One-dimensional resolution limit theory and algorithms
Particle tracking problem
Super-resolution/DoA algorithms
Vandermonde matrix and applications
  1. A Theory of Computational Resolution Limit for Line Spectral Estimation
    Ping Liu, Hai Zhang*, IEEE Transactions on Information Theory, 67(7):4812-4827, 2021.
  1. A Mathematical Theory of Computational Resolution Limit in Multi-dimensional Spaces
    Ping Liu, Hai Zhang*, Inverse Problems, 37(10):104001, 2021.
  1. A mathematical theory of computational resolution limit in one dimension
    Ping Liu, Hai Zhang*, Applied and Computational Harmonic Analysis, 56:402-446, 2022.
  1. A mathematical theory of super-resolution and diffraction limit
    Ping Liu*, Habib Ammari, submitted to Forum of Mathematics Sigma.
Multi-dimensional resolution limit theory and algorithms
  1. Improved resolution estimate for the two-dimensional super-resolution and a new algorithm for direction of arrival estimation with uniform rectangular array
    Ping Liu*, Habib Ammari, Foundations of Computational Mathematics, pages 1-50, 2023.
  1. Dynamic super-resolution in particle tracking problems
    Ping Liu*, Habib Ammari, Applied and Computational Harmonic Analysis, 64:143-193, 2023.
Resolution theory for multi-illumination imaging
  1. A mathematical theory of resolution limits for super-resolution of positive sources
    Ping Liu*, Yanchen He, Habib Ammari
  1. Super-resolution of positive near-colliding point sources
    Ping Liu*, Habib Ammari, Information and Inference: a Journal of the IMA, 12(4):iaad048, 2023.
  1. Mathematical foundation of sparsity-based multi-illumination super-resolution
    Ping Liu*, Sanghyeon Yu, Ola Sabet, Lucas Pelkmans, and Habib Ammari, In revision for Applied and Computational Harmonic Analysis.
  1. An Operator Theory for Analyzing the Resolution of Multi-illumination Imaging Modalities
    Ping Liu*, Habib Ammari, SIAM Journal on Imaging Sciences, 16.4:2105–2143, 2023.
  1. A measurement decoupling based fast algorithm for super-resolving point sources with multi-cluster structure
    Ping Liu, Hai Zhang*, submitted to Inverse Problems.