Locally and globally uniform approximations for ruin probabilities of a nonstandard bidimensional risk model with subexponential claims

Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.

Remote Sensing Image Fusion Using Bidimensional Empirical Mode Decomposition and the Least Squares Theory

Due to the data acquired by most optical earth observation satellite such as IKONOS, QuickBird-2 and GF-1 consist of a panchromatic image with high spatial resolution and multiple multispectral images with low spatial resolution. Many image fusion techniques have been developed to produce high resolution multispectral image. Considering panchromatic image and multispectral images contain the same spatial information with different accuracy, using the least square theory could estimate optimal spatial information. Compared with previous spatial details injection mode, this mode is more accurate and robust. In this paper, an image fusion method using Bidimensional Empirical Mode Decomposition (BEMD) and the least square theory is proposed to merge multispectral images and panchromatic image. After multi-spectral images were transformed from RGB space into IHS space, next I component and Panchromatic are decomposed by BEMD, then using the least squares theory to evaluate optimal spatial information and inject spatial information, finally completing fusion through inverse BEMD and inverse intensity-hue-saturation transform. Two data sets are used to evaluate the proposed fusion method, GF-1 images and QuickBird-2 images. The fusion images were evaluated visually and statistically. The evaluation results show the method proposed in this paper achieves the best performance compared with the conventional method.

A novel oil spill detection method from synthetic aperture radar imageries via a bidimensional empirical mode decomposition

Oil spills pose a major threat to ocean ecosystems and their health. Synthetic aperture radar（SAR） sensors can detect oil spills on the sea surface. These oil spills appear as dark spots in SAR images. However, dark formations can be caused by a number of phenomena. It is aimed to distinguishing oil spills or look-alike objects. A novel method based on a bidimensional empirical mode decomposition is proposed. The selected dark formations are first decomposed into several bidimensional intrinsic mode functions and the residue. Subsequently, 64 dimension feature sets are calculated using the Hilbert spectral analysis and five new features are extracted with a relief algorithm. Mahalanobis distances are then used for classification. Three data sets containing oil spills or look-alikes are used to test the accuracy rate of the method. The accuracy rate is more than 90%. The experimental results demonstrate that the novel method can detect oil spills validly and accurately.

A fusion algorithm for remote sensing images based on nonsubsampled pyramids and bidimensional empirical decomposition

In order to improve the quality of remote sensing image fusion,a new method combining nonsubsampled Laplacian pyramid (NLP)and bidimensional empirical mode decomposition(BEMD)is proposed.First,the high resolution panchromatic image (PAN)is decomposed using NLP until the approximate component and the low resolution multispectral image(MS)contain features with a similar scale.Then,the approximation component and the MS are decomposed by BEMD,resulting in a number of bidimensional intrinsic mode functions(BIMF)and a residue respectively.The instantaneous frequency is computed in 4 directions of the BIMFs.Considering the positive or negative coefficients in the corresponding position,a weighted algorithm is designed for fusing the high frequency details using the instantaneous frequency and the coefficient absolute value of the BIMFs as fusion feature.The fused image is then obtained through inverse BEMD and NLP.Experimental results have illustrated the advantage of this method over the IHS,DWT andà-Trous wavelet in both spectral and spatial detail qualities.

Relative vibration identification of cutter and workpiece based on improved bidimensional empirical mode decomposition

In the process of cutting,the relative vibration between the cutter and the workpiece has an important effect on the surface topography.In this study,the bidimensional empirical mode decomposition(BEMD)method is used to identify such effect.According to Riesz transform theory,a type of isotropic monogenic signal is proposed.The boundary data is extended on the basis of a similarity principle that deals with serious boundary effect problem.The decomposition examples show that the improved BEMD can effectively solve the problem of boundary effect and decompose the original machined surface topography at multiple scales.The characteristic surface topography representing the relative vibration between the cutter and the workpiece through feature identification is selected.In addition,the spatial spectrum analysis of the extracted profile is carried out.The decimal part of the frequency ratio that has an important effect on the shape of the contour can be accurately identified through contour extraction and spatial spectrum analysis.The decomposition results of simulation and experimental surface morphology demonstrate the validity of the improved BEMD algorithm in realizing the relative vibration identification between the cutter and the workpiece.

Two-Dimensional Continuous Model in Bimolecular Reactive Transport

In this work, a continuum 2D model is proposed to study the interaction at the interface of reactive transport processes in porous media. The analysis of the segregation produced by poor reactant homogenization at the poral scale is addressed by a parametric heuristic model that considers the relative gradient of the reacting species involved in the process. The micro inhomogeneities are incorporated by means of longitudinal and transversal mechanical dispersion coefficients. A two-dimensional continuous model for the bimolecular reactive transport is considered where modelling parameters are estimated numerically from experimental data. A competitive effect between segregation and dispersion is observed that is analyzed by means of numerical experiments. The two-dimensional model reproduces properly both the total mass of the product as well as its increase with the velocity of flow and the inhomogeneity of the advanced front. The methodology used is simple and fast, and the numerical results presented here indicate its effectiveness.

Refined Spatialization of 10-Day Precipitation in China Based on GPM IMERG Data and Terrain Decomposition Using the BEMD Algorithm

Continuous high spatial-resolution 10-day precipitation data are essential for crop growth services and phenological research.In this study,we first use the bidimensional empirical mode decomposition(BEMD)algorithm to decompose the digital elevation model(DEM)data and obtain high-frequency(OR3),intermediate-frequency(OR5),and low-frequency(OR8)margin terrains.Then,we propose a refined precipitation spatialization model,which uses ground-based meteorological observation data,integrated multi-satellite retrievals for global precipitation measurement(GPM IMERG)satellite precipitation products,DEM data,terrain decomposition data,prevailing precipitation direction(PPD)data,and other multisource data,to construct China's high-resolution 10-day precipitation data from2001 to 2018.The decomposition results show mountainous terrain from fine to coarse scales;and the influences of altitude,slope,and aspect on precipitation are better represented in the model after topography is decomposed.Moreover,terrain decomposition data can be added to the model simulation to improve the quality of the simulation product;the simulation quality of the model in summer is better than that in spring and autumn,and is relatively poor in winter;and OR5 and OR8 can be improved in the simulation,with better OR5 and OR8 dynamically selected.In addition,preprocessing the data before precipitation spatialization is particularly important.For example,adding 0.01to the 0 value of precipitation,multiplying the small value of precipitation less than 1 by 10,and performing the normal distributions transform(e.g.,Yeo–Johnson)on the data can improve the simulation quality.

Construction of wavelet bases with hexagonal symmetry

A new method of the construction of bidimensional wavelet bases is presented. An example of orthonormal bases of compactly supported bidimensional wavelets with hexagonal symmetry is given.