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.

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.

A Perturbation Analysis of Low-Rank Matrix Recovery by Schatten p-Minimization

A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.

Multi-Modal Medical Image Fusion Based on Improved Parameter Adaptive PCNN and Latent Low-Rank Representation

Multimodal medical image fusion can help physicians provide more accurate treatment plans for patients, as unimodal images provide limited valid information. To address the insufficient ability of traditional medical image fusion solutions to protect image details and significant information, a new multimodality medical image fusion method(NSST-PAPCNNLatLRR) is proposed in this paper. Firstly, the high and low-frequency sub-band coefficients are obtained by decomposing the source image using NSST. Then, the latent low-rank representation algorithm is used to process the low-frequency sub-band coefficients;An improved PAPCNN algorithm is also proposed for the fusion of high-frequency sub-band coefficients. The improved PAPCNN model was based on the automatic setting of the parameters, and the optimal method was configured for the time decay factor αe. The experimental results show that, in comparison with the five mainstream fusion algorithms, the new algorithm has significantly improved the visual effect over the comparison algorithm,enhanced the ability to characterize important information in images, and further improved the ability to protect the detailed information;the new algorithm has achieved at least four firsts in six objective indexes.

Two exact first-order k-space formulations for low-rank viscoacoustic wave propagation on staggered grids

Wave propagation in the viscoacoustic media is physically dispersive and dissipated.Completely excluding the numerical dispersion error from the physical dispersion in the viscoacoustic wave simu-lation is indispensable to understanding the intrinsic property of the wave propagation in attenuated media for the petroleum exploration geophysics.In recent years,a viscoacoustic wave equation char-acterized by fractional Laplacian gains wide attention in geophysical community.However,the first-order form of the viscoacoustic wave equation,often solved by the conventional staggered-grid pseu-dospectral method,suffers from the numerical dispersion error in time due to the low-order finite-difference approximation.It is challenging to completely eliminate the error because the viscoacoustic wave equation contains two temporal derivatives,which stem from the time stepping and the amplitude attenuation terms,respectively.To tackle the issue,we derive two exact first-order k-space viscoacoustic formulations that can fully exclude the numerical error from the physical dispersion.For the homoge-neous case,two formulations agree with the viscoacoustic analytical solution very well and have the same efficiency.For the heterogeneous case,our second k-space formulation is more efficient than the first one because the second formulation significantly reduces the number of the wavenumber-space mixed-domain operators,which are the expensive part of the viscoacoustic k-space simulation.Nu-merical cases validate that the two first-order k-space formulations are effective and efficient alternatives to the current staggered-grid pseudospectral formulation for the viscoacoustic wave simulation.

Synergistic effects of dodecane-castor oil acid mixture on the flotation responses of low-rank coal:A combined simulation and experimental study

The utilization of an appropriate collector or surfactant is crucial for the beneficiation of low-rank coal.However,in previous studies,the selection of surfactants was primarily based on flotation procedures,which hinders the understanding of the interaction mechanism between surfactant groups and oxygen-containing functional groups at the surface of low-rank coal.In this study,we investigate the flotation of low-rank coal in the presence of a composite collector by using a combined theoretical and experimental approach.The maximum flotation mass recovery achieved was 82.89%using a 3:1 mixture of dodecane and castor oil acid.Fourier-transform infrared and X-ray photoelectron spectroscopic analyses showed that castor oil acid was effectively adsorbed onto the surface of low-rank coal,enhancing the hydrophobicity of the coal.In addition,the diffusion coefficient of water molecules in the water-composite collector-coal system was greater than that in the dodecane system.Moreover,due to the presence of castor oil acid in the flotation process,the adsorption distance of dodecane and low-rank coal became shorter.Molecular dynamics simulations revealed that the diffusion and interaction of surfactant molecules at the interface of low-rank coal particles and water was enhanced because the adsorption of the dodecane-castor oil acid mixture is primarily controlled by hydrogen bonds and electrostatic attraction.Based on these results,a better surfactant for flotation of low-rank coal is also proposed.

Multimodal Medical Image Fusion Based on Parameter Adaptive PCNN and Latent Low-rank Representation

Medical image fusion has been developed as an efficient assistive technology in various clinical applications such as medical diagnosis and treatment planning.Aiming at the problem of insufficient protection of image contour and detail information by traditional image fusion methods,a new multimodal medical image fusion method is proposed.This method first uses non-subsampled shearlet transform to decompose the source image to obtain high and low frequency subband coefficients,then uses the latent low rank representation algorithm to fuse the low frequency subband coefficients,and applies the improved PAPCNN algorithm to fuse the high frequency subband coefficients.Finally,based on the automatic setting of parameters,the optimization method configuration of the time decay factorαe is carried out.The experimental results show that the proposed method solves the problems of difficult parameter setting and insufficient detail protection ability in traditional PCNN algorithm fusion images,and at the same time,it has achieved great improvement in visual quality and objective evaluation indicators.

Research on infrared dim and small target detection algorithm based on low-rank tensor recovery

In order to rapidly and accurately detect infrared small and dim targets in the infrared image of complex scene collected by virtual prototyping of space-based downward-looking multiband detection,an improved detection algorithm of infrared small and dim target is proposed in this paper.Firstly,the original infrared images are changed into a new infrared patch tensor mode through data reconstruction.Then,the infrared small and dim target detection problems are converted to low-rank tensor recovery problems based on tensor nuclear norm in accordance with patch tensor characteristics,and inverse variance weighted entropy is defined for self-adaptive adjustment of sparseness.Finally,the low-rank tensor recovery problem with noise is solved by alternating the direction method to obtain the sparse target image,and the final small target is worked out by a simple partitioning algorithm.The test results in various spacebased downward-looking complex scenes show that such method can restrain complex background well by virtue of rapid arithmetic speed with high detection probability and low false alarm rate.It is a kind of infrared small and dim target detection method with good performance.

基于Low-rank一步法波场延拓的黏声各向异性介质纯qP波正演模拟

各向异性介质纯qP波正演模拟及逆时偏移近年受到广泛关注,但它虽考虑了地下介质的各向异性特征,却忽略了黏滞性特征,使得最终偏移结果中噪声增加、分辨率降低。常规拟声波方程存在伪横波干扰、受模型参数限制(ε≥δ)、传播不稳定等因素影响,极大地限制了其应用。为此,引入一步法波场延拓方法,推导了黏声介质方程在空间—波数域的表达形式;结合空间—波数域各向异性介质延拓算子,构建一种适用于黏声各向异性介质的空间—波数域纯qP波波场延拓算子;引入Low-rank分解算法,实现基于Low-rank一步法波场延拓的黏声各向异性介质纯qP波正演模拟。数值模拟结果表明:①地震波场能同时表现出各向异性特征和黏滞性特征,更符合实际地下介质情况;②该方法克服了拟声波方程的局限性,消除了伪横波干扰,不受模型参数限制且地震波场能稳定传播;③在适当增大时间步长情形下无数值频散现象,所提算法能同时兼顾计算效率和计算精度,是一种稳定、高效的正演模拟方法,为基于Q补偿的各向异性介质逆时偏移提供了理论依据。

基于混沌吸引子重构和Low-rank聚类的跳频信号电台分选

辐射源无调制信息的暂态信号能够表征辐射源发射机的无意调制特性,对该暂态信号分析可实现辐射源识别。而跳频电台在开机以及频率转换瞬间,都存在一个无信息传送的暂态调整时间,该暂态调整瞬间,电台发射的信号是无调制信息的非线性、非平稳和非高斯信号。该暂态时间序列可反映跳频电台的器件特性,同时该序列往往呈现复杂的混沌特性。因此,借鉴混沌时间序列分析的思想,同时利用暂态信号的Low-rank特性,该文提出了一种基于暂态信号混沌吸引子重构和Low-rank聚类的跳频信号电台分选算法。实验测试表明:跳频电台的暂态信号时间序列属于混沌时间序列,同时实测多跳频信号的电台分选结果证明了Low-rank聚类算法在跳频电台分选上的可行性。

基于Low-rank分解的复杂TI介质纯qP波正演模拟与逆时偏移

近年来,面向实际应用的TI介质准P波正演模拟与逆时偏移成像技术受到空前的关注.基于常规耦合型传播方程的正演模拟方法不仅存在伪横波及频散假象干扰,而且还遭受模型参数限制(η>0)和不稳定影响;而纯qP波方程的推导繁琐,且由于方程中包含拟微分算子造成求解难度大且精度有限.为此,本文首先构建了一种适用于任意TI介质的纯qP波传播算子,然后借助Low-rank分解求取该算子中的空间-波数域矩阵,同时引入Cerjan衰减边界条件来压制边界反射干扰,最终实现了一种间接的纯qP波波场外推方案,并将其成功应用于复杂TI介质正演模拟与逆时偏移成像中.通过开展数值模拟,并与其他方法对比表明:①该方法既避免了纯qP波方程的繁琐推导,又克服了耦合型方程对模型参数的限制;②还彻底消除了残余伪横波噪音及数值频散;③且能适应较大时间或空间步长及高频震源,是一种相对准确且稳定的各向异性纵波正演与成像策略.

各向异性介质Low-rank有限差分法纯qP波叠前平面波最小二乘逆时偏移

拟声波最小二乘逆时偏移是一种极具潜力的地震波成像工具,但该方法遭受各向异性拟声波近似的限制,TTI介质正演模拟不稳定、反偏移记录中遭受伪横波二次扰动及数值频散假象,另外拟声波最小二乘逆时偏移还面临计算效率低、收敛速度慢、对速度等模型参数依赖性高等问题.为了克服各向异性拟声波最小二乘逆时偏移的缺陷,在反演框架下,本文借助Low-rank有限差分算法首次提出并实现了TTI介质纯qP波线性正演模拟及纯qP波最小二乘逆时偏移;为了进一步提升反演成像效率,同时改善反演成像方法对模型参数误差的依赖性及对地震数据噪声的适应性,通过引入叠前平面波优化策略,发展了TTI介质纯qP波叠前平面波最小二乘逆时偏移成像方法.在编程实现方法的基础上,通过开展模型成像测试,展示了本方法的优势和潜力:一方面加快了反演成像效率,另一方面也提升了方法的抗噪性,同时还降低了方法对模型参数的依赖性.

TTI介质Low-rank有限差分法高效正演模拟及逆时偏移

计算效率是制约各向异性逆时偏移实用化的关键因素,此外,伪横波假象、数值频散以及不稳定问题也是TTI介质qP波正演模拟及逆时偏移的固有难题。Low-rank波场延拓算法虽能解决上述三方面问题,但其运算速度受模型参数限制,计算效率较低。为此,本文基于混合网格有限差分思想,给出一种新的紧致差分模板,并借助Low-rank分解求取与模型匹配的自适应差分系数,进而实现一种针对TTI介质的Low-rank有限差分法高效正演模拟及逆时偏移成像策略。数值模型测试结果表明:本文方法既继承了有限差分法高效灵活的特点,又拥有Low-rank波场延拓方法准确计算纯qP波波场的优势,即在提高计算效率的同时避免了伪横波假象和数值不稳定,是一种兼顾成像精度与计算效率的各向异性逆时偏移实用方法。

Development and application of an efficient gas extraction model for low-rank high-gas coal beds

To promote gas extraction in low-rank high-gas coal beds, the pore structure characteristics of the coal and their effect on gas desorption were studied. The results show that micropores are relatively rare in low-rank coal; mesopores are usually semi-open and inkpot-shaped whereas macropores are usually slit-shaped. Gas desorption is relatively easy at high- pressure stages, whereas it is difficult at low-pressure stages because of the ＇bottleneck effect＇ of the semi-open inkpot-shaped mesopores. A ＇two-three-two＇ gas extraction model was established following experimental analysis and engineering practice applied in the Binchang mining area. In this model, gas extraction is divided into three periods： a planning period, a transitional period and a production period. In each period, surface extraction and underground extraction are performed simultaneously, and pressure-relief extraction and conventional extraction are coupled to each other. After applying this model, the gas extraction rate rose to 78.8 %.

The mechanism and products for co-thermal extraction of biomass and low-rank coal with NMP

The high-value utilization of low-rank coal would allow for expanding energy sources,improving energy efficiencies,and alleviating environmental issues.In order to use low-rank coal effectively,the hypercoals(HPCs)were co-extracted from two types of low-rank coal and biomass via N-methyl-2-purrolidinone(NMP)under mild conditions.The structures of the HPCs and residues were characterized by proximate and ultimate analysis,Raman spectra,and Fourier transform infrared(FT-IR)spectra.The carbon structure changes within the raw coals and HPCs were discussed.The individual thermal dissolution of Xibu(XB)coal,Guandi(GD)coal,and the biomass demonstrated that the biomass provided the lowest thermal dissolution yield Y1 and the highest thermal soluble yield Y2 at 280℃,and the ash content of three HPCs decreased as the extraction temperature rose.Co-thermal extractions in NMP at various coal/biomass mass ratios were performed,demonstrating a positive synergic effect for Y2 in the whole coal/biomass mass ratios.The maximum value of Y2 was 52.25wt% for XB coal obtained with a XB coal/biomass of 50wt% biomass.The maximum value of Y2 was 50.77wt% for GD coal obtained with a GD coal/biomass of 1:4.The difference for the optimal coal/biomass mass ratios between XB and GD coals could be attributed to the different co-extraction mechanisms for this two type coals.

Co-pyrolysis characteristics and interaction route between low-rank coals and Shenhua coal direct liquefaction residue

To reasonably utilize the coal direct liquefaction residue(DLR), contrasting research on the co-pyrolysis between different low-rank coals and DLR was investigated using a TGA coupled with an FT-IR spectrophotometer and a fixed-bed reactor. GC–MS, FTIR, and XRD were used to explore the reaction mechanisms of the various co-pyrolysis processes. Based on the TGA results, it was confirmed that the tetrahydrofuran insoluble fraction of DLR helped to catalyze the conversion reaction of lignite. Also, the addition of DLR improved the yield of tar in the fixed-bed, with altering the composition of the tar. Moreover, a kinetic analysis during the co-pyrolysis was conducted using a distributed activation energy model. The co-pyrolysis reactions showed an approximate double-Gaussian distribution.

Study of sodium lignosulfonate prepare low-rank coal-water slurry:Experiments and simulations

The effect of sodium lignosulfonate(SL)as additive on the preparation of low-rank coal-water slurry(LCWS)was studied by experiments and molecular dynamics(MD)simulation s.The experimental results show that the appropriate amount of additives is beneficial to reduce the viscosity of LCWS and increase the slurry concentration.Adsorption isotherm studies showed that SL conforms to single-layer adsorption on the coal surface,andΔG_(ads)^(0) was negative,proving that the reaction was spontaneous.Zeta potential measurements showed that SL increased the negative charge on coal.FTIR scanning and XPS wide-range scanning were performed on the coal before and after adsorption,and it was found that the content of oxygen functional groups on coal increased after adsorption.Simulation results show that when a large number of SL molecules exist in the solution,some SL molecules will bind to hydrophobic hydrocarbon groups on coal.The rest of the SL molecule s,their hydrophobic alkyl tails,come into contact with each other and aggregate in solution.The agglomeration of SL molecules and the surface of coal with static electricity will also produce electrostatic interaction,which is conducive to the even dispersion of coal particles.The results of mean square displacement(MSD)and self-diffusion coefficient(D)show that the addition of SL reduces the diffusion rate of water molecules.Simulation results correspond to experimental results,indicating that MD simulation is accurate and feasible.

Nested Alternating Direction Method of Multipliers to Low-Rank and Sparse-Column Matrices Recovery

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.

Low-field NMR inversion based on low-rank and sparsity restraint of relaxation spectra

In this paper,we proposed a novel method for low-field nuclear magnetic resonance(NMR)inversion based on low-rank and sparsity restraint(LRSR)of relaxation spectra,with which high quality construction is made possible for one-and two-dimensional low-field and low signal to noise ratio NMR data.In this method,the low-rank and sparsity restraints are introduced into the objective function instead of the smoothing term.The low-rank features in relaxation spectra are extracted to ensure the local characteristics and morphology of spectra.The sparsity and residual term are contributed to the resolution and precision of spectra,with the elimination of the redundant relaxation components.Optimization process of the objective function is designed with alternating direction method of multiples,in which the objective function is decomposed into three subproblems to be independently solved.The optimum solution can be obtained by alternating iteration and updating process.At first,numerical simulations are conducted on synthetic echo data with different signal-to-noise ratios,to optimize the desirable regularization parameters and verify the feasibility and effectiveness of proposed method.Then,NMR experiments on solutions and artificial sandstone samples are conducted and analyzed,which validates the robustness and reliability of the proposed method.The results from simulations and experiments have demonstrated that the suggested method has unique advantages for improving the resolution of relaxation spectra and enhancing the ability of fluid quantitative identification.