Related papers: Analysis of scattered higher dimensional data usin…
This paper presents a fast wavefield evaluation method for two-dimensional wave scattering problems. The proposed method is based on a modified version of proxy-surface-accelerated interpolative decomposition, making it effective even if…
An important problem in applications is the approximation of a function $f$ from a finite set of randomly scattered data $f(x_j)$. A common and powerful approach is to construct a trigonometric least squares approximation based on the set…
This paper describes a very efficient algorithm for image signal extrapolation. It can be used for various applications in image and video communication, e.g. the concealment of data corrupted by transmission errors or prediction in video…
In mesh-based numerical simulations, the interpolation of mesh-defined functions across different meshes is a critical task, and achieving high-precision interpolation is of great significance for improving the computational efficiency and…
The increasing complexity of the power grid, due to higher penetration of distributed resources and the growing availability of interconnected, distributed metering devices re- quires novel tools for providing a unified and consistent view…
Scattered data fitting is a frequently encountered problem for reconstructing an unknown function from given scattered data. Radial basis function (RBF) methods have proven to be highly useful to deal with this problem. We describe two…
We propose computationally efficient methods for estimating stationary multivariate spatial and spatial-temporal spectra from incomplete gridded data. The methods are iterative and rely on successive imputation of data and updating of model…
The purpose of this paper is to introduce a very efficient algorithm for signal extrapolation. It can widely be used in many applications in image and video communication, e. g. for concealment of block errors caused by transmission errors…
Spectral methods for solving partial differential equations (PDEs) and stochastic partial differential equations (SPDEs) often use Fourier or polynomial spectral expansions on either uniform and non-uniform grids. However, while very widely…
Detrend fluctuation analysis (DFA) has become a choice method for effective analysis of a broad variety of nonstationary signals. We show in the present article that, provided the nonstationary fluctuations occur at a large enough time…
Calculating dynamical diffraction patterns for X-ray topography and similar x-ray scattering-imaging techniques require the numerical integration of the Takagi-Taupin equations. This is usually performed with a simple second order finite…
A set of semi-analytical techniques based on Fourier analysis is used to solve wave scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are newly developed conformal mapping…
Spectral Method is a commonly used scheme to cluster data points lying close to Union of Subspaces by first constructing a Random Geometry Graph, called Subspace Clustering. This paper establishes a theory to analyze this method. Based on…
Scatterplots provide a visual representation of bivariate data (or 2D embeddings of multivariate data) that allows for effective analyses of data dependencies, clusters, trends, and outliers. Unfortunately, classical scatterplots suffer…
The manifold scattering transform is a deep feature extractor for data defined on a Riemannian manifold. It is one of the first examples of extending convolutional neural network-like operators to general manifolds. The initial work on this…
We investigate phaseless inverse scattering problem for the Schr\"odinger equation and develop reconstruction methods based on the inverse Born series (IBS). We consider three types of phaseless data: the far-field total field, the total…
We continue our study of scattering theory and dispersive properties for one-dimensional charge transfer models, namely linear Schr\"odinger equations with multiple moving potentials. By the discovery of a refined structure of the…
This paper introduces a method for spatial interpolation of extreme values, and in particular targets the case in which conventional data, resulting from a measurement for example, are available at only a few locations. To overcome this the…
We advocate a compressed sensing strategy that consists of multiplying the signal of interest by a wide bandwidth modulation before projection onto randomly selected vectors of an orthonormal basis. Firstly, in a digital setting with random…
This paper is concerned with a rate-distortion theory for sequences of i.i.d. random variables with general distribution supported on general sets including manifolds and fractal sets. Manifold structures are prevalent in data science,…