**One-dimensional resolution limit theory and algorithms**

**Particle tracking problem**

**Super-resolution/DoA algorithms**

**Vandermonde matrix and applications**

**A Theory of Computational Resolution Limit for Line Spectral Estimation****Ping Liu, Hai Zhang*,****IEEE Transactions on Information Theory,****67(7):4812-4827, 2021.**

**A Mathematical Theory of Computational Resolution Limit in Multi-dimensional Spaces****Ping Liu, Hai Zhang*,****Inverse Problems,****37(10):104001, 2021.**

**A mathematical theory of computational resolution limit in one dimension****Ping Liu, Hai Zhang*,****Applied and Computational Harmonic Analysis,****56:402-446, 2022.**

**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**

**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.**

**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**

**A mathematical theory of resolution limits for super-resolution of positive sources****Ping Liu*, Yanchen He, Habib Ammari**

**Super-resolution of positive near-colliding point sources****Ping Liu*, Habib Ammari,****Information and Inference: a Journal of the IMA,****12(4):iaad048, 2023****.**

**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.**

**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.**

**A measurement decoupling based fast algorithm for super-resolving point sources with multi-cluster structure****Ping Liu, Hai Zhang*, submitted to****Inverse Problems.**