Communications in Mathematical Sciences

Volume 21 (2023)

Number 2

Blind super-resolution of point sources via fast iterative hard thresholding

Pages: 581 – 590

(Fast Communication)

DOI: https://dx.doi.org/10.4310/CMS.2023.v21.n2.a13

Authors

Zengying Zhu (School of Mathematical Sciences, Fudan University, Shanghai, China)

Jinchi Chen (School of Data Science, Fudan University, Shanghai, China)

Weiguo Gao (School of Mathematical Sciences and School of Data Science, Fudan University, Shanghai, China)

Abstract

In this work, we develop a provable fast algorithm for blind super-resolution based on the low rank structure of vectorized Hankel matrix associated with the target matrix. Theoretical results show that the proposed method converges to the ground truth with linear convergence rate. Numerical experiments are also conducted to illustrate the linear convergence and effectiveness of the proposed approach.

Keywords

blind super-resolution, low rank matrix recovery, fast iterative hard thresholding, vectorized Hankel lift

2010 Mathematics Subject Classification

15A83, 90C26, 94A12

Full Text (PDF format)

The research of this work was supported by National Key R&D Program of China under Grant No. 2021YFA1003300. Jinchi Chen was partially supported by National Natural Science Foundation of China under Grant No. 12001108. Weiguo Gao was partially supported by National Natural Science Foundation of China under Grant No. 71991471, U1811461.

Received 25 January 2022

Received revised 21 June 2022

Accepted 4 November 2022

Published 1 February 2023