Related papers: Constructing spatial discretizations for sparse mu…
We present a computationally efficient algorithm for stable numerical differentiation from noisy, uniformly-sampled data on a bounded interval. The method combines multi-interval Fourier extension approximations with an adaptive domain…
Sampling strategies are important for sparse imaging methodologies, especially those employing the discrete Fourier transform (DFT). Chaotic sensing is one such methodology that employs deterministic, fractal sampling in conjunction with…
Polymorphism offers rich and virtually unexplored space for discovering novel functional materials. To harness this potential approaches capable of both exploring the space of polymorphs and assessing their realizability are needed. One…
We consider the multidimensional space-fractional diffusion equations with spatially varying diffusivity and fractional order. Significant computational challenges are encountered when solving these equations due both to the kernel…
We propose a new lifting and recombination scheme for rational bivariate polynomial factorization that takes advantage of the Newton polytope geometry. We obtain a deterministic algorithm that can be seen as a sparse version of an algorithm…
In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…
In this letter, a fast Fourier transform (FFT)-enhanced low-complexity super-resolution sensing algorithm for near-field source localization with both angle and range estimation is proposed. Most traditional near-field source localization…
We study multivariate trigonometric polynomials, satisfying a set of constraints close to the known Strung-Fix conditions. Based on the polyphase representation of these polynomials relative to a general dilation matrix, we develop a simple…
The common methods of spectral analysis for multivariate ($n$-dimensional) time series, like discrete Frourier transform (FT) or Wavelet transform, are based on Fourier series to decompose discrete data into a set of trigonometric model…
The performance of multivariate kernel density estimation (KDE) depends strongly on the choice of bandwidth matrix. The high computational cost required for its estimation provides a big motivation to develop fast and accurate methods. One…
The stochastic density functional theory (sDFT) has exhibited advantages over the standard Kohn-Sham DFT method and has become an attractive approach for large-scale electronic structure calculations. The sDFT method avoids the expensive…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
Computing the Sparse Fast Fourier Transform(sFFT) of a K-sparse signal of size N has emerged as a critical topic for a long time. The sFFT algorithms decrease the runtime and sampling complexity by taking advantage of the signal inherent…
Multivariate spatio-temporal data arise more and more frequently in a wide range of applications; however, there are relatively few general statistical methods that can readily use that incorporate spatial, temporal and variable…
Higher order digital nets are special classes of point sets for quasi-Monte Carlo rules which achieve the optimal convergence rate for numerical integration of smooth functions. An explicit construction of higher order digital nets was…
We introduce a deterministic sparse Fourier transform framework based on a keyed multi-view gating mechanism that leverages 2-of-3 Chinese Remainder Theorem (CRT) agreement to reduce candidate frequency pairs from $O(k^2)$ to $\Theta(k)$…
This paper introduces a sparse projection matrix composed of discrete (digital) periodic lines that create a pseudo-random (p.frac) sampling scheme. Our approach enables random Cartesian sampling whilst employing deterministic and…
We present the Fast Newton Transform (FNT), an algorithm for performing $m$-variate Newton interpolation in downward closed polynomial spaces with time complexity $\mathcal{O}(|A|m\overline{n})$. Here, $A$ is a downward closed set of…
We revisit the classical problem of Fourier-sparse signal reconstruction -- a variant of the \emph{Set Query} problem -- which asks to efficiently reconstruct (a subset of) a $d$-dimensional Fourier-sparse signal ($\|\hat{x}(t)\|_0 \leq…
The dominant paradigm in computational materials discovery relies on heavily parameterized deep architectures, including message-passing graph networks and equivariant models, that require millions of DFT-labeled training structures and…