5 papers
A sharp analysis of Root-MUSIC: locations of correct and extraneous roots
Hana Huber, Weilin Li
Root-MUSIC is a spectral estimation algorithm that approximates the unknown signal frequencies by constructing a high-degree polynomial and finding a subset of roots which are clos…
Optimal structured approximation of Fourier subspaces, Toeplitz matrices, and exponential sums
Albert Fannjiang, Weilin Li
This paper studies three structured approximation problems: (1) Recovering the range of a Fourier matrix from a single observation, (2) Recovering a corrupted low-rank Toeplitz/Han…
Optimality of Gradient-MUSIC for spectral estimation
Albert Fannjiang, Weilin Li, Wenjing Liao
We introduce the Gradient-MUSIC algorithm for estimating the unknown frequencies and amplitudes of a nonharmonic signal from noisy time samples. While the classical MUSIC algorithm…
An explicit spectral decomposition of the ADRT
Weilin Li, Karl Otness, Kui Ren +1
The approximate discrete Radon transform (ADRT) is a hierarchical multiscale approximation of the Radon transform. In this paper, we factor the ADRT into a product of linear transf…
Concerning the stability of exponential systems and Fourier matrices
Oleg Asipchuk, Laura De Carli, Weilin Li
Fourier matrices naturally appear in many applications and their stability is closely tied to performance guarantees of algorithms. The starting point of this article is a result t…