paper,we focus on the recovery of piecewise sparse signals containing both fast-decaying and slow-decaying nonzero entries.In order to improve the performance of classic Orthogonal Matching Pursuit(OMP)and Generalized Orthogonal Matching Pursuit(GOMP)algorithms for solving this problem,we propose the Piecewise Generalized Orthogonal Matching Pursuit(PGOMP)algorithm,by considering the mixed-decaying sparse signals as piecewise sparse signals with two components containing nonzero entries with different decay factors.The algorithm incorporates piecewise selection and deletion to retain the most significant entries according to the sparsity of each component.We provide a theoretical analysis based on the mutual coherence of the measurement matrix and the decay factors of the nonzero entries,establishing a sufficient condition for the PGOMP algorithm to select at least two correct indices in each iteration.Numerical simulations and an image decomposition experiment demonstrate that the proposed algorithm significantly improves the support recovery probability by effectively matching piecewise sparsity with decay factors.
基金National Natural Science Foundation of China(62203118)。
文摘Piezo actuators are widely used in ultra-precision fields because of their high response and nano-scale step length.However,their hysteresis characteristics seriously affect the accuracy and stability of piezo actuators.Existing methods for fitting hysteresis loops include operator class,differential equation class,and machine learning class.The modeling cost of operator class and differential equation class methods is high,the model complexity is high,and the process of machine learning,such as neural network calculation,is opaque.The physical model framework cannot be directly extracted.Therefore,the sparse identification of nonlinear dynamics(SINDy)algorithm is proposed to fit hysteresis loops.Furthermore,the SINDy algorithm is improved.While the SINDy algorithm builds an orthogonal candidate database for modeling,the sparse regression model is simplified,and the Relay operator is introduced for piecewise fitting to solve the distortion problem of the SINDy algorithm fitting singularities.The Relay-SINDy algorithm proposed in this paper is applied to fitting hysteresis loops.Good performance is obtained with the experimental results of open and closed loops.Compared with the existing methods,the modeling cost and model complexity are reduced,and the modeling accuracy of the hysteresis loop is improved.
文摘In this paper,a sparse graph neural network-aided(SGNN-aided)decoder is proposed for improving the decoding performance of polar codes under bursty interference.Firstly,a sparse factor graph is constructed using the encoding characteristic to achieve high-throughput polar decoding.To further improve the decoding performance,a residual gated bipartite graph neural network is designed for updating embedding vectors of heterogeneous nodes based on a bidirectional message passing neural network.This framework exploits gated recurrent units and residual blocks to address the gradient disappearance in deep graph recurrent neural networks.Finally,predictions are generated by feeding the embedding vectors into a readout module.Simulation results show that the proposed decoder is more robust than the existing ones in the presence of bursty interference and exhibits high universality.
文摘At present, although the human speech separation has achieved fruitful results, it is not ideal for the separation of singing and accompaniment. Based on low-rank and sparse optimization theory, in this paper, we propose a new singing voice separation algorithm called Low-rank, Sparse Representation with pre-learned dictionaries and side Information (LSRi). The algorithm incorporates both the vocal and instrumental spectrograms as sparse matrix and low-rank matrix, meanwhile combines pre-learning dictionary and the reconstructed voice spectrogram form the annotation. Evaluations on the iKala dataset show that the proposed methods are effective and efficient for singing voice separation.
基金Project supported by the National Natural Science Foundation of China(Nos.12172291,12472357,and 12232015)the Shaanxi Province Outstanding Youth Fund Project(No.2024JC-JCQN-05)the 111 Project(No.BP0719007)。
文摘Sparse identification of nonlinear dynamics(SINDy)has made significant progress in data-driven dynamics modeling.However,determining appropriate hyperparameters and addressing the time-consuming symbolic regression process remain substantial challenges.This study proposes the adaptive backward stepwise selection of fast SINDy(ABSS-FSINDy),which integrates statistical learning-based estimation and technical advancements to significantly reduce simulation time.This approach not only provides insights into the conditions under which SINDy performs optimally but also highlights potential failure points,particularly in the context of backward stepwise selection(BSS).By decoding predefined features into textual expressions,ABSS-FSINDy significantly reduces the simulation time compared with conventional symbolic regression methods.We validate the proposed method through a series of numerical experiments involving both planar/spatial dynamics and high-dimensional chaotic systems,including Lotka-Volterra,hyperchaotic Rossler,coupled Lorenz,and Lorenz 96 benchmark systems.The experimental results demonstrate that ABSS-FSINDy autonomously determines optimal hyperparameters within the SINDy framework,overcoming the curse of dimensionality in high-dimensional simulations.This improvement is substantial across both lowand high-dimensional systems,yielding efficiency gains of one to three orders of magnitude.For instance,in a 20D dynamical system,the simulation time is reduced from 107.63 s to just 0.093 s,resulting in a 3-order-of-magnitude improvement in simulation efficiency.This advancement broadens the applicability of SINDy for the identification and reconstruction of high-dimensional dynamical systems.
基金supported by National Science and Technology Major Project(Grant No.2017ZX05018-001)。
文摘Deblending is a data processing procedure used to separate the source interferences of blended seismic data,which are obtained by simultaneous sources with random time delays to reduce the cost of seismic acquisition.There are three types of deblending algorithms,i.e.,filtering-type noise suppression algorithm,inversion-based algorithm and deep-learning based algorithm.We review the merits of these techniques,and propose to use a sparse inversion method for seismic data deblending.Filtering-based deblending approach is applicable to blended data with a low blending fold and simple geometry.Otherwise,it can suffer from signal distortion and noise leakage.At present,the deep learning based deblending methods are still under development and field data applications are limited due to the lack of high-quality training labels.In contrast,the inversion-based deblending approaches have gained industrial acceptance.Our used inversion approach transforms the pseudo-deblended data into the frequency-wavenumber-wavenumher(FKK)domain,and a sparse constraint is imposed for the coherent signal estimation.The estimated signal is used to predict the interference noise for subtraction from the original pseudo-deblended data.Via minimizing the data misfit,the signal can be iteratively updated with a shrinking threshold until the signal and interference are fully separated.The used FKK sparse inversion algorithm is very accurate and efficient compared with other sparse inversion methods,and it is widely applied in field cases.Synthetic example shows that the deblending error is less than 1%in average amplitudes and less than-40 dB in amplitude spectra.We present three field data examples of land,marine OBN(Ocean Bottom Nodes)and streamer acquisitions to demonstrate its successful applications in separating the source interferences efficiently and accurately.
文摘3D sparse convolution has emerged as a pivotal technique for efficient voxel-based perception in autonomous systems,enabling selective feature extraction from non-empty voxels while suppressing computational waste.Despite its theoretical efficiency advantages,practical implementations face under-explored limitations:the fixed geometric patterns of conventional sparse convolutional kernels inevitably process non-contributory positions during sliding-window operations,particularly in regions with uneven point cloud density.To address this,we propose Hierarchical Shape Pruning for 3D Sparse Convolution(HSP-S),which dynamically eliminates redundant kernel stripes through layer-adaptive thresholding.Unlike static soft pruning methods,HSP-S maintains trainable sparsity patterns by progressively adjusting pruning thresholds during optimization,enlarging original parameter search space while removing redundant operations.Extensive experiments validate effectiveness of HSP-S acrossmajor autonomous driving benchmarks.On KITTI’s 3D object detection task,our method reduces 93.47%redundant kernel computations whilemaintaining comparable accuracy(1.56%mAP drop).Remarkably,on themore complexNuScenes benchmark,HSP-S achieves simultaneous computation reduction(21.94%sparsity)and accuracy gains(1.02%mAP(mean Average Precision)and 0.47%NDS(nuScenes detection score)improvement),demonstrating its scalability to diverse perception scenarios.This work establishes the first learnable shape pruning framework that simultaneously enhances computational efficiency and preserves detection accuracy in 3D perception systems.
基金Supported by the Guangdong Major Project of Basic and Applied Basic Research (2023B0303000016)the National Natural Science Foundation of China (U21A20515)。
文摘Efficient three-dimensional(3D)building reconstruction from drone imagery often faces data acquisition,storage,and computational challenges because of its reliance on dense point clouds.In this study,we introduced a novel method for efficient and lightweight 3D building reconstruction from drone imagery using line clouds and sparse point clouds.Our approach eliminates the need to generate dense point clouds,and thus significantly reduces the computational burden by reconstructing 3D models directly from sparse data.We addressed the limitations of line clouds for plane detection and reconstruction by using a new algorithm.This algorithm projects 3D line clouds onto a 2D plane,clusters the projections to identify potential planes,and refines them using sparse point clouds to ensure an accurate and efficient model reconstruction.Extensive qualitative and quantitative experiments demonstrated the effectiveness of our method,demonstrating its superiority over existing techniques in terms of simplicity and efficiency.
