Multi-label feature selection(MFS)is a crucial dimensionality reduction technique aimed at identifying informative features associated with multiple labels.However,traditional centralized methods face significant chal...Multi-label feature selection(MFS)is a crucial dimensionality reduction technique aimed at identifying informative features associated with multiple labels.However,traditional centralized methods face significant challenges in privacy-sensitive and distributed settings,often neglecting label dependencies and suffering from low computational efficiency.To address these issues,we introduce a novel framework,Fed-MFSDHBCPSO—federated MFS via dual-layer hybrid breeding cooperative particle swarm optimization algorithm with manifold and sparsity regularization(DHBCPSO-MSR).Leveraging the federated learning paradigm,Fed-MFSDHBCPSO allows clients to perform local feature selection(FS)using DHBCPSO-MSR.Locally selected feature subsets are encrypted with differential privacy(DP)and transmitted to a central server,where they are securely aggregated and refined through secure multi-party computation(SMPC)until global convergence is achieved.Within each client,DHBCPSO-MSR employs a dual-layer FS strategy.The inner layer constructs sample and label similarity graphs,generates Laplacian matrices to capture the manifold structure between samples and labels,and applies L2,1-norm regularization to sparsify the feature subset,yielding an optimized feature weight matrix.The outer layer uses a hybrid breeding cooperative particle swarm optimization algorithm to further refine the feature weight matrix and identify the optimal feature subset.The updated weight matrix is then fed back to the inner layer for further optimization.Comprehensive experiments on multiple real-world multi-label datasets demonstrate that Fed-MFSDHBCPSO consistently outperforms both centralized and federated baseline methods across several key evaluation metrics.展开更多
Objective To address the challenges of systematically identifying herb pairs in traditional Chinese medicine(TCM),we proposed HerbGL,a framework for predicting potential herb pairs that integrates network propagation ...Objective To address the challenges of systematically identifying herb pairs in traditional Chinese medicine(TCM),we proposed HerbGL,a framework for predicting potential herb pairs that integrates network propagation and graph regularization.Methods Based on the assumption that herbal actions induce subtle perturbations in biological systems,a framework named HerbGL was proposed.Random walk with restart(RWR)was first applied to the protein-protein interaction(PPI)network to reconstruct herb-specific perturbation effects and generate weighted subnetworks.Then,to quantify affinity between herb pairs,two network-proximity metrics,Closeness and PageRank,were computed from the weighted subnetworks to construct herb-pair affinity matrices.Finally,these matrices,together with known herb pairs(derived from co-occurrence analysis of TCM formulas with a threshold determined from the inflection point of the frequency distribution),were incorporated into a graph regularization model to predict potential herb pairs.Model performance was assessed through baseline comparison,ablation and robustness experiment under different ratios of positive and negative samples,using the area under the receiver operating characteristic curve(AUROC),the area under the precision-recall curve(AUPRC),accuracy,and precision as evaluation metrics.Furthermore,the predicted herb pairs were validated through both literature evidence and Gene Ontology(GO)and Kyoto Encyclopedia of Genes and Genomes(KEGG)enrichment analyses.Results The weighted subnetworks constructed by RWR provided a refined simulation of herb-specific perturbation effects,which formed the basis for subsequent affinity modeling and prediction.Analysis of herb pair co-occurrence frequencies revealed a marked change around 150,which was selected as the threshold to distinguish herb pairs from non-herb pairs.HerbGL exhibited superior predictive performance compared with baseline models(AUROC=0.9705,AUPRC=0.9555,accuracy=0.7266,precision=0.9706).Ablation results showed that removing the Closeness and PageRank metrics substantially degraded performance(AUROC=0.8191,AUPRC=0.8768),confirming their necessity.Robustness evaluation under an imbalanced positive-to-negative sample ratio of 1:5 yielded AUROC=0.9696 and AUPRC=0.8404,indicating stable predictive ability.Moreover,multiple case studies further validated the rationality of the predicted herb pairs,such as Fangfeng(Saposhnikoviae Radix)and Qingpi(Citri Reticulatae Pericarpium Viride)which are recorded in Liangpeng Huiji(《良朋汇集》,Collection of Excellent Recipes)Vol.3:Fangfeng Shengma Tang(防风升麻汤).Additionally,pathway enrichment analysis of the Renshen(Ginseng Radix et Rhizoma)and Lianqiao(Forsythiae Fructus)pair further supported the biological plausibility of their compatibility.Conclusion HerbGL offers an effective and biologically informed framework for identifying herb pairs in TCM.Beyond improving herb pair prediction,the framework also provides data support for research on herb compounds and mechanisms,thereby supporting data-driven exploration of TCM compatibility.展开更多
In order to address the issue of overly conservative offline reinforcement learning(RL) methods that limit the generalization of policy in the out-of-distribution(OOD) region,this article designs a surrogate target fo...In order to address the issue of overly conservative offline reinforcement learning(RL) methods that limit the generalization of policy in the out-of-distribution(OOD) region,this article designs a surrogate target for OOD value function based on dataset distance and proposes a novel generalized Q-learning mechanism with distance regularization(GQDR).In theory,we not only prove the convergence of GQDR,but also ensure that the difference between the Q-value learned by GQDR and its true value is bounded.Furthermore,an offline generalized actor-critic method with distance regularization(OGACDR) is proposed by combining GQDR with actor-critic learning framework.Two implementations of OGACDR,OGACDR-EXP and OGACDRSQR,are introduced according to exponential(EXP) and opensquare(SQR) distance weight functions,and it has been theoretically proved that OGACDR provides a safe policy improvement.Experimental results on Gym-MuJoCo continuous control tasks show that OGACDR can not only alleviate the overestimation and overconservatism of Q-value function,but also outperform conservative offline RL baselines.展开更多
Many linear-in-parameters models arising in identification and control can be expressed as singlelayer artificial neural networks(ANNs)with linear activation,enabling online learning viafirst-order optimization.In pra...Many linear-in-parameters models arising in identification and control can be expressed as singlelayer artificial neural networks(ANNs)with linear activation,enabling online learning viafirst-order optimization.In practice,however,standard gradient descent ofien exhibits slow convergence,large intermediate weights,and stagnation when the regressor data are ill-conditioned or computations are performed underfinite precision.This paper proposes Gradient Descent with Time-Decaying Regularization(GD-TDR),a training algorithm that augments the quadratic loss with a regularization term whose weight decays exponentially in time.fie proposed schedule enforces uniform strong convexity during early iterations,efiectively mitigating neural-paralysis-like behavior associated withfiat directions,while asymptotically vanishing so that the unregularized least-squares solution is recovered.A convergence theorem for GD-TDR is established and a concise pseudocode implementation is provided.Numerical and embedded experiments on an online identification problem of a Chua-type chaotic oscillator demonstrate that GD-TDR converges faster and avoids stagnation compared to standard gradient descent,without introducing the steady-state bias characteristic offixed quadratic regularization.展开更多
In subsalt hydrocarbon exploration,the strong velocity contrast associated with salt structures poses significant challenges to conventional full waveform inversion(FWI)method.While direct envelope inversion can inver...In subsalt hydrocarbon exploration,the strong velocity contrast associated with salt structures poses significant challenges to conventional full waveform inversion(FWI)method.While direct envelope inversion can invert large-scale salt dome,it fails to invert the salt-bottom velocity structures due to the absence of waveform phase information.To solve this problem,we first use a sliding Gaussian window to decompose seismic data into the local scale waveform.Subsequently,we combine the local scale envelope signal with waveform instantaneous phase to obtain the polarity envelope.The resulting polarity envelope can invert low-frequency components while preserving the phase characteristics of seismic data,enabling more accurate low-wavenumber velocity structures.Based on this,we propose a phase-based polarized direct envelope inversion with total variation regularization for simultaneous source seismic data(simultaneous source TV-PDEI)to improve the accuracy of velocity inversion,remove the crosstalk noise,and enhance the computational efficiency.Numerical experiments on salt models and Chevron blind dataset test demonstrate that the simultaneous source TV-PDEI efficiently provides a robust initial velocity model for FWI.展开更多
In the numerical solution of wave propagation problems,spurious oscillations occur in the exact time integration of the related equation of motion.This is due to the high frequencies introduced by the spatial discreti...In the numerical solution of wave propagation problems,spurious oscillations occur in the exact time integration of the related equation of motion.This is due to the high frequencies introduced by the spatial discretization,given the small size of the mesh elements and the integration step required to capture the wave phenomena.Currently,an answer to this problem is given by the use of the smoothing properties,intrinsic to the scheme or obtained through artificial viscosity,of dissipative time integration methods.More recently,in an alternative approach to the problem,the solution has been regularized via a post processing smoothing technique.In particular,on the basis of an initial nondissipative scheme,at a fixed observation time a series of steps of an appropriate dissipative time integration method achieves the desired smoothing.However,in both approaches,as the dissipative steps are performed,the noise progressively decreases,but the important values related to the peak regions of the solution degrade significantly.Here we describe a regularization process that automatically returns a solution where the noise has been eliminated but does not affect the significant regions of the solution.The presented technique recognizes the flat or peak shapes of the original solution among the oscillating components representing the noise.Operationally,the presented algorithm,starting from a nondissipative stepby-step scheme for time integration,iteratively smooths the related kinematic quantities and finally recovers the regularized solution as a suitable composition of smoothed and unsmoothed subdomains.展开更多
Absorption compensation is a process involving the exponential amplification of reflection amplitudes.This process amplifies the seismic signal and noise,thereby substantially reducing the signal-tonoise ratio of seis...Absorption compensation is a process involving the exponential amplification of reflection amplitudes.This process amplifies the seismic signal and noise,thereby substantially reducing the signal-tonoise ratio of seismic data.Therefore,this paper proposes a multichannel inversion absorption compensation method based on structure tensor regularization.First,the structure tensor is utilized to extract the spatial inclination of seismic signals,and the spatial prediction filter is designed along the inclination direction.The spatial prediction filter is then introduced into the regularization condition of multichannel inversion absorption compensation,and the absorption compensation is realized under the framework of multichannel inversion theory.The spatial predictability of seismic signals is also introduced into the objective function of absorption compensation inversion.Thus,the inversion system can effectively suppress the noise amplification effect during absorption compensation and improve the recovery accuracy of high-frequency signals.Synthetic and field data tests are conducted to demonstrate the accuracy and effectiveness of the proposed method.展开更多
Modern warfare demands weapons capable of penetrating substantial structures,which presents sig-nificant challenges to the reliability of the electronic devices that are crucial to the weapon's perfor-mance.Due to...Modern warfare demands weapons capable of penetrating substantial structures,which presents sig-nificant challenges to the reliability of the electronic devices that are crucial to the weapon's perfor-mance.Due to miniaturization of electronic components,it is challenging to directly measure or numerically predict the mechanical response of small-sized critical interconnections in board-level packaging structures to ensure the mechanical reliability of electronic devices in projectiles under harsh working conditions.To address this issue,an indirect measurement method using the Bayesian regularization-based load identification was proposed in this study based on finite element(FE)pre-dictions to estimate the load applied on critical interconnections of board-level packaging structures during the process of projectile penetration.For predicting the high-strain-rate penetration process,an FE model was established with elasto-plastic constitutive models of the representative packaging ma-terials(that is,solder material and epoxy molding compound)in which material constitutive parameters were calibrated against the experimental results by using the split-Hopkinson pressure bar.As the impact-induced dynamic bending of the printed circuit board resulted in an alternating tensile-compressive loading on the solder joints during penetration,the corner solder joints in the edge re-gions experience the highest S11 and strain,making them more prone to failure.Based on FE predictions at different structural scales,an improved Bayesian method based on augmented Tikhonov regulariza-tion was theoretically proposed to address the issues of ill-posed matrix inversion and noise sensitivity in the load identification at the critical solder joints.By incorporating a wavelet thresholding technique,the method resolves the problem of poor load identification accuracy at high noise levels.The proposed method achieves satisfactorily small relative errors and high correlation coefficients in identifying the mechanical response of local interconnections in board-level packaging structures,while significantly balancing the smoothness of response curves with the accuracy of peak identification.At medium and low noise levels,the relative error is less than 6%,while it is less than 10%at high noise levels.The proposed method provides an effective indirect approach for the boundary conditions of localized solder joints during the projectile penetration process,and its philosophy can be readily extended to other scenarios of multiscale analysis for highly nonlinear materials and structures under extreme loading conditions.展开更多
Full waveform inversion is a precise method for parameter inversion,harnessing the complete wavefield information of seismic waves.It holds the potential to intricately characterize the detailed features of the model ...Full waveform inversion is a precise method for parameter inversion,harnessing the complete wavefield information of seismic waves.It holds the potential to intricately characterize the detailed features of the model with high accuracy.However,due to inaccurate initial models,the absence of low-frequency data,and incomplete observational data,full waveform inversion(FWI)exhibits pronounced nonlinear characteristics.When the strata are buried deep,the inversion capability of this method is constrained.To enhance the accuracy and precision of FWI,this paper introduces a novel approach to address the aforementioned challenges—namely,a fractional-order anisotropic total p-variation regularization for full waveform inversion(FATpV-FWI).This method incorporates fractional-order total variation(TV)regularization to construct the inversion objective function,building upon TV regularization,and subsequently employs the alternating direction multiplier method for solving.This approach mitigates the step effect stemming from total variation in seismic inversion,thereby facilitating the reconstruction of sharp interfaces of geophysical parameters while smoothing background variations.Simultaneously,replacing integer-order differences with fractional-order differences bolsters the correlation among seismic data and diminishes the scattering effect caused by integer-order differences in seismic inversion.The outcomes of model tests validate the efficacy of this method,highlighting its ability to enhance the overall accuracy of the inversion process.展开更多
Energy resolution calibration is crucial for gamma-ray spectral analysis,as measured using a scintillation detector.A locally constrained regularization method was proposed to determine the resolution calibration para...Energy resolution calibration is crucial for gamma-ray spectral analysis,as measured using a scintillation detector.A locally constrained regularization method was proposed to determine the resolution calibration parameters.First,a Monte Carlo simulation model consistent with an actual measurement system was constructed to obtain the energy deposition distribution in the scintillation crystal.Subsequently,the regularization objective function is established based on weighted least squares and additional constraints.Additional constraints were designed using a special weighting scheme based on the incident gamma-ray energies.Subsequently,an intelligent algorithm was introduced to search for the optimal resolution calibration parameters by minimizing the objective function.The most appropriate regularization parameter was determined through mathematical experiments.When the regularization parameter was 30,the calibrated results exhibited the minimum RMSE.Simulations and test pit experiments were conducted to verify the performance of the proposed method.The simulation results demonstrate that the proposed algorithm can determine resolution calibration parameters more accurately than the traditional weighted least squares,and the test pit experimental results show that the R-squares between the calibrated and measured spectra are larger than 0.99.The accurate resolution calibration parameters determined by the proposed method lay the foundation for gamma-ray spectral processing and simulation benchmarking.展开更多
Downward continuation is a key step in processing airborne geomagnetic data.However,downward continuation is a typically ill-posed problem because its computation is unstable;thus,regularization methods are needed to ...Downward continuation is a key step in processing airborne geomagnetic data.However,downward continuation is a typically ill-posed problem because its computation is unstable;thus,regularization methods are needed to realize effective continuation.According to the Poisson integral plane approximate relationship between observation and continuation data,the computation formulae combined with the fast Fourier transform(FFT)algorithm are transformed to a frequency domain for accelerating the computational speed.The iterative Tikhonov regularization method and the iterative Landweber regularization method are used in this paper to overcome instability and improve the precision of the results.The availability of these two iterative regularization methods in the frequency domain is validated by simulated geomagnetic data,and the continuation results show good precision.展开更多
Target tracking is an essential task in contemporary computer vision applications.However,its effectiveness is susceptible to model drift,due to the different appearances of targets,which often compromises tracking ro...Target tracking is an essential task in contemporary computer vision applications.However,its effectiveness is susceptible to model drift,due to the different appearances of targets,which often compromises tracking robustness and precision.In this paper,a universally applicable method based on correlation filters is introduced to mitigate model drift in complex scenarios.It employs temporal-confidence samples as a priori to guide the model update process and ensure its precision and consistency over a long period.An improved update mechanism based on the peak side-lobe to peak correlation energy(PSPCE)criterion is proposed,which selects high-confidence samples along the temporal dimension to update temporal-confidence samples.Extensive experiments on various benchmarks demonstrate that the proposed method achieves a competitive performance compared with the state-of-the-art methods.Especially when the target appearance changes significantly,our method is more robust and can achieve a balance between precision and speed.Specifically,on the object tracking benchmark(OTB-100)dataset,compared to the baseline,the tracking precision of our model improves by 8.8%,8.8%,5.1%,5.6%,and 6.9%for background clutter,deformation,occlusion,rotation,and illumination variation,respectively.The results indicate that this proposed method can significantly enhance the robustness and precision of target tracking in dynamic and challenging environments,offering a reliable solution for applications such as real-time monitoring,autonomous driving,and precision guidance.展开更多
In this study,we present a deterministic convergence analysis of Gated Recurrent Unit(GRU)networks enhanced by a smoothing L1regularization technique.While GRU architectures effectively mitigate gradient vanishing/...In this study,we present a deterministic convergence analysis of Gated Recurrent Unit(GRU)networks enhanced by a smoothing L1regularization technique.While GRU architectures effectively mitigate gradient vanishing/exploding issues in sequential modeling,they remain prone to overfitting,particularly under noisy or limited training data.Traditional L1regularization,despite enforcing sparsity and accelerating optimization,introduces non-differentiable points in the error function,leading to oscillations during training.To address this,we propose a novel smoothing L1regularization framework that replaces the non-differentiable absolute function with a quadratic approximation,ensuring gradient continuity and stabilizing the optimization landscape.Theoretically,we rigorously establish threekey properties of the resulting smoothing L1-regularizedGRU(SL1-GRU)model:(1)monotonic decrease of the error function across iterations,(2)weak convergence characterized by vanishing gradients as iterations approach infinity,and(3)strong convergence of network weights to fixed points under finite conditions.Comprehensive experiments on benchmark datasets-spanning function approximation,classification(KDD Cup 1999 Data,MNIST),and regression tasks(Boston Housing,Energy Efficiency)-demonstrate SL1-GRUs superiority over baseline models(RNN,LSTM,GRU,L1-GRU,L2-GRU).Empirical results reveal that SL1-GRU achieves 1.0%-2.4%higher test accuracy in classification,7.8%-15.4%lower mean squared error in regression compared to unregularized GRU,while reducing training time by 8.7%-20.1%.These outcomes validate the method’s efficacy in balancing computational efficiency and generalization capability,and they strongly corroborate the theoretical calculations.The proposed framework not only resolves the non-differentiability challenge of L1regularization but also provides a theoretical foundation for convergence guarantees in recurrent neural network training.展开更多
Owing to the constraints of depth sensing technology,images acquired by depth cameras are inevitably mixed with various noises.For depth maps presented in gray values,this research proposes a novel denoising model,ter...Owing to the constraints of depth sensing technology,images acquired by depth cameras are inevitably mixed with various noises.For depth maps presented in gray values,this research proposes a novel denoising model,termed graph-based transform(GBT)and dual graph Laplacian regularization(DGLR)(DGLR-GBT).This model specifically aims to remove Gaussian white noise by capitalizing on the nonlocal self-similarity(NSS)and the piecewise smoothness properties intrinsic to depth maps.Within the group sparse coding(GSC)framework,a combination of GBT and DGLR is implemented.Firstly,within each group,the graph is constructed by using estimates of the true values of the averaged blocks instead of the observations.Secondly,the graph Laplacian regular terms are constructed based on rows and columns of similar block groups,respectively.Lastly,the solution is obtained effectively by combining the alternating direction multiplication method(ADMM)with the weighted thresholding method within the domain of GBT.展开更多
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....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.展开更多
The presented iterative multiuser detection technique was based on joint deregularized and box-constrained solution to quadratic optimization with iterations similar to that used in the nonstationary Tikhonov iterated...The presented iterative multiuser detection technique was based on joint deregularized and box-constrained solution to quadratic optimization with iterations similar to that used in the nonstationary Tikhonov iterated algorithm.The deregularization maximized the energy of the solution,which was opposite to the Tikhonov regularization where the energy was minimized.However,combined with box-constraints,the deregularization forced the solution to be close to the binary set.It further exploited the box-constrained dichotomous coordinate descent algorithm and adapted it to the nonstationary iterative Tikhonov regularization to present an efficient detector.As a result,the worst-case and average complexity are reduced down as K2.8 and K2.5 floating point operation per second,respectively.The development improves the "efficient frontier" in multiuser detection,which is illustrated by simulation results.In addition,most operations in the detector are additions and bit-shifts.This makes the proposed technique attractive for fixed-point hardware implementation.展开更多
In this paper we discuss the edge-preserving regularization method in the reconstruction of physical parameters from geophysical data such as seismic and ground-penetrating radar data. In the regularization method a p...In this paper we discuss the edge-preserving regularization method in the reconstruction of physical parameters from geophysical data such as seismic and ground-penetrating radar data. In the regularization method a potential function of model parameters and its corresponding functions are introduced. This method is stable and able to preserve boundaries, and protect resolution. The effect of regularization depends to a great extent on the suitable choice of regularization parameters. The influence of the edge-preserving parameters on the reconstruction results is investigated and the relationship between the regularization parameters and the error of data is described.展开更多
In this paper,we consider the inverse problem for identifying the source term of the time-fractional equation with a hyper-Bessel operator.First,we prove that this inverse problem is ill-posed,and give the conditional...In this paper,we consider the inverse problem for identifying the source term of the time-fractional equation with a hyper-Bessel operator.First,we prove that this inverse problem is ill-posed,and give the conditional stability.Then,we give the optimal error bound for this inverse problem.Next,we use the fractional Tikhonov regularization method and the fractional Landweber iterative regularization method to restore the stability of the ill-posed problem,and give corresponding error estimates under different regularization parameter selection rules.Finally,we verify the effectiveness of the method through numerical examples.展开更多
Nuclear Magnetic inversion is the basis of NMR Resonance (NMR) T2 logging interpretation. The regularization parameter selection of the penalty term directly influences the NMR T2 inversion result. We implemented bo...Nuclear Magnetic inversion is the basis of NMR Resonance (NMR) T2 logging interpretation. The regularization parameter selection of the penalty term directly influences the NMR T2 inversion result. We implemented both norm smoothing and curvature smoothing methods for NMR T2 inversion, and compared the inversion results with respect to the optimal regular- ization parameters ((Xopt) which were selected by the dis- crepancy principle (DP), generalized cross-validation (GCV), S-curve, L-curve, and the slope of L-curve methods, respectively. The numerical results indicate that the DP method can lead to an oscillating or oversmoothed solution which is caused by an inaccurately estimated noise level. The (Xopt selected by the L-curve method is occa- sionally small or large which causes an undersmoothed or oversmoothed T2 distribution. The inversion results from GCV, S-curve and the slope of L-curve methods show satisfying inversion results. The slope of the L-curve method with less computation is more suitable for NMR T2 inversion. The inverted T2 distribution from norm smoothing is better than that from curvature smoothing when the noise level is high.展开更多
According to the conclusion of the simulation experiments in paper I, the Tikhonov regularization method is applied to cyclone wind retrieval with a rain-effect-considering geophysical model function (called CMF+Rai...According to the conclusion of the simulation experiments in paper I, the Tikhonov regularization method is applied to cyclone wind retrieval with a rain-effect-considering geophysical model function (called CMF+Rain). The CMF+Rain model which is based on the NASA scatterometer-2 (NSCAT2) GMF is presented to compensate for the effects of rain on cyclone wind retrieval. With the multiple solution scheme (MSS), the noise of wind retrieval is effectively suppressed, but the influence of the background increases. It will cause a large wind direction error in ambiguity removal when the background error is large. However, this can be mitigated by the new ambiguity removal method of Tikhonov regularization as proved in the simulation experiments. A case study on an extratropical cyclone of hurricane observed with SeaWinds at 25-km resolution shows that the retrieved wind speed for areas with rain is in better agreement with that derived from the best track analysis for the GMF+Rain model, but the wind direction obtained with the two-dimensional variational (2DVAR) ambiguity removal is incorrect. The new method of Tikhonov regularization effectively improves the performance of wind direction ambiguity removal through choosing appropriate regularization parameters and the retrieved wind speed is almost the same as that obtained from the 2DVAR.展开更多
摘要Multi-label feature selection(MFS)is a crucial dimensionality reduction technique aimed at identifying informative features associated with multiple labels.However,traditional centralized methods face significant challenges in privacy-sensitive and distributed settings,often neglecting label dependencies and suffering from low computational efficiency.To address these issues,we introduce a novel framework,Fed-MFSDHBCPSO—federated MFS via dual-layer hybrid breeding cooperative particle swarm optimization algorithm with manifold and sparsity regularization(DHBCPSO-MSR).Leveraging the federated learning paradigm,Fed-MFSDHBCPSO allows clients to perform local feature selection(FS)using DHBCPSO-MSR.Locally selected feature subsets are encrypted with differential privacy(DP)and transmitted to a central server,where they are securely aggregated and refined through secure multi-party computation(SMPC)until global convergence is achieved.Within each client,DHBCPSO-MSR employs a dual-layer FS strategy.The inner layer constructs sample and label similarity graphs,generates Laplacian matrices to capture the manifold structure between samples and labels,and applies L2,1-norm regularization to sparsify the feature subset,yielding an optimized feature weight matrix.The outer layer uses a hybrid breeding cooperative particle swarm optimization algorithm to further refine the feature weight matrix and identify the optimal feature subset.The updated weight matrix is then fed back to the inner layer for further optimization.Comprehensive experiments on multiple real-world multi-label datasets demonstrate that Fed-MFSDHBCPSO consistently outperforms both centralized and federated baseline methods across several key evaluation metrics.
基金National Natural Science Foundation of China(82575255)Open Research Project of Jiangsu Provincial Research Institute of Chinese Medicine Schools(JSZYLP2024060)Postgraduate Research&Practice Innovation Program of Jiangsu Province(KYCX24_2156).
摘要Objective To address the challenges of systematically identifying herb pairs in traditional Chinese medicine(TCM),we proposed HerbGL,a framework for predicting potential herb pairs that integrates network propagation and graph regularization.Methods Based on the assumption that herbal actions induce subtle perturbations in biological systems,a framework named HerbGL was proposed.Random walk with restart(RWR)was first applied to the protein-protein interaction(PPI)network to reconstruct herb-specific perturbation effects and generate weighted subnetworks.Then,to quantify affinity between herb pairs,two network-proximity metrics,Closeness and PageRank,were computed from the weighted subnetworks to construct herb-pair affinity matrices.Finally,these matrices,together with known herb pairs(derived from co-occurrence analysis of TCM formulas with a threshold determined from the inflection point of the frequency distribution),were incorporated into a graph regularization model to predict potential herb pairs.Model performance was assessed through baseline comparison,ablation and robustness experiment under different ratios of positive and negative samples,using the area under the receiver operating characteristic curve(AUROC),the area under the precision-recall curve(AUPRC),accuracy,and precision as evaluation metrics.Furthermore,the predicted herb pairs were validated through both literature evidence and Gene Ontology(GO)and Kyoto Encyclopedia of Genes and Genomes(KEGG)enrichment analyses.Results The weighted subnetworks constructed by RWR provided a refined simulation of herb-specific perturbation effects,which formed the basis for subsequent affinity modeling and prediction.Analysis of herb pair co-occurrence frequencies revealed a marked change around 150,which was selected as the threshold to distinguish herb pairs from non-herb pairs.HerbGL exhibited superior predictive performance compared with baseline models(AUROC=0.9705,AUPRC=0.9555,accuracy=0.7266,precision=0.9706).Ablation results showed that removing the Closeness and PageRank metrics substantially degraded performance(AUROC=0.8191,AUPRC=0.8768),confirming their necessity.Robustness evaluation under an imbalanced positive-to-negative sample ratio of 1:5 yielded AUROC=0.9696 and AUPRC=0.8404,indicating stable predictive ability.Moreover,multiple case studies further validated the rationality of the predicted herb pairs,such as Fangfeng(Saposhnikoviae Radix)and Qingpi(Citri Reticulatae Pericarpium Viride)which are recorded in Liangpeng Huiji(《良朋汇集》,Collection of Excellent Recipes)Vol.3:Fangfeng Shengma Tang(防风升麻汤).Additionally,pathway enrichment analysis of the Renshen(Ginseng Radix et Rhizoma)and Lianqiao(Forsythiae Fructus)pair further supported the biological plausibility of their compatibility.Conclusion HerbGL offers an effective and biologically informed framework for identifying herb pairs in TCM.Beyond improving herb pair prediction,the framework also provides data support for research on herb compounds and mechanisms,thereby supporting data-driven exploration of TCM compatibility.
基金supported by the National Natural Science Foundation of China(62373364,62176259)the Key Research and Development Program of Jiangsu Province(BE2022095)。
摘要In order to address the issue of overly conservative offline reinforcement learning(RL) methods that limit the generalization of policy in the out-of-distribution(OOD) region,this article designs a surrogate target for OOD value function based on dataset distance and proposes a novel generalized Q-learning mechanism with distance regularization(GQDR).In theory,we not only prove the convergence of GQDR,but also ensure that the difference between the Q-value learned by GQDR and its true value is bounded.Furthermore,an offline generalized actor-critic method with distance regularization(OGACDR) is proposed by combining GQDR with actor-critic learning framework.Two implementations of OGACDR,OGACDR-EXP and OGACDRSQR,are introduced according to exponential(EXP) and opensquare(SQR) distance weight functions,and it has been theoretically proved that OGACDR provides a safe policy improvement.Experimental results on Gym-MuJoCo continuous control tasks show that OGACDR can not only alleviate the overestimation and overconservatism of Q-value function,but also outperform conservative offline RL baselines.
基金Funding was provided by the IPN-SIP(SIP 20250023,20250424,20251300,20251721,20253411,MULTI-2026-0035)SECIHTI(CF-2023-I-1635)the Sistema Nacional de Investigadores e Investigadoras(SNII)of Mexico.
摘要Many linear-in-parameters models arising in identification and control can be expressed as singlelayer artificial neural networks(ANNs)with linear activation,enabling online learning viafirst-order optimization.In practice,however,standard gradient descent ofien exhibits slow convergence,large intermediate weights,and stagnation when the regressor data are ill-conditioned or computations are performed underfinite precision.This paper proposes Gradient Descent with Time-Decaying Regularization(GD-TDR),a training algorithm that augments the quadratic loss with a regularization term whose weight decays exponentially in time.fie proposed schedule enforces uniform strong convexity during early iterations,efiectively mitigating neural-paralysis-like behavior associated withfiat directions,while asymptotically vanishing so that the unregularized least-squares solution is recovered.A convergence theorem for GD-TDR is established and a concise pseudocode implementation is provided.Numerical and embedded experiments on an online identification problem of a Chua-type chaotic oscillator demonstrate that GD-TDR converges faster and avoids stagnation compared to standard gradient descent,without introducing the steady-state bias characteristic offixed quadratic regularization.
基金supported by the National Natural Science Foundation of China(Grant Nos.42104116,42230803)。
摘要In subsalt hydrocarbon exploration,the strong velocity contrast associated with salt structures poses significant challenges to conventional full waveform inversion(FWI)method.While direct envelope inversion can invert large-scale salt dome,it fails to invert the salt-bottom velocity structures due to the absence of waveform phase information.To solve this problem,we first use a sliding Gaussian window to decompose seismic data into the local scale waveform.Subsequently,we combine the local scale envelope signal with waveform instantaneous phase to obtain the polarity envelope.The resulting polarity envelope can invert low-frequency components while preserving the phase characteristics of seismic data,enabling more accurate low-wavenumber velocity structures.Based on this,we propose a phase-based polarized direct envelope inversion with total variation regularization for simultaneous source seismic data(simultaneous source TV-PDEI)to improve the accuracy of velocity inversion,remove the crosstalk noise,and enhance the computational efficiency.Numerical experiments on salt models and Chevron blind dataset test demonstrate that the simultaneous source TV-PDEI efficiently provides a robust initial velocity model for FWI.
摘要In the numerical solution of wave propagation problems,spurious oscillations occur in the exact time integration of the related equation of motion.This is due to the high frequencies introduced by the spatial discretization,given the small size of the mesh elements and the integration step required to capture the wave phenomena.Currently,an answer to this problem is given by the use of the smoothing properties,intrinsic to the scheme or obtained through artificial viscosity,of dissipative time integration methods.More recently,in an alternative approach to the problem,the solution has been regularized via a post processing smoothing technique.In particular,on the basis of an initial nondissipative scheme,at a fixed observation time a series of steps of an appropriate dissipative time integration method achieves the desired smoothing.However,in both approaches,as the dissipative steps are performed,the noise progressively decreases,but the important values related to the peak regions of the solution degrade significantly.Here we describe a regularization process that automatically returns a solution where the noise has been eliminated but does not affect the significant regions of the solution.The presented technique recognizes the flat or peak shapes of the original solution among the oscillating components representing the noise.Operationally,the presented algorithm,starting from a nondissipative stepby-step scheme for time integration,iteratively smooths the related kinematic quantities and finally recovers the regularized solution as a suitable composition of smoothed and unsmoothed subdomains.
基金funded by the National Key R&D Program of China(Grant no.2018YFA0702504)the Sinopec research project(P22162).
摘要Absorption compensation is a process involving the exponential amplification of reflection amplitudes.This process amplifies the seismic signal and noise,thereby substantially reducing the signal-tonoise ratio of seismic data.Therefore,this paper proposes a multichannel inversion absorption compensation method based on structure tensor regularization.First,the structure tensor is utilized to extract the spatial inclination of seismic signals,and the spatial prediction filter is designed along the inclination direction.The spatial prediction filter is then introduced into the regularization condition of multichannel inversion absorption compensation,and the absorption compensation is realized under the framework of multichannel inversion theory.The spatial predictability of seismic signals is also introduced into the objective function of absorption compensation inversion.Thus,the inversion system can effectively suppress the noise amplification effect during absorption compensation and improve the recovery accuracy of high-frequency signals.Synthetic and field data tests are conducted to demonstrate the accuracy and effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China(Grant Nos.52475166,52175148)the Regional Collaboration Project of Shanxi Province(Grant No.202204041101044).
摘要Modern warfare demands weapons capable of penetrating substantial structures,which presents sig-nificant challenges to the reliability of the electronic devices that are crucial to the weapon's perfor-mance.Due to miniaturization of electronic components,it is challenging to directly measure or numerically predict the mechanical response of small-sized critical interconnections in board-level packaging structures to ensure the mechanical reliability of electronic devices in projectiles under harsh working conditions.To address this issue,an indirect measurement method using the Bayesian regularization-based load identification was proposed in this study based on finite element(FE)pre-dictions to estimate the load applied on critical interconnections of board-level packaging structures during the process of projectile penetration.For predicting the high-strain-rate penetration process,an FE model was established with elasto-plastic constitutive models of the representative packaging ma-terials(that is,solder material and epoxy molding compound)in which material constitutive parameters were calibrated against the experimental results by using the split-Hopkinson pressure bar.As the impact-induced dynamic bending of the printed circuit board resulted in an alternating tensile-compressive loading on the solder joints during penetration,the corner solder joints in the edge re-gions experience the highest S11 and strain,making them more prone to failure.Based on FE predictions at different structural scales,an improved Bayesian method based on augmented Tikhonov regulariza-tion was theoretically proposed to address the issues of ill-posed matrix inversion and noise sensitivity in the load identification at the critical solder joints.By incorporating a wavelet thresholding technique,the method resolves the problem of poor load identification accuracy at high noise levels.The proposed method achieves satisfactorily small relative errors and high correlation coefficients in identifying the mechanical response of local interconnections in board-level packaging structures,while significantly balancing the smoothness of response curves with the accuracy of peak identification.At medium and low noise levels,the relative error is less than 6%,while it is less than 10%at high noise levels.The proposed method provides an effective indirect approach for the boundary conditions of localized solder joints during the projectile penetration process,and its philosophy can be readily extended to other scenarios of multiscale analysis for highly nonlinear materials and structures under extreme loading conditions.
基金supported by the China Postdoctoral Science Foundation(Grant No.2024MF750281)the Postdoctoral Fellowship Program of CPSF(Grant No.GZC20230326)+1 种基金the Natural Science Foundation Project of Sichuan Province(Grant No.2025ZNSFSC1170)Sichuan Science and Technology Program(Grant No.2023ZYD0158).
摘要Full waveform inversion is a precise method for parameter inversion,harnessing the complete wavefield information of seismic waves.It holds the potential to intricately characterize the detailed features of the model with high accuracy.However,due to inaccurate initial models,the absence of low-frequency data,and incomplete observational data,full waveform inversion(FWI)exhibits pronounced nonlinear characteristics.When the strata are buried deep,the inversion capability of this method is constrained.To enhance the accuracy and precision of FWI,this paper introduces a novel approach to address the aforementioned challenges—namely,a fractional-order anisotropic total p-variation regularization for full waveform inversion(FATpV-FWI).This method incorporates fractional-order total variation(TV)regularization to construct the inversion objective function,building upon TV regularization,and subsequently employs the alternating direction multiplier method for solving.This approach mitigates the step effect stemming from total variation in seismic inversion,thereby facilitating the reconstruction of sharp interfaces of geophysical parameters while smoothing background variations.Simultaneously,replacing integer-order differences with fractional-order differences bolsters the correlation among seismic data and diminishes the scattering effect caused by integer-order differences in seismic inversion.The outcomes of model tests validate the efficacy of this method,highlighting its ability to enhance the overall accuracy of the inversion process.
基金supported by the National Natural Science Foundation of China(No.41804141)。
摘要Energy resolution calibration is crucial for gamma-ray spectral analysis,as measured using a scintillation detector.A locally constrained regularization method was proposed to determine the resolution calibration parameters.First,a Monte Carlo simulation model consistent with an actual measurement system was constructed to obtain the energy deposition distribution in the scintillation crystal.Subsequently,the regularization objective function is established based on weighted least squares and additional constraints.Additional constraints were designed using a special weighting scheme based on the incident gamma-ray energies.Subsequently,an intelligent algorithm was introduced to search for the optimal resolution calibration parameters by minimizing the objective function.The most appropriate regularization parameter was determined through mathematical experiments.When the regularization parameter was 30,the calibrated results exhibited the minimum RMSE.Simulations and test pit experiments were conducted to verify the performance of the proposed method.The simulation results demonstrate that the proposed algorithm can determine resolution calibration parameters more accurately than the traditional weighted least squares,and the test pit experimental results show that the R-squares between the calibrated and measured spectra are larger than 0.99.The accurate resolution calibration parameters determined by the proposed method lay the foundation for gamma-ray spectral processing and simulation benchmarking.
基金supported by the National Natural Science Foundation of China(41304022,41174026,41104047)the National 973 Foundation(61322201,2013CB733303)+1 种基金the Key laboratory Foundation of Geo-space Environment and Geodesy of the Ministry of Education(13-01-08)the Youth Innovation Foundation of High Resolution Earth Observation(GFZX04060103-5-12)
摘要Downward continuation is a key step in processing airborne geomagnetic data.However,downward continuation is a typically ill-posed problem because its computation is unstable;thus,regularization methods are needed to realize effective continuation.According to the Poisson integral plane approximate relationship between observation and continuation data,the computation formulae combined with the fast Fourier transform(FFT)algorithm are transformed to a frequency domain for accelerating the computational speed.The iterative Tikhonov regularization method and the iterative Landweber regularization method are used in this paper to overcome instability and improve the precision of the results.The availability of these two iterative regularization methods in the frequency domain is validated by simulated geomagnetic data,and the continuation results show good precision.
基金supported by the Natural Science Foundation of Sichuan Province of China under Grant No.2025ZNSFSC0522partially supported by the National Natural Science Foundation of China under Grants No.61775030 and No.61571096.
摘要Target tracking is an essential task in contemporary computer vision applications.However,its effectiveness is susceptible to model drift,due to the different appearances of targets,which often compromises tracking robustness and precision.In this paper,a universally applicable method based on correlation filters is introduced to mitigate model drift in complex scenarios.It employs temporal-confidence samples as a priori to guide the model update process and ensure its precision and consistency over a long period.An improved update mechanism based on the peak side-lobe to peak correlation energy(PSPCE)criterion is proposed,which selects high-confidence samples along the temporal dimension to update temporal-confidence samples.Extensive experiments on various benchmarks demonstrate that the proposed method achieves a competitive performance compared with the state-of-the-art methods.Especially when the target appearance changes significantly,our method is more robust and can achieve a balance between precision and speed.Specifically,on the object tracking benchmark(OTB-100)dataset,compared to the baseline,the tracking precision of our model improves by 8.8%,8.8%,5.1%,5.6%,and 6.9%for background clutter,deformation,occlusion,rotation,and illumination variation,respectively.The results indicate that this proposed method can significantly enhance the robustness and precision of target tracking in dynamic and challenging environments,offering a reliable solution for applications such as real-time monitoring,autonomous driving,and precision guidance.
基金supported by the National Science Fund for Distinguished Young Scholarship(No.62025602)National Natural Science Foundation of China(Nos.U22B2036,11931015)+2 种基金the Fok Ying-Tong Education Foundation China(No.171105)the Fundamental Research Funds for the Central Universities(No.G2024WD0151)in part by the Tencent Foundation and XPLORER PRIZE.
摘要In this study,we present a deterministic convergence analysis of Gated Recurrent Unit(GRU)networks enhanced by a smoothing L1regularization technique.While GRU architectures effectively mitigate gradient vanishing/exploding issues in sequential modeling,they remain prone to overfitting,particularly under noisy or limited training data.Traditional L1regularization,despite enforcing sparsity and accelerating optimization,introduces non-differentiable points in the error function,leading to oscillations during training.To address this,we propose a novel smoothing L1regularization framework that replaces the non-differentiable absolute function with a quadratic approximation,ensuring gradient continuity and stabilizing the optimization landscape.Theoretically,we rigorously establish threekey properties of the resulting smoothing L1-regularizedGRU(SL1-GRU)model:(1)monotonic decrease of the error function across iterations,(2)weak convergence characterized by vanishing gradients as iterations approach infinity,and(3)strong convergence of network weights to fixed points under finite conditions.Comprehensive experiments on benchmark datasets-spanning function approximation,classification(KDD Cup 1999 Data,MNIST),and regression tasks(Boston Housing,Energy Efficiency)-demonstrate SL1-GRUs superiority over baseline models(RNN,LSTM,GRU,L1-GRU,L2-GRU).Empirical results reveal that SL1-GRU achieves 1.0%-2.4%higher test accuracy in classification,7.8%-15.4%lower mean squared error in regression compared to unregularized GRU,while reducing training time by 8.7%-20.1%.These outcomes validate the method’s efficacy in balancing computational efficiency and generalization capability,and they strongly corroborate the theoretical calculations.The proposed framework not only resolves the non-differentiability challenge of L1regularization but also provides a theoretical foundation for convergence guarantees in recurrent neural network training.
基金National Natural Science Foundation of China(No.62372100)。
摘要Owing to the constraints of depth sensing technology,images acquired by depth cameras are inevitably mixed with various noises.For depth maps presented in gray values,this research proposes a novel denoising model,termed graph-based transform(GBT)and dual graph Laplacian regularization(DGLR)(DGLR-GBT).This model specifically aims to remove Gaussian white noise by capitalizing on the nonlocal self-similarity(NSS)and the piecewise smoothness properties intrinsic to depth maps.Within the group sparse coding(GSC)framework,a combination of GBT and DGLR is implemented.Firstly,within each group,the graph is constructed by using estimates of the true values of the averaged blocks instead of the observations.Secondly,the graph Laplacian regular terms are constructed based on rows and columns of similar block groups,respectively.Lastly,the solution is obtained effectively by combining the alternating direction multiplication method(ADMM)with the weighted thresholding method within the domain of GBT.
基金Projects(U1562215,41674130,41404088)supported by the National Natural Science Foundation of ChinaProjects(2013CB228604,2014CB239201)supported by the National Basic Research Program of China+1 种基金Projects(2016ZX05027004-001,2016ZX05002006-009)supported by the National Oil and Gas Major Projects of ChinaProject(15CX08002A)supported by the Fundamental Research Funds for the Central Universities,China
摘要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.
摘要The presented iterative multiuser detection technique was based on joint deregularized and box-constrained solution to quadratic optimization with iterations similar to that used in the nonstationary Tikhonov iterated algorithm.The deregularization maximized the energy of the solution,which was opposite to the Tikhonov regularization where the energy was minimized.However,combined with box-constraints,the deregularization forced the solution to be close to the binary set.It further exploited the box-constrained dichotomous coordinate descent algorithm and adapted it to the nonstationary iterative Tikhonov regularization to present an efficient detector.As a result,the worst-case and average complexity are reduced down as K2.8 and K2.5 floating point operation per second,respectively.The development improves the "efficient frontier" in multiuser detection,which is illustrated by simulation results.In addition,most operations in the detector are additions and bit-shifts.This makes the proposed technique attractive for fixed-point hardware implementation.
基金supported in part by the National Natural Science Foundation of China under Grant-in-Aid 40574053the Program for New Century Excellent Talents in University of China (NCET-06-0602)the National 973 Key Basic Research Development Program (No.2007CB209601)
摘要In this paper we discuss the edge-preserving regularization method in the reconstruction of physical parameters from geophysical data such as seismic and ground-penetrating radar data. In the regularization method a potential function of model parameters and its corresponding functions are introduced. This method is stable and able to preserve boundaries, and protect resolution. The effect of regularization depends to a great extent on the suitable choice of regularization parameters. The influence of the edge-preserving parameters on the reconstruction results is investigated and the relationship between the regularization parameters and the error of data is described.
基金supported by the National Natural Science Foundation of China(11961044)the Doctor Fund of Lan Zhou University of Technologythe Natural Science Foundation of Gansu Provice(21JR7RA214)。
摘要In this paper,we consider the inverse problem for identifying the source term of the time-fractional equation with a hyper-Bessel operator.First,we prove that this inverse problem is ill-posed,and give the conditional stability.Then,we give the optimal error bound for this inverse problem.Next,we use the fractional Tikhonov regularization method and the fractional Landweber iterative regularization method to restore the stability of the ill-posed problem,and give corresponding error estimates under different regularization parameter selection rules.Finally,we verify the effectiveness of the method through numerical examples.
基金funded by Shell International Exploration and Production Inc.(PT45371)the National Natural Science Foundation of China-China National Petroleum Corporation Petrochemical Engineering United Fund(U1262114)the National Natural Science Foundation of China(41272163)
摘要Nuclear Magnetic inversion is the basis of NMR Resonance (NMR) T2 logging interpretation. The regularization parameter selection of the penalty term directly influences the NMR T2 inversion result. We implemented both norm smoothing and curvature smoothing methods for NMR T2 inversion, and compared the inversion results with respect to the optimal regular- ization parameters ((Xopt) which were selected by the dis- crepancy principle (DP), generalized cross-validation (GCV), S-curve, L-curve, and the slope of L-curve methods, respectively. The numerical results indicate that the DP method can lead to an oscillating or oversmoothed solution which is caused by an inaccurately estimated noise level. The (Xopt selected by the L-curve method is occa- sionally small or large which causes an undersmoothed or oversmoothed T2 distribution. The inversion results from GCV, S-curve and the slope of L-curve methods show satisfying inversion results. The slope of the L-curve method with less computation is more suitable for NMR T2 inversion. The inverted T2 distribution from norm smoothing is better than that from curvature smoothing when the noise level is high.
基金Project supported by the National Natural Science Foundation of China (Grant No. 40775023)
摘要According to the conclusion of the simulation experiments in paper I, the Tikhonov regularization method is applied to cyclone wind retrieval with a rain-effect-considering geophysical model function (called CMF+Rain). The CMF+Rain model which is based on the NASA scatterometer-2 (NSCAT2) GMF is presented to compensate for the effects of rain on cyclone wind retrieval. With the multiple solution scheme (MSS), the noise of wind retrieval is effectively suppressed, but the influence of the background increases. It will cause a large wind direction error in ambiguity removal when the background error is large. However, this can be mitigated by the new ambiguity removal method of Tikhonov regularization as proved in the simulation experiments. A case study on an extratropical cyclone of hurricane observed with SeaWinds at 25-km resolution shows that the retrieved wind speed for areas with rain is in better agreement with that derived from the best track analysis for the GMF+Rain model, but the wind direction obtained with the two-dimensional variational (2DVAR) ambiguity removal is incorrect. The new method of Tikhonov regularization effectively improves the performance of wind direction ambiguity removal through choosing appropriate regularization parameters and the retrieved wind speed is almost the same as that obtained from the 2DVAR.