Related papers: Stability and Robustness of RBF Interpolation
The paper is concerned with classic kernel interpolation methods, in addition to approximation methods that are augmented by gradient measurements. To apply kernel interpolation using radial basis functions (RBFs) in a stable way, we…
Flux calibration of spectra in reverberation mapping (RM) is most often performed by assuming the flux constancy of some specified narrow emission lines, which stem from an extended region that is sometimes partially spatially resolved, in…
Rotation measure synthesis allows the estimation of Faraday dispersion via a Fourier transform and is the primary tool to probe cosmic magnetic fields. We show this can be considered mathematically equivalent to the one dimensional…
Modeling real-world distributions can often be challenging due to sample data that are subjected to perturbations, e.g., instrumentation errors, or added random noise. Since flow models are typically nonlinear algorithms, they amplify these…
We study algorithms to estimate geometric properties of raw point cloud data through implicit surface representations. Given that any level-set function with a constant level set corresponding to the surface can be used for such…
Recent developments have made it possible to overcome grid-based limitations of finite difference (FD) methods by adopting the kernel-based meshless framework using radial basis functions (RBFs). Such an approach provides a meshless…
We present two developments for the numerical integration of a function over the Brillouin zone. First, we introduce a nonuniform grid, which we refer to as the Farey grid, that generalizes regular grids. Second, we introduce…
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered datasets in d-dimensional space. It is non-separable approximation, as it is…
This paper presents an innovative set of tools to support a methodology for the multichannel interpolation (MCI) of a discrete signal. It is shown that a bandlimited signal $f$ can be exactly reconstructed from finite samples of $g_k$…
The basic principle of astronomical interferometry is to derive the angular distribution of radiation in the sky from the Fourier transform of the electric field on the ground. What is so special about the Fourier transform? Nothing, it…
Fourier transform is applied to annular beams of simplified flat two-level geometry: bright outer ring with a darker core. The pattern of focal beam profile (i.e. far field) is calculated and characterized with respect of its intensity…
In image reconstruction there are techniques that use analytical formulae for the Radon transform to recover an image from a continuum of data. In practice, however, one has only discrete data available. Thus one often resorts to sampling…
Recently, in [Electronic Transaction on Numerical Analysis, 41 (2014), pp. 420-442] authors introduced a new class of rational cubic fractal interpolation functions with linear denominators via fractal perturbation of traditional…
This paper provides a general introduction to the problem of image reconstruction from interferometric data. A simple model of the interferometric observables is given and the issues arising from sparse Fourier data are discussed. The…
Hybrid methods for simulating rarefied gas flows reduce computational cost by coupling a particle-based model, typically the direct simulation Monte Carlo (DSMC) method, to a continuum-based solver, i.e. a computational fluid dynamics (CFD)…
To obtain the initial pressure from the collected data on a planar sensor arrangement in Photoacoustic tomography, there exists an exact analytic frequency domain reconstruction formula. An efficient realization of this formula needs to…
In interpretation of remote sensing images, it is possible that some images which are supplied by different sensors become incomprehensible. For better visual perception of these images, it is essential to operate series of pre-processing…
We consider different norms for the Radon transform $Rf$ of a function $f$ and investigate under which conditions they can be estimated from above or below by some standard norms for $f$. We define Fourier-based norms for $Rf$ which can be…
In this paper two common collocation approaches based on radial basis functions have been considered; one be computed through the integration process (IRBF) and one be computed through the differentiation process (DRBF). We investigated the…
A method is presented for estimating the background at a given location on a sky map by interpolating the estimated background from a set of concentric annuli which surround this location. If the background is nonuniform but smoothly…