We find low order approximations to the spherical nonreflecting boundary kernel for the wave equation in three dimensions. First we express the Laplace transform of the kernel as a rational function by solving for the zeros of a modified Bessel function. Then we formulate a linear time-invariant dynamical system whose transfer function is this rational function. Finally we use the Balanced Trun...

Histograms are ubiquitous tools in numerous machine learning and computer vision tasks. It is common practice to use distances such as L2 for comparing histograms. This practice assumes that the histogram domains are aligned. However this assumption is violated through quantization, shape deformation, light changes, etc. The Earth Mover’s Distance (EMD) [12] is a cross-bin distance that address...

I apply the iterative hyperbolic Radon transform to CMP gathers to create a velocity panel where multiples and primaries are separable. The velocity panel is created using three different inversion schemes: (1) l2 norm inversion, (2) l1 norm inversion and (3) l1 norm with l1 regularization inversion. The third technique is particularly efficient at separating primaries and multiples in the pres...

*Correspondence: [email protected] School of Mathematical Science, Qufu Normal University, Jingxuanxi Road 57, Qufu, Shandong 273165, P.R. China Abstract One class of singular integral equations of convolution type with Hilbert kernel is studied in the space L2[–π ,π ] in the article. Such equations can be changed into either a system of discrete equations or a discrete jump problem depending o...

Abstract: A complete characterization is given of closed shift-invariant subspaces of L2(IR) which provide a specified approximation order. When such a space is principal (i.e., generated by a single function), then this characterization is in terms of the Fourier transform of the generator. As a special case, we obtain the classical Strang-Fix conditions, but without requiring the generating f...

We present a group-theoretical derivation of the continuous wavelet transform (CWT) on the 2-sphere S2, based on the construction of coherent states associated to square integrable group representations. The parameter space X is the product of SO(3) x J&, embedded into the Lorentz group S00(3, 1) via the Iwasawa decomposition, and X Y SO,(3,1)/C. The space L2(S2, a!~) carries a unitary irreduci...

A preconditioning procedure is developed for the L2 and more general optimal transport problems. The procedure is based on a family of affine map pairs which transforms the original measures into two new measures that are closer to each other while preserving the optimality of solutions. It is proved that the preconditioning procedure minimizes the remaining transportation cost among all admiss...

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d ≥ 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their anti...

This paper aims to develop simple statistical methods for indexing into an aerial image database using a cartographic model. The images contain severe distortions due to the acquisition process and the data cannot be recovered by applying a simple Euclidean transform to the model. The underlying representation of the infra-red image map within the database is based on histograms of line-segment...

A preconditioning procedure is developed for the L2 and more general optimal 3 transport problems. The procedure is based on a family of affine map pairs which transforms the 4 original measures into two new measures that are closer to each other, while preserving the optimality 5 of solutions. It is proved that the preconditioning procedure minimizes the remaining transportation 6 cost among a...