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We address the problem of approximating parametric Fourier imaging problems via interpolation/ extrapolation algorithms that impose smoothing constraints across contiguous values of the parameter. Previous works already proved that…

Numerical Analysis · Mathematics 2025-05-21 Anna Volpara , Alessandro Lupoli , Emma Perracchione

This article constructs a fractal interpolation function, also referred to as $\alpha$-fractal function, using Suzuki-type generalized $\varphi$-contraction mappings (STGPC). The STGPC is a generalization of $\varphi$-contraction mappings.…

Functional Analysis · Mathematics 2025-01-29 Mridul Patel , G. Verma , A. Eberhard , A. Rao

In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we…

Statistics Theory · Mathematics 2017-09-26 Nhat Ho , XuanLong Nguyen , Ya'acov Ritov

Material response of real, passive, linear, time-invariant media to external influences is described by complex analytic functions of frequency that can always be written in terms of Stieltjes functions -- a special class of analytic…

Optimization and Control · Mathematics 2022-03-25 Yury Grabovsky

To describe longitudinal fine structure like microbunching within a particle beam, a classical approach is to define a bunching factor which is the Fourier transform of the particle longitudinal density distribution. Such a 1D definition of…

Accelerator Physics · Physics 2025-11-12 Xiujie Deng

We introduce a continuous domain framework for the recovery of points on a surface in high dimensional space, represented as the zero-level set of a bandlimited function. We show that the exponential maps of the points on the surface…

Computer Vision and Pattern Recognition · Computer Science 2018-03-21 Sunrita Poddar , Mathews Jacob

Spherical Bessel functions appear commonly in many areas of physics wherein there is both translation and rotation invariance, and often integrals over products of several arise. Thus, analytic evaluation of such integrals with different…

Mathematical Physics · Physics 2023-12-25 Jessica Chellino , Zachary Slepian

We are interested in the nonparametric estimation of the probability density of price returns, using the kernel approach. The output of the method heavily relies on the selection of a bandwidth parameter. Many selection methods have been…

Statistical Finance · Quantitative Finance 2023-05-23 Matthieu Garcin

This paper extends earlier work on the distribution in the complex plane of the roots of random polynomials. In this paper, the random polynomials are generalized to random finite sums of given "basis" functions. The basis functions are…

Probability · Mathematics 2016-08-04 Robert J. Vanderbei

Synthetic aperture sonar (SAS) image resolution is constrained by waveform bandwidth and array geometry. Specifically, the waveform bandwidth determines a point spread function (PSF) that blurs the locations of point scatterers in the…

Computer Vision and Pattern Recognition · Computer Science 2021-12-17 Albert Reed , Thomas Blanford , Daniel C. Brown , Suren Jayasuriya

The density of polynomials in a weighted space of infinitely differentiable functions in a multidimensional real space is proved under minimal conditions on weight functions and on differences between weight functions. We apply this result…

Classical Analysis and ODEs · Mathematics 2007-05-23 P. V. Fedotova , I. Kh. Musin

We study the problem of stable reconstruction of the short-time Fourier transform from samples taken from trajectories in $\R^2$. We first consider the interplay between relative density of the trajectory and the reconstruction property.…

Functional Analysis · Mathematics 2021-12-06 Michael Speckbacher

In this paper a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier basis functions in high spatial dimensions, a so-called…

Numerical Analysis · Mathematics 2020-06-24 Lutz Kämmerer , Felix Krahmer , Toni Volkmer

In this paper we obtain approximated numerical solutions for the 2D Helmholtz equation using a radial basis function-generated finite difference scheme (RBF-FD), where weights are calculated by applying an oscillatory radial basis function…

Numerical Analysis · Mathematics 2019-03-05 Mauricio A. Londoño-Arboleda. , Hebert Montegranario

In areas such as kernel smoothing and non-parametric regression there is emphasis on smooth interpolation and smooth statistical models. Splines are known to have optimal smoothness properties in one and higher dimensions. It is shown, with…

Computation · Statistics 2008-09-29 Ron A. Bates , Hugo Maruri-Aguilar , Henry P. Wynn

We consider and provide an accurate study for the fractional Zernike functions on the punctured unit disc, generalizing the classical Zernike polynomials and their associated $\beta$-restricted Zernike functions. Mainly, we give the…

Complex Variables · Mathematics 2023-01-23 Hajar Dkhissi , Allal Ghanmi , Safa Snoun

Here we introduce the Delaunay Density Estimator Method. Its purpose is rendering a fully volume-covering reconstruction of a density field from a set of discrete data points sampling this field. Reconstructing density or intensity fields…

Astrophysics · Physics 2007-05-23 W. E. Schaap , R. van de Weygaert

The image reconstruction problem consists in finding an approximation of a function f starting from its Radon transform Rf. This problem arises in the ambit of medical imaging when one tries to reconstruct the internal structure of the…

Numerical Analysis · Mathematics 2011-11-28 Amos Sironi

We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…

Analysis of PDEs · Mathematics 2017-06-15 Jingzhi Li , Xiaofei Li , Hongyu Liu

The Hermite radial basis functions (HRBFs) implicits have been used to reconstruct surfaces from scattered Hermite data points. In this work, we propose a closed-form formulation to construct HRBF-based implicits by a quasi-solution…

Graphics · Computer Science 2015-07-13 Shengjun Liu , Charlie C. L. Wang , Guido Brunnett , Jun Wang