Related papers: Digital terrain modeling with the Chebyshev polyno…
Application of root density estimator to problems of statistical data analysis is demonstrated. Four sets of basis functions based on Chebyshev-Hermite, Laguerre, Kravchuk and Charlier polynomials are considered. The sets may be used for…
We improve a recently developed expansion technique for calculating real frequency spectral functions of any one-dimensional model with short-range interactions, by postprocessing computed Chebyshev moments with linear prediction. This can…
Nowadays dense stereo matching has become one of the dominant tools in 3D reconstruction of urban regions for its low cost and high flexibility in generating dense 3D points. However, state-of-the-art stereo matching algorithms usually…
Self-adjoint operators on infinite-dimensional spaces with continuous spectra are abundant but do not possess a basis of eigenfunctions. Rather, diagonalization is achieved through spectral measures. The SpecSolve package [SIAM Rev., 63(3)…
Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…
This note presents an online pseudospectral method for system identification using Chebyshev polynomial basis under aperiodic sampling. The system dynamics are approximated piecewise by introducing a sliding time window. The number of…
One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…
Partial Differential Equations (PDEs) have long been recognized as powerful tools for image processing and analysis, providing a framework to model and exploit structural and geometric properties inherent in visual data. Over the years,…
Neural operators have emerged as powerful deep learning frameworks for approximating solution operators of parameterized partial differential equations (PDE). However, current methods predominantly rely on multilayer perceptrons (MLPs) for…
Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…
The wavenumber integration model is considered to be the most accurate algorithm for arbitrary horizontally stratified media in computational ocean acoustics. In contrast to the normal mode approach, it considers not only the discrete…
Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral…
Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…
The normal mode model is one of the most popular approaches for solving underwater sound propagation problems. Among other methods, the finite difference method is widely used in classic normal mode programs. In many recent studies, the…
In 3D image/video acquisition, different views are often captured with varying noise levels across the views. In this paper, we propose a graph-based image enhancement technique that uses a higher quality view to enhance a degraded view. A…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
We estimate the density and its derivatives using a local polynomial approximation to the logarithm of an unknown density $f$. The estimator is guaranteed to be nonnegative and achieves the same optimal rate of convergence in the interior…
We discuss a numerical algorithm for solving nonlinear integro-differential equations, and illustrate our findings for the particular case of Volterra type equations. The algorithm combines a perturbation approach meant to render a…
This paper is focused on performing a new method for solving linear and nonlinear higher-order boundary value problems (HBVPs). This direct numerical method based on spectral method. The trial function of this method is the Monic Chebyshev…
Dense matching is crucial for 3D scene reconstruction since it enables the recovery of scene 3D geometry from image acquisition. Deep Learning (DL)-based methods have shown effectiveness in the special case of epipolar stereo disparity…