46 citations · 146 across the 18 of their papers we have counts for
19 papers
Multiscale estimates for the condition number of non-harmonic Fourier matrices
Weilin Li
This paper studies the extreme singular values of non-harmonic Fourier matrices. Such a matrix of size can be written as $Φ=[ e^{-2πi j x_k}]_{j=0,1,\dots,m-1, k=1,2,\d…
Approximation with one-bit polynomials in Bernstein form
C. Sinan Güntürk, Weilin Li
We prove various theorems on approximation using polynomials with integer coefficients in the Bernstein basis of any given order. In the extreme, we draw the coefficients from $\{…
Approximation of functions with one-bit neural networks
C. Sinan Güntürk, Weilin Li
The celebrated universal approximation theorems for neural networks roughly state that any reasonable function can be arbitrarily well-approximated by a network whose parameters ar…
Stability and Super-resolution of MUSIC and ESPRIT for Multi-snapshot Spectral Estimation
Weilin Li, Zengying Zhu, Weiguo Gao +1
This paper studies the spectral estimation problem of estimating the locations of a fixed number of point sources given multiple snapshots of Fourier measurements collected by a un…
Exploring the high dimensional geometry of HSI features
Wojciech Czaja, Ilya Kavalerov, Weilin Li
We explore feature space geometries induced by the 3-D Fourier scattering transform and deep neural network with extended attribute profiles on four standard hyperspectral images.…
Maximal function pooling with applications
Wojciech Czaja, Weilin Li, Yiran Li +1
Inspired by the Hardy-Littlewood maximal function, we propose a novel pooling strategy which is called maxfun pooling. It is presented both as a viable alternative to some of the m…
Quantization for spectral super-resolution
C. Sinan Güntürk, Weilin Li
We show that the method of distributed noise-shaping beta-quantization offers superior performance for the problem of spectral super-resolution with quantization whenever there is…
A range characterization of the single-quadrant ADRT
Weilin Li, Kui Ren, Donsub Rim
This work characterizes the range of the single-quadrant approximate discrete Radon transform (ADRT) of square images. The characterization follows from a set of linear constraints…
Generalization error of minimum weighted norm and kernel interpolation
Weilin Li
We study the generalization error of functions that interpolate prescribed data points and are selected by minimizing a weighted norm. Under natural and general conditions, we prov…
Three-Dimensional Fourier Scattering Transform and Classification of Hyperspectral Images
Ilya Kavalerov, Weilin Li, Wojciech Czaja +1
Recent developments in machine learning and signal processing have resulted in many new techniques that are able to effectively capture the intrinsic yet complex properties of hype…
Conditioning of restricted Fourier matrices and super-resolution of MUSIC
Weilin Li, Wenjing Liao
This paper studies stable recovery of a collection of point sources from its noisy low-frequency Fourier coefficients. We focus on the super-resolution regime where the minim…
Super-resolution limit of the ESPRIT algorithm
Weilin Li, Wenjing Liao, Albert Fannjiang
The problem of imaging point objects can be formulated as estimation of an unknown atomic measure from its consecutive noisy Fourier coefficients. The standard resolution of…
High-performance quantization for spectral super-resolution
C. Sinan Güntürk, Weilin Li
We show that the method of distributed noise-shaping beta-quantization offers superior performance for the problem of spectral super-resolution with quantization whenever there is…
Rotationally invariant time-frequency scattering transforms
Wojciech Czaja, Weilin Li
In this paper we construct directionally sensitive functions that can be viewed as directional time-frequency representations. We call such a sequence a rotational uniform covering…
Stable super-resolution limit and smallest singular value of restricted Fourier matrices
Weilin Li, Wenjing Liao
We consider the inverse problem of recovering the locations and amplitudes of a collection of point sources represented as a discrete measure, given of its noisy low-frequenc…
Elementary error estimates for super-resolution de-noising
Weilin Li
This paper studies the problem of recovering a discrete complex measure on the torus from a finite number of corrupted Fourier samples. We assume the support of the unknown discret…
Analysis of time-frequency scattering transforms
Wojciech Czaja, Weilin Li
In this paper we address the problem of constructing a feature extractor which combines Mallat's scattering transform framework with time-frequency (Gabor) representations. To do t…
Super-resolution by means of Beurling minimal extrapolation
John J. Benedetto, Weilin Li
Let be the space of complex bounded Radon measures defined on the -dimensional torus group , equipped with the total va…
Boundary Value Problems on a Half Sierpinski Gasket
Weilin Li, Robert S. Strichartz
We study boundary value problems for the Laplacian on a domain consisting of the left half of the Sierpinski Gasket (), whose boundary is essentially a countable set of poi…