Enhanced accuracy by post-processing for finite element methods for hyperbolic equations

We consider the enhancement of accuracy, by means of a simple post-processing technique, for finite element approximations to transient hyperbolic equations. The post-processing is a convolution with a kernel whose support has measure of order one in the case of arbitrary unstructured meshes; if the mesh is locally translation invariant, the support of the kernel is a cube whose edges are of size of the order of only. For example, when polynomials of degree are used in the discontinuous Galerkin (DG) method, and the exact solution is globally smooth, the DG method is of order in the -norm, whereas the post-processed approximation is of order ; if the exact solution is in only, in which case no order of convergence is available for the DG method, the post-processed approximation converges with order in , where is a subdomain over which the exact solution is smooth. Numerical results displaying the sharpness of the estimates are presented.

     

Retrospective intra-scan motion correction

This paper analyzes the effects of intra-scan motion and demonstrates the possibility of correcting them directly in k-space with a new automatic retrospective method. The method is presented for series of 2D acquisitions with Cartesian sampling. Using a reference k-space acquisition (corrected for translations) within the series, intra-scan motion parameters are accurately estimated for each trajectory in k-space of each data set in the series resulting in pseudo-random sample positions. The images are reconstructed with a Bayesian estimator that can handle sparse arbitrary sampling in k-space and reduces intra-scan rotation artefacts to the noise level. The method has been assessed by means of a Monte Carlo study on axial brain images for different signal-to-noise ratios. The accuracy of motion estimates is better than 0.1 degrees for rotation, and 0.1 and 0.05 pixel, respectively, for translation along the read and phase directions for signal-to-noise ratios higher than 6 of the signals on each trajectory. An example of reconstruction from experimental data corrupted by head motion is also given.     

Legendre integrators, post-processing and quasiequilibrium

A toolbox for the development and reduction of the dynamical models of nonequilibrium systems is presented. The main components of this toolbox are: Legendre integrators, dynamical post-processing, and the thermodynamic projector. The thermodynamic projector is the tool to transform almost any anzatz to a thermodynamically consistent model. The post-processing is the cheapest way to improve the solution obtained by the Legendre integrators. Legendre integrators give the opportunity to solve linear equations instead of nonlinear ones for quasiequilibrium (“maximum entropy”, MaxEnt) approximations. The essentially new element of this toolbox, the method of thermodynamic projector, is demonstrated on application to the FENE-P model of polymer kinetic theory. The multi-peak model of polymer dynamics is developed.     

A hybrid-stress element based on Hamilton principle

A novel hybrid-stress finite element method is proposed for constructing simple 4-node quadrilateral plane elements, and the new element is denoted as HH4-3fl here. Firstly, the theoretical basis of the traditional hybrid-stress elements, i.e., the Hellinger-Reissner variational principle, is replaced by the Hamilton variational principle, in which the number of the stress variables is reduced from 3 to 2. Secondly, three stress parameters and corresponding trial functions are introduced into the system equations. Thirdly, the displacement fields of the conventional bilinear isoparametric element are employed in the new models. Finally, from the stationary condition, the stress parameters can be expressed in terms of the displacement parameters, and thus the new element stiffness matrices can be obtained. Since the required number of stress variables in the Hamilton variational principle is less than that in the Hellinger-Reissner variational principle, and no additional incompatible displacement modes are considered, the new hybrid-stress element is simpler than the traditional ones. Furthermore, in order to improve the accuracy of the stress solutions, two enhanced post-processing schemes are also proposed for element HH4-3β. Numerical examples show that the proposed model exhibits great improvements in both displacement and stress solutions, implying that the proposed technique is an effective way for developing simple finite element models with high performance.     

结合机载LiDAR数据与航空可见光影像多层次规则分类建筑物变化检测

建议了一种结合Lidar点云与航空可见光影像的建筑物变化检测新方法,利用多层次规则分类算法解决这两种异元异构数据间建筑物变化检测难题。并建议了一种结合面积阈值的形态学后处理方法,从而形成一套完整的处理流程,可应用于实际生产。最终,利用中国吉林省长春市2010年机载LiDAR点云数据和2009年高分辨率航空影像对该方法的有效性进行了评价,通过与基于支持向量机(SVM)面向对象分类的建筑物变化检测算法比较,进一步对本研究建议的方法进行了验证与分析。结果显示,此方法效果理想,其精度优于基于SVM面向对象分类的建筑物变化检测方法。Kappa系数达到0.90,correctness达到0.87。     

Effects of including spatial information in clustering multivariate image data

Multivariate image data provide detailed information in variable and image space. Most traditional clustering methods are based on variable information only and ignore spatial information. A method based on both variable and spatial information could improve the results substantially.

In this review, we study the benefits and the pitfalls of including spatial information in chemometric clustering techniques. Spatial information is taken into account in initialization of clustering parameters, during cluster iterations by adjusting the similarity measure or at a post-processing step. We illustrate the effect of taking spatial information into account by a univariate synthetic data set and two real-world multivariate data sets. We show that methods that include neighboring pixel information in the clustering procedure improve the performance accuracy of the clustering in most cases. Homogeneous regions in the image are better recognized and the amount of noise is reduced by these methods.     

Parallel algorithm for training multiclass proximal Support Vector Machines

In this paper we describe a proximal Support Vector Machine algorithm for multiclassification problem by one-vs-all scheme. The computational requirement for the new algorithm is almost the same as training one of its element binary proximal Support Vector Machines. Low rank approximation is taken to reduce computational costs when the kernel matrix is too large. An error bound estimation for the approximated solution is given, which is used as a stopping criteria for low rank approximation. A post-processing strategy is developed to overcome the difficulty arising from unbalanced data and to improve the classification accuracy. A parallel implementation of the algorithm using standard MPI communication routines is provided to handle large-scale problems and to accelerate the training process. Experiment results on several public datasets validate the effectiveness of our proposed algorithm.     

Post-processing central k-space subtraction for high-resolution arterial peripheral MR angiography

Peripheral MR angiography requires high resolution and arterial contrast. Neither can be obtained simultaneously due to the short arterial phase of the contrast agent. To improve temporal resolution, keyhole imaging was developed, which combines high resolution and arterial k-spaces at the time of image acquisition. Here, a related approach is introduced for image post-processing in the Fourier domain. It is demonstrated that simple substitution of the central k-space with low-resolution data leads to severe distortion. Hence, a dedicated calculation scheme is necessary for composite k-space post-processing. A solution is presented for high-resolution arterial peripheral MR angiography that uses subtraction of venous intensities from the central high-resolution k-space. The calculations in the Fourier domain do not require interpolations between the different resolutions. High-resolution steady-state MR angiography, which exhibits contrast-enhanced arteries and veins at an isotropic resolution of 0.65 mm, and standard resolution arterial first-pass MR angiography were combined to obtain images with the resolution of the steady-state images and arterial contrast. Numerical simulations on software phantoms are presented. The operation of the method is demonstrated in five patients.