**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

##### A Mathematical Theory of Computational Resolution Limit in Multi-dimensional Spaces

Ping Liu, Hai Zhang*, Inverse Problems

##### A mathematical theory of computational resolution limit in one dimension

Ping Liu, Hai Zhang*, Applied and Computational Harmonic Analysis

##### A mathematical theory of super-resolution and diffraction limit

Ping Liu*, Habib Ammari

**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

##### Dynamic super-resolution in particle tracking problems

Ping Liu*, Habib Ammari, Applied and Computational Harmonic Analysis

**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

##### Mathematical foundation of sparsity-based multi-illumination super-resolution

Ping Liu*, Sanghyeon Yu, Ola Sabet, Lucas Pelkmans, and Habib Ammari

##### An Operator Theory for Analyzing the Resolution of Multi-illumination Imaging Modalities

Ping Liu*, Habib Ammari, SIAM Journal on Imaging Sciences

##### A measurement decoupling based fast algorithm for super-resolving point sources with multi-cluster structure

Ping Liu, Hai Zhang*