Related papers: Multifractal Interpolation of Universal Multifract…
Multifractal analysis has become a powerful signal processing tool that characterizes signals or images via the fluctuations of their pointwise regularity, quantified theoretically by the so-called multifractal spectrum. The practical…
A multilevel kernel-based interpolation method, suitable for moderately high-dimensional function interpolation problems, is proposed. The method, termed multilevel sparse kernel-based interpolation (MLSKI, for short), uses both level-wise…
Motivated by polynomial approximations of differential forms, we study analytical and numerical properties of a polynomial interpolation problem that relies on function averages over interval segments. The usage of segment data gives rise…
In this article, we investigate partial integrals and partial derivatives of bivariate fractal interpolation functions. We prove also that the mixed Riemann-Liouville fractional integral and derivative of order $\gamma = (p, q); p > 0,q >…
We prove a.s. (almost sure) unisolvency of interpolation by continuous random sampling with respect to any given density, in spaces of multivariate a.e. (almost everywhere) analytic functions. Examples are given concerning polynomial and…
We investigate an interpolation/extrapolation method that, given scattered observations of the Fourier transform, approximates its inverse. The interpolation algorithm takes advantage of modelling the available data via a shape-driven…
We consider non-linear generalizations of fractal interpolating functions applied to functions of one and two variables. The use of such interpolating functions in resizing images is illustrated.
We present here an overview of the history, applications and important properties of a function which we refer to as the Levy integral. For certain values of its characteristic parameter the Levy integral defines the symmetric Levy stable…
Multilinear interpolation is a powerful tool used in obtaining strong type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear…
Texture characterization is a central element in many image processing applications. Multifractal analysis is a useful signal and image processing tool, yet, the accurate estimation of multifractal parameters for image texture remains a…
This paper examines the wavelet multiplicity function. An explicit formula for the multiplicity function is derived. An application to operator interpolation is then presented. We conclude with several remarks regarding the wavelet…
Interpolation inequalities for $C^m$ functions allow to bound derivatives of intermediate order $0 < j<m$ by bounds for the derivatives of order $0$ and $m$. We review various interpolation inequalities for $L^p$-norms ($1 \le p \le…
Traditional approaches to interpolate/extrapolate frames in a video sequence require accurate pixel correspondences between images, e.g., using optical flow. Their results stem on the accuracy of optical flow estimation, and could generate…
A multiresolution analysis is a nested chain of related approximation spaces.This nesting in turn implies relationships among interpolation bases in the approximation spaces and their derived wavelet spaces. Using these relationships, a…
Fractal Interpolation has been proposed in the literature as an efficient way to construct closure models for the numerical solution of coarse-grained Navier-Stokes equations. It is based on synthetically generating a scale-invariant…
Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing…
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…
The aim of this work is to show how symbolic computation can be used to perform multivariate Lagrange, Hermite and Birkhoff interpolation and help us to build more realistic interpolating functions. After a theoretical introduction in which…
We provide a general framework to construct fractal interpolation surfaces (FISs) for a prescribed countably infinite data set on a rectangular grid. Using this as a crucial tool, we obtain a parameterized family of bivariate fractal…
We propose a parallel version of the cross interpolation algorithm and apply it to calculate high-dimensional integrals motivated by Ising model in quantum physics. In contrast to mainstream approaches, such as Monte Carlo and quasi Monte…