Low-Rank Multi-View Subspace Clustering Based on Sparse Regularization

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.

Robust Principal Component Analysis Integrating Sparse and Low-Rank Priors

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.

Huber inversion-based reverse-time migration with de-primary imaging condition and curvelet-domain sparse constraint

Least-squares reverse-time migration(LSRTM) formulates reverse-time migration(RTM) in the leastsquares inversion framework to obtain the optimal reflectivity image. It can generate images with more accurate amplitudes, higher resolution, and fewer artifacts than RTM. However, three problems still exist:(1) inversion can be dominated by strong events in the residual;(2) low-wavenumber artifacts in the gradient affect convergence speed and imaging results;(3) high-wavenumber noise is also amplified as iteration increases. To solve these three problems, we have improved LSRTM: firstly, we use Hubernorm as the objective function to emphasize the weak reflectors during the inversion;secondly, we adapt the de-primary imaging condition to remove the low-wavenumber artifacts above strong reflectors as well as the false high-wavenumber reflectors in the gradient;thirdly, we apply the L1-norm sparse constraint in the curvelet-domain as the regularization term to suppress the high-wavenumber migration noise. As the new inversion objective function contains the non-smooth L1-norm, we use a modified iterative soft thresholding(IST) method to update along the Polak-Ribie re conjugate-gradient direction by using a preconditioned non-linear conjugate-gradient(PNCG) method. The numerical examples,especially the Sigsbee2 A model, demonstrate that the Huber inversion-based RTM can generate highquality images by mitigating migration artifacts and improving the contribution of weak reflection events.

Single color image super-resolution using sparse representation and color constraint

Color image super-resolution reconstruction based on the sparse representation model usually adopts the regularization norm(e.g.,L1 or L2).These methods have limited ability to keep image texture detail to some extent and are easy to cause the problem of blurring details and color artifacts in color reconstructed images.This paper presents a color super-resolution reconstruction method combining the L2/3 sparse regularization model with color channel constraints.The method converts the low-resolution color image from RGB to YCbCr.The L2/3 sparse regularization model is designed to reconstruct the brightness channel of the input low-resolution color image.Then the color channel-constraint method is adopted to remove artifacts of the reconstructed highresolution image.The method not only ensures the reconstruction quality of the color image details,but also improves the removal ability of color artifacts.The experimental results on natural images validate that our method has improved both subjective and objective evaluation.

Low-Rank and Sparse Representation with Adaptive Neighborhood Regularization for Hyperspectral Image Classification

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.

Efficient tracker based on sparse coding with Euclidean local structure-based constraint

Abstract:Sparse coding(SC)based visual tracking(l1-tracker)is gaining increasing attention,and many related algorithms are developed.In these algorithms,each candidate region is sparsely represented as a set of target templates.However,the structure connecting these candidate regions is usually ignored.Lu proposed an NLSSC-tracker with non-local self-similarity sparse coding to address this issue,which has a high computational cost.In this study,we propose an Euclidean local-structure constraint based sparse coding tracker with a smoothed Euclidean local structure.With this tracker,the optimization procedure is transformed to a small-scale l1-optimization problem,significantly reducing the computational cost.Extensive experimental results on visual tracking demonstrate the eectiveness and efficiency of the proposed algorithm.

Proximity point algorithm for low-rank matrix recovery from sparse noise corrupted data

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.

Low-Rank Sparse Representation with Pre-Learned Dictionaries and Side Information for Singing Voice Separation

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.

Compressed sensing estimation of sparse underwater acoustic channels with a large time delay spread

The estimation of sparse underwater acoustic channels with a large time delay spread is investigated under the framework of compressed sensing. For these types of channels, the excessively long impulse response will significantly degrade the convergence rate and tracking capability of the traditional estimation algorithms such as least squares （LS）, while excluding the use of the delay-Doppler spread function due to huge computational complexity. By constructing a Toeplitz matrix with a training sequence as the measurement matrix, the estimation problem of long sparse acoustic channels is formulated into a compressed sensing problem to facilitate the efficient exploitation of sparsity. Furthermore, unlike the traditional l1 norm or exponent-based approximation l0 norm sparse recovery strategy, a novel variant of approximate l0 norm called AL0 is proposed, minimization of which leads to the derivation of a hybrid approach by iteratively projecting the steepest descent solution to the feasible set. Numerical simulations as well as sea trial experiments are compared and analyzed to demonstrate the superior performance of the proposed algorithm.

Three-dimensional gravity inversion based on sparse recovery iteration using approximate zero norm

This research proposes a novel three-dimensional gravity inversion based on sparse recovery in compress sensing. Zero norm is selected as the objective function, which is then iteratively solved by the approximate zero norm solution. The inversion approach mainly employs forward modeling; a depth weight function is introduced into the objective function of the zero norms. Sparse inversion results are obtained by the corresponding optimal mathematical method. To achieve the practical geophysical and geological significance of the results, penalty function is applied to constrain the density values. Results obtained by proposed provide clear boundary depth and density contrast distribution information. The method's accuracy, validity, and reliability are verified by comparing its results with those of synthetic models. To further explain its reliability, a practical gravity data is obtained for a region in Texas, USA is applied. Inversion results for this region are compared with those of previous studies, including a research of logging data in the same area. The depth of salt dome obtained by the inversion method is 4.2 km, which is in good agreement with the 4.4 km value from the logging data. From this, the practicality of the inversion method is also validated.

Weighted Sparse Image Classification Based on Low Rank Representation

The conventional sparse representation-based image classification usually codes the samples independently,which will ignore the correlation information existed in the data.Hence,if we can explore the correlation information hidden in the data,the classification result will be improved significantly.To this end,in this paper,a novel weighted supervised spare coding method is proposed to address the image classification problem.The proposed method firstly explores the structural information sufficiently hidden in the data based on the low rank representation.And then,it introduced the extracted structural information to a novel weighted sparse representation model to code the samples in a supervised way.Experimental results show that the proposed method is superiority to many conventional image classification methods.

Truncated sparse approximation property and truncated q-norm minimization

This paper considers approximately sparse signal and low-rank matrix’s recovery via truncated norm minimization minx∥xT∥q and minX∥XT∥Sq from noisy measurements.We first introduce truncated sparse approximation property,a more general robust null space property,and establish the stable recovery of signals and matrices under the truncated sparse approximation property.We also explore the relationship between the restricted isometry property and truncated sparse approximation property.And we also prove that if a measurement matrix A or linear map A satisfies truncated sparse approximation property of order k,then the first inequality in restricted isometry property of order k and of order 2k can hold for certain different constantsδk andδ2k,respectively.Last,we show that ifδs(k+|T^c|)<√(s-1)/s for some s≥4/3,then measurement matrix A and linear map A satisfy truncated sparse approximation property of order k.It should be pointed out that when Tc=Ф,our conclusion implies that sparse approximation property of order k is weaker than restricted isometry property of order sk.

Robust least squares projection twin SVM and its sparse solution

Least squares projection twin support vector machine(LSPTSVM)has faster computing speed than classical least squares support vector machine(LSSVM).However,LSPTSVM is sensitive to outliers and its solution lacks sparsity.Therefore,it is difficult for LSPTSVM to process large-scale datasets with outliers.In this paper,we propose a robust LSPTSVM model(called R-LSPTSVM)by applying truncated least squares loss function.The robustness of R-LSPTSVM is proved from a weighted perspective.Furthermore,we obtain the sparse solution of R-LSPTSVM by using the pivoting Cholesky factorization method in primal space.Finally,the sparse R-LSPTSVM algorithm(SR-LSPTSVM)is proposed.Experimental results show that SR-LSPTSVM is insensitive to outliers and can deal with large-scale datasets fastly.

Nonlocally Centralized Simultaneous Sparse Coding

The concept of structured sparse coding noise is introduced to exploit the spatial correlations and nonlocal constraint of the local structure. Then the model of nonlocally centralized simultaneous sparse coding(NCSSC)is proposed for reconstructing the original image, and an algorithm is proposed to transform the simultaneous sparse coding into reweighted low-rank approximation. Experimental results on image denoisng, deblurring and super-resolution demonstrate the advantage of the proposed NC-SSC method over the state-of-the-art image restoration methods.

Low-Rank Optimal Transport for Robust Domain Adaptation

When encountering the distribution shift between the source(training) and target(test) domains, domain adaptation attempts to adjust the classifiers to be capable of dealing with different domains. Previous domain adaptation research has achieved a lot of success both in theory and practice under the assumption that all the examples in the source domain are welllabeled and of high quality. However, the methods consistently lose robustness in noisy settings where data from the source domain have corrupted labels or features which is common in reality. Therefore, robust domain adaptation has been introduced to deal with such problems. In this paper, we attempt to solve two interrelated problems with robust domain adaptation:distribution shift across domains and sample noises of the source domain. To disentangle these challenges, an optimal transport approach with low-rank constraints is applied to guide the domain adaptation model training process to avoid noisy information influence. For the domain shift problem, the optimal transport mechanism can learn the joint data representations between the source and target domains using a measurement of discrepancy and preserve the discriminative information. The rank constraint on the transport matrix can help recover the corrupted subspace structures and eliminate the noise to some extent when dealing with corrupted source data. The solution to this relaxed and regularized optimal transport framework is a convex optimization problem that can be solved using the Augmented Lagrange Multiplier method, whose convergence can be mathematically proved. The effectiveness of the proposed method is evaluated through extensive experiments on both synthetic and real-world datasets.

Experimental analysis and application of sparsity constrained deconvolution

Sparsity constrained deconvolution can improve the resolution of band-limited seismic data compared to conventional deconvolution. However, such deconvolution methods result in nonunique solutions and suppress weak reflections. The Cauchy function, modified Cauchy function, and Huber function are commonly used constraint criteria in sparse deconvolution. We used numerical experiments to analyze the ability of sparsity constrained deconvolution to restore reflectivity sequences and protect weak reflections under different constraint criteria. The experimental results demonstrate that the performance of sparsity constrained deconvolution depends on the agreement between the constraint criteria and the probability distribution of the reflectivity sequences; furthermore, the modified Cauchy- constrained criterion protects the weak reflections better than the other criteria. Based on the model experiments, the probability distribution of the reflectivity sequences of carbonate and clastic formations is statistically analyzed by using well-logging data and then the modified Cauchy-constrained deconvolution is applied to real seismic data much improving the resolution.

Extraction method of typical IEQ spatial distributions based on low-rank sparse representation and multi-step clustering

Indoor environment quality(IEQ)is one of the most concerned building performances during the operation stage.The non-uniform spatial distribution of various IEQ parameters in large-scale public buildings has been demonstrated to be an essential factor affecting occupant comfort and building energy consumption.Currently,IEQ sensors have been widely employed in buildings to monitor thermal,visual,acoustic and air quality.However,there is a lack of effective methods for exploring the typical spatial distribution of indoor environmental quality parameters,which is crucial for assessing and controlling non-uniform indoor environments.In this study,a novel clustering method for extracting IEQ spatial distribution patterns is proposed.Firstly,representation vectors reflecting IEQ distributions in the concerned space are generated based on the low-rank sparse representation.Secondly,a multi-step clustering method,which addressed the problems of the“curse of dimensionality”,is designed to obtain typical IEQ distribution patterns of the entire indoor space.The proposed method was applied to the analysis of indoor thermal environment in Beijing Daxing international airport terminal.As a result,four typical temperature spatial distribution patterns of the terminal were extracted from a four-month monitoring,which had been validated for their good representativeness.These typical patterns revealed typical environmental issues in the terminal,such as long-term localized overheating and temperature increases due to a sudden influx of people.The extracted typical IEQ spatial distribution patterns could assist building operators in effectively assessing the uneven distribution of IEQ space under current environmental conditions,facilitating targeted environmental improvements,optimization of thermal comfort levels,and application of energy-saving measures.

Robust elastic impedance inversion using L1-norm misfit function and constraint regularization

The classical elastic impedance （EI） inversion method, however, is based on the L2-norm misfit function and considerably sensitive to outliers, assuming the noise of the seismic data to be the Guassian-distribution. So we have developed a more robust elastic impedance inversion based on the Ll-norm misfit function, and the noise is assumed to be non-Gaussian. Meanwhile, some regularization methods including the sparse constraint regularization and elastic impedance point constraint regularization are incorporated to improve the ill-posed characteristics of the seismic inversion problem. Firstly, we create the Ll-norm misfit objective function of pre-stack inversion problem based on the Bayesian scheme within the sparse constraint regularization and elastic impedance point constraint regularization. And then, we obtain more robust elastic impedances of different angles which are less sensitive to outliers in seismic data by using the IRLS strategy. Finally, we extract the P-wave and S-wave velocity and density by using the more stable parameter extraction method. Tests on synthetic data show that the P-wave and S-wave velocity and density parameters are still estimated reasonable with moderate noise. A test on the real data set shows that compared to the results of the classical elastic impedance inversion method, the estimated results using the proposed method can get better lateral continuity and more distinct show of the gas, verifying the feasibility and stability of the method.

稀疏约束与时间一致的背景感知相关滤波目标跟踪

背景感知滤波算法通过循环移位采集真实负样本,有效解决了边界效应.但在复杂场景例如遮挡、快速移动、背景干扰等,其较大的采样区域导致过多背景在杂波干扰,从而影响跟踪效果.针对这一问题,本文首先提取灰度HOG特征与颜色CN特征来提高目标外观模型,在基准目标函数基础上引入L1稀疏正则约束形成弹性网络以自适应筛选关键特征,增强滤波器在复杂背景下的判别能力.同时针对BACF在跟踪过程中目标快速变化,本文引入时间正则项提高滤波器抑制畸变的能力.最后,本文提出了一种独立的尺度滤波器算法,准确提供目标尺度大小.实验仿真结果表明,在公开数据集OTB-2013和OTB-2015上,本文算法较基准算法有很大提升,能够较好应对不同复杂场景下的跟踪难题.

基于重加权L1的ATpV正则化叠前反演方法

地震叠前反演能够准确获取地下储层介质的各类参数,是油气的勘探与开发中重要技术之一。然而,地震反演是典型的病态问题,为了克服此问题,通常使用正则化约束目标函数,来减轻反演问题的病态性。但是正则化约束忽略了地层边界的振幅信息,使用重加权方法可以很好地克服这一问题,更好地恢复稀疏性。提出了一种基于重加权L1的ATpV正则化叠前三参数反演方法(ATpV-L1方法),首次将重加权L1方法与ATpV方法结合,并引入到叠前反演中。采用交替方向乘子算法(ADMM)建立反演框架,对目标函数进行分块优化,有效提高了收敛速度。首先,介绍ATpV-L1方法,建立了基于ATpV-L1的叠前反演目标函数;然后,应用理论模拟数据对比新方法和ATpV方法反演结果,验证了方法的效果;最后,使用实际数据进行实验分析,进一步验证了ATpV-L1方法的反演精度及可行性。实验结果表明,提出的ATpV-L1方法可以有效恢复反演结果的稀疏性,提高反演精度。