Related papers: Fourier Extension Based on Weighted Generalized In…
Vertically weighted averages perform a bilateral filtering of data, in order to preserve fine details of the underlying signal, especially discontinuities such as jumps (in dimension one) or edges (in dimension two). In homogeneous regions…
Currently, iTransformer is one of the most popular and effective models for multivariate time series (MTS) forecasting. Thanks to its inverted framework, iTransformer effectively captures multivariate correlation. However, the inverted…
In this paper, a novel linear method for shape reconstruction is proposed based on the generalized multiple measurement vectors (GMMV) model. Finite difference frequency domain (FDFD) is applied to discretized Maxwell's equations, and the…
The generalization capacity of various machine learning models exhibits different phenomena in the under- and over-parameterized regimes. In this paper, we focus on regression models such as feature regression and kernel regression and…
We develop a framework for solving the stationary, incompressible Stokes equations in an axisymmetric domain. By means of Fourier expansion with respect to the angular variable, the three-dimensional Stokes problem is reduced to an…
We present a Fourier-based approach for high-dimensional function approximation. To this end, we analyze the truncated ANOVA (analysis of variance) decomposition and learn the anisotropic smoothness properties of the target function from…
The Lagrange multiplier method has proven highly effective for mitigating the ill-conditioning of full waveform inversion (FWI), enabling robust and computationally efficient algorithms that converge to accurate velocity models even from…
In this paper we obtain new sufficient conditions for representation of a function as an absolutely convergent Fourier integral. Unlike those known earlier, these conditions are given in terms of belonging to weighted spaces. Adding weights…
In this paper, we present a new approach to derive series expansions for some Gaussian processes based on harmonic analysis of their covariance function. In particular, we propose a new simple rate-optimal series expansion for fractional…
A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integral equations and uses the (approximate) solutions to…
This paper investigates the consistency of a posterior distribution in the single-measurement fractional Calder\'on problem with additive Gaussian noise. We consider a Bayesian framework with rescaled and Gaussian sieve priors, using a…
We consider inverse problems in Hilbert spaces under correlated Gaussian noise and use a Bayesian approach to find their regularised solution. We focus on mildly ill-posed inverse problems with the noise being generalised derivative of…
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…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
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…
In this work, a method for obtaining pixel-wise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal…
We propose a numerical algorithm for backward stochastic differential equations based on time discretization and trigonometric wavelets. This method combines the effectiveness of Fourier-based methods and the simplicity of a wavelet-based…
The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods…
The recently proposed soft finite element method (SoftFEM) reduces the stiffness (condition numbers), consequently improving the overall approximation accuracy. The method subtracts a least-square term that penalizes the gradient jumps…
An inverse elastic source problem with sparse measurements is of concern. A generic mathematical framework is proposed which incorporates a low- dimensional manifold regularization in the conventional source reconstruction algorithms…