The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition

In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.

An improved four-dimensional variation source term inversion model with observation error regularization

Aiming at the Four-Dimensional Variation source term inversion algorithm proposed earlier,the observation error regularization factor is introduced to improve the prediction accuracy of the diffusion model,and an improved Four-Dimensional Variation source term inversion algorithm with observation error regularization(OER-4DVAR STI model)is formed.Firstly,by constructing the inversion process and basic model of OER-4DVAR STI model,its basic principle and logical structure are studied.Secondly,the observation error regularization factor estimation method based on Bayesian optimization is proposed,and the error factor is separated and optimized by two parameters:error statistical time and deviation degree.Finally,the scientific,feasible and advanced nature of the OER-4DVAR STI model are verified by numerical simulation and tracer test data.The experimental results show that OER-4DVAR STI model can better reverse calculate the hazard source term information under the conditions of high atmospheric stability and flat underlying surface.Compared with the previous inversion algorithm,the source intensity estimation accuracy of OER-4DVAR STI model is improved by about 46.97%,and the source location estimation accuracy is improved by about 26.72%.

Regularization Methods to Approximate Solutions of Variational Inequalities

In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regularization methods to approximate solutions of following variational inequalities: and with operator A being monotone hemi-continuous form real Banach reflexive X into its dual space X*, but instead of knowing the exact data (y0, A), we only know its approximate data satisfying certain specified conditions and D is a nonempty convex closed subset of X;the real function f defined on X is assumed to be lower semi-continuous, convex and is not identical to infinity. At the same time, we will evaluate the convergence rate of the approximate solution. The regularization methods here are different from the previous ones.

Finite Time Ruin Probability with Variable Interest Rate and Extended Regular Variation

Consider an insurance risk model, in which the surplus process satisfies a recursive equationU n =U n?1(1+r n )?X n forn≥1, whereU 0=x≥0 is the initial surplus, {r n ;n≥1} the interest rate sequence, {X n ;n≥1} the sequence of i. i. d. real-valued random variables with common distribution functionF, which denotes the gross loss during thenth year. We investigate the ruin probability within a finite time horizon and give the asymptotic result asx→∞. Key words variable interest rate - extend regular variation - finite time ruin probability CLC number O 211.9 Foundation item: Supported by the National Natural Science Foundation of China (10071058, 70273029)Biography: WEI Xiao (1979-), female, Ph. D candidate, research direction: large deviations and its applications, insurance mathematics.

Variational regularization method of solving the Cauchy problem for Laplace's equation: Innovation of the Grad–Shafranov(GS) reconstruction

The simplified linear model of Grad-Shafranov （GS） reconstruction can be reformulated into an inverse boundary value problem of Laplace＇s equation. Therefore, in this paper we focus on the method of solving the inverse boundary value problem of Laplace＇s equation. In the first place, the variational regularization method is used to deal with the ill- posedness of the Cauchy problem for Laplace＇s equation. Then, the ＇L-Curve＇ principle is suggested to be adopted in choosing the optimal regularization parameter. Finally, a numerical experiment is implemented with a section of Neumann and Dirichlet boundary conditions with observation errors. The results well converge to the exact solution of the problem, which proves the efficiency and robustness of the proposed method. When the order of observation error δ is 10-1, the order of the approximate result error can reach 10-3.

Variational assimilation in combination with a regularization method for sea level pressure retrieval from QuikSCAT scatterometer data Ⅱ:simulation experiment and actual case study

The sea level pressure field can be computed from sea surface winds retrieved from satellite microwave scatterometer measurements, based on variational assimilation in combination with a regularization method given in part I of this paper. First, the validity of the new method is proved with a simulation experiment. Then, a new processing procedure for the sea level pressure retrieval is built by combining the geostrophic wind, which is computed from the scatterometer 10-meter wind using the University of Washington planetary boundary layer model using this method. Finally, the feasibility of the method is proved using an actual case study.

Variational assimilation in combination with the regularization method for sea level pressure retrieval from QuikSCAT scatterometer data I:Theoretical frame construction

A new method of constructing a sea level pressure field from satellite microwave scatterometer measurements is presented. It is based on variational assimilation in combination with a regularization method using geostrophic vorticity to construct a sea level pressure field from scatterometer data that are given in this paper, which offers a new idea for the application of scatterometer measurements. Firstly, the geostrophic vorticity from the scatterometer data is computed to construct the observation field, and the vorticity field in an area and the sea level pressure on the borders are assimilated. Secondly, the gradient of sea level pressure （semi-norm） is used as the stable functional to educe the adjoint system, the adjoint boundary condition and the gradient of the cost functional in which a weight parameter is introduced for the harmony of the system and the Tikhonov regularization techniques in inverse problem are used to overcome the ill-posedness of the assimilation. Finally, the iteration method of the sea level pressure field is developed.

Parameter Optimization of Regularization Variational Merging and Its Application in GNSS/MET Water Vapor

The paper discusses the core parameters of the 3 D and 4 D variational merging based on L1 norm regularization,namely optimization characteristic correlation length of background error covariance matrix and regularization parameter. Classical 3 D/4 D variational merging is based on the theory that error follows Gaussian distribution. It involves the solution of the objective functional gradient in minimization iteration,which requires the data to have continuity and differentiability. Classic 3 D/4 D-dimensional variational merging method was extended,and L1 norm was used as the constraint coupling to the classical variational merged model. Experiment was carried out by using linear advection-diffusion equation as four-dimensional prediction model,and parameter optimization of this method is discussed. Considering the strong temporal and spatial variation of water vapor,this method is further applied to the precipitable water vapor( PWV) merging by calculating reanalysis data and GNSS retrieval.Parameters were adjusted gradually to analyze the influence of background field on the merging result,and the experiment results show that the mathematical algorithm adopted in this paper is feasible.

A Hybrid Regularization-Based Multi-Frame Super-Resolution Using Bayesian Framework

The prime purpose for the image reconstruction of a multi-frame super-resolution is to reconstruct a higher-resolution image through incorporating the knowledge obtained from a series of relevant low-resolution images,which is useful in numerousfields.Nevertheless,super-resolution image reconstruction methods are usually damaged by undesirable restorative artifacts,which include blurring distortion,noises,and stair-casing effects.Consequently,it is always challenging to achieve balancing between image smoothness and preservation of the edges inside the image.In this research work,we seek to increase the effectiveness of multi-frame super-resolution image reconstruction by increasing the visual information and improving the automated machine perception,which improves human analysis and interpretation processes.Accordingly,we propose a new approach to the image reconstruction of multi-frame super-resolution,so that it is created through the use of the regularization framework.In the proposed approach,the bilateral edge preserving and bilateral total variation regularizations are employed to approximate a high-resolution image generated from a sequence of corresponding images with low-resolution to protect significant features of an image,including sharp image edges and texture details while preventing artifacts.The experimental results of the synthesized image demonstrate that the new proposed approach has improved efficacy both visually and numerically more than other approaches.

Seismic high-resolution processing method based on spectral simulation and total variation regularization constraints

There is little low-and-high frequency information on seismic data in seismic exploration,resulting in narrower bandwidth and lower seismic resolution.It considerably restricts the prediction accuracy of thin reservoirs and thin interbeds.This study proposes a novel method to constrain improving seismic resolution in the time and frequency domain.The expected wavelet spectrum is used in the frequency domain to broaden the seismic spectrum range and increase the octave.In the time domain,the Frobenius vector regularization of the Hessian matrix is used to constrain the horizontal continuity of the seismic data.It eff ectively protects the signal-to-noise ratio of seismic data while the longitudinal seismic resolution is improved.This method is applied to actual post-stack seismic data and pre-stack gathers dividedly.Without abolishing the phase characteristics of the original seismic data,the time resolution is signifi cantly improved,and the structural features are clearer.Compared with the traditional spectral simulation and deconvolution methods,the frequency distribution is more reasonable,and seismic data has higher resolution.

ON THE REGULARITY OF THE MINIMUM SOLUTION OF THE RESTRAINED VARIATIONAL PROBLEMS

This paper is concerned with the regularity of minimum solution u of the following functional L(u) = integral(Omega) a alpha(beta)(x)g(ij)(u)D alpha u(i)D(beta)upsilon(i)dx on the restraint E = {u is an element of W-0(1,2) (Omega, R(N))\parallel to u parallel to L(D) = 1}. Under appropriate conditions, the bounded minimum solution u of the above functional is proved to be nothing but Holder continuous.

基于复合正则化的稀疏SAR成像方法研究

随着高分辨率对地观测要求的不断提高,合成孔径雷达(Synthetic Aperture Radar,SAR)的应用将越来越广泛。针对高分辨率SAR成像存在数据量大、存储难度高、计算时间长等问题,目前常用的解决方法是在SAR成像模型中引入压缩感知(Compressed Sensing,CS)的方法降低采样率和数据量。通常使用单一的正则化作为约束条件,可以抑制点目标旁瓣,实现点目标特征增强,但是观测场景中可能存在多种目标类型,因此使用单一正则化约束难以满足多种特征增强的要求。本文提出了一种基于复合正则化的稀疏高分辨SAR成像方法,通过压缩感知降低数据量,并使用多种正则化的线性组合作为约束条件,增强观测场景中不同类型目标的特征,实现复杂场景中高分辨率对地观测的要求。该方法在稀疏SAR成像模型中引入非凸正则化和全变分(Total Variation,TV)正则化作为约束条件,减小稀疏重构误差、增强区域目标的特征,降低噪声对成像结果的影响,提高成像质量;采用改进的交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)实现复合正则化约束的求解,减少计算时间、快速重构图像;使用方位距离解耦算子代替观测矩阵及其共轭转置,进一步降低计算复杂度。仿真和实测数据实验表明,本文所提算法可以对点目标和区域目标进行特征增强,减小计算复杂度,提高收敛性能,实现快速高分辨的图像重构。

基于GRACE星间重力位差的Slepian局部地表质量变化反演法

根据Slepian基函数在频域和空域的局部集中特性,建立了利用GRACE星间重力位差(GPD)估计局部地表质量变化的Slepian基函数反演模型及病态问题求解算法,并以亚马逊流域的陆地水储量变化(TWSC)反演为例,评估了反演方法的精度和有效性.首先,通过闭环数值模拟比较了Slepian基函数法(GPD SBF)、基于GPD的mascon方法(GPD Mascon)和球谐系数法(GPD SH)反演2005年亚马逊流域TWSC的性能,结果表明:Slepian基函数法通过限定信号的频域和空域范围,降低了反演过程中向下延拓带来的不确定性,有效削弱了法方程求解的病态性,其解算结果的稳定性明显优于GPD Mascon;GPD SBF的反演精度及可靠性总体上优于GPD Mascon和GPD SH,并且能够更好地恢复边缘区域的信号和减小泄漏误差的影响.其次,利用实测的GRACE GPD数据反演了2004—2015年亚马逊流域的TWSC时间序列,结果显示:GPDSBF相比GPDMascon反演的TWSC与官方mascon模型(CSR、JPL和GSFC RL06 mascon)更为一致,并且GPD SBF反演结果呈现出更多的空间细节和更好的信噪比.最后,利用不同GRACE反演结果计算的(TWSC的一阶导数)和水文气象数据(GPCP降水、ERA5蒸散发)由水量平衡方程估计了亚马逊流域Obidos水文站的月平均径流量,并采用测站的实测径流量进行检验,结果表明:GPD SBF和GPD Mascon估计的径流量与实测值扣除季节性信号后的差值STD分别为12.35 mm和14.54 mm,相关系数分别为0.71和0.69,并且GPD SBF和各种官方mascon模型估计的径流量与实测径流量更为接近.本文研究证明Slepian基函数法可削弱病态问题求解对正则化约束的依赖,其比传统的GPD Mascon解算精度和可靠性更高,为反演高精度、高分辨率的局部地表质量变化提供了一种新的解决方案.

余庆县2011—2022年农区鼠种组成与种群数量变化

探讨鼠种组成及种群数量变化规律,为农区鼠类预测预报及科学防控提供参考依据。对贵州省余庆县2011—2022年住宅区、稻田区、旱作区鼠情进行监测分析。结果表明,所捕获的3492只样本隶属2目(啮齿目、食虫目)2科(鼠科、鼩鼱科)10种,即黑线姬鼠、褐家鼠、黄胸鼠、小家鼠、高山姬鼠、社鼠、针毛鼠、白腹鼠、红耳巢鼠、鼩鼱。住宅区鼠种种类有3种,以褐家鼠为优势种,占总鼠数的88.57%;稻田区、早作区鼠种种类有10种,以黑线姬鼠为优势种,平均占总鼠数的83.42%。不同时期鼠种组成明显不同,住宅区褐家鼠、稻田区和早作区黑线姬鼠是当地监测和防治的主要对象。与当地1986—2010年相比,鼠类种群数量呈明显下降趋势,总平均捕获率为4.79%,其中,住宅区、稻田区、早作区平均捕获率分别为0.24%、6.35%、5.48%。不同年度、月份、季节鼠类种群数量存在明显差异。

基于VB-EKF的GPS/INS松组合导航定位算法

针对应用在无人机(Unmanned Aerial Vehicle,UAV)中的全球定位系统/惯性导航系统(GPS/INS)松组合导航非线性系统受到外界噪声干扰导致量测噪声在滤波时不断变化,从而造成滤波精度下降等问题,提出一种变分贝叶斯扩展卡尔曼滤波(VB-EKF)算法。该算法利用EKF(Extended Kalman Filter)将非线性系统中的状态函数和量测函数展开为线性方程,并将两个不同的导航系统数据进行融合,避免了单系统导航定位发散的问题。考虑到组合系统中量测噪声的时变特性,引入变分贝叶斯算法进行改进,有效解决了系统滤波精度下降问题。仿真结果表明,VB-EKF较EKF算法可有效提高滤波稳定性,进而提高系统导航定位精度。

一种基于稀疏重构的多视角MIMO雷达关联成像算法研究

为改善复杂目标的成像表现、提升雷达图像的视觉效果,提出一种基于稀疏重构的多视角多输入多输出(multiple input multiple output,MIMO)雷达关联成像方法,设计了多视角雷达散射面积(radar cross section,RCS)起伏的稀疏重构关联成像模型。所提算法能提高辐射场信号随机性,改善复杂目标雷达关联成像参考信号与回波之间相关性退化的情况,减小多视角RCS起伏对相关性的影响,提升多视角下的关联成像质量。最后,通过仿真验证了所提方法的有效性。

基于超拉普拉斯正则化的冲击波超压层析重建

超压层析成像是利用传感器采集到的冲击波信号来反演测试区域的超压分布,是典型的不完全数据重建问题,为了提高求解精度,本文提出了一种基于高斯牛顿迭代联合超拉普拉斯正则化的冲击波超压层析重建方法。由于实际采集到的冲击波信号通常与干扰信号混叠在一起,会影响超压值的测量精度,本文首先采用改进的小波阈值算法对冲击波信号进行去噪处理;其次利用超拉普拉斯先验对图像边缘和二维层析模型进行正则约束;然后采用高斯牛顿迭代算法和交替方向乘子算法,解决大型病态稀疏矩阵的求解问题。实际实验结果表明本文的正则化方法与传统的全变分正则化和广义全变分正则化相比,重建精度可保持在15%左右,在实际场景中具有一定的应用价值。

基于一维变分法的微波辐射计反演边界层温湿廓线

地基微波辐射计能够克服星载遥感对低层大气不敏感的缺点,在边界层大气探测方面更具优势.一维变分反演算法考虑了辐射传输过程等物理机制,在应用于微波辐射计的反演时具有很高的可信度.针对微波辐射计信息含量较低以及一维变分算法收敛率不高等问题,提出利用地面气象要素改进算法在近地面层的反演精度和引入正则化算子提升算法的收敛特性.利用探空数据对上述改进方法的提升效果进行验证,结果表明:地面气象要素的引入使得反演算法在地表温湿度的均方根误差分别降低了78.2%和55.5%,对于上层大气温湿廓线也有小幅提升;正则化算子对算法的反演时间和反演精度影响很小,但是可以显著地减少未收敛样本个数和提升反演廓线的质量.

CFSv2对浙江省延伸期逐日降水预报性能评估及解释应用初探

利用CFSv2长序列回报资料和近6 a实时预报数据,系统分析了模式对浙江短中期(Short-medium Range,SMR,1~10 d)和延伸期(Extended Range,ER,11~30 d)逐日降水的预测性能,并基于系统误差订正(Systematic Bias Correction,SBC)技术开展了解释应用。结果表明:(1)模式回报技巧在SMR时段快速衰减,而在ER时段的衰减明显趋缓;SMR时段的相关系数远高于ER时段,但这两个时段的均方根误差较为接近;(2)从季节演变来看,模式技巧在秋冬季较高而在春夏季相对较低;(3)模式回报结果表现出显著的系统性偏差,这一偏差在各个起报日(提前1~30 d起报)中稳定存在,采用SBC技术开展解释应用,发现订正后模式的回报技巧在ER时段显著提升;(4)进一步将SBC技术应用于实时预报,发现实时预报的技巧也得到了一定的改善,且ER时段的改进效果更为显著。

变分分数阶PDE的自适应图像保边缘去噪方法

为了优化图像去噪过程中的边缘保真问题,本文以ROF模型及其改进模型为基础,以分数阶变分偏微分方程方法为工具,通过构造自适应的边缘检测函数,提出了一种能更好地保护图像的边缘特征,有利于纹理细节保持和“阶梯效应”抑制的基于自适应分数阶变分PDE的图像去噪模型,并以标准图像测试了新模型的去噪效果。实验结果表明:与同类方法相比,新方法可以更加有效地提高图像的信噪比;从去噪前后的图像差可以看出,新方法在去噪的同时更好地保护了图像的边缘特征及纹理细节信息。文中提出的方法可以用于遥感成像、医学图像处理及地震图像处理等领域。