Super-resolution of positive near-colliding point sources, Ping Liu*, Habib Ammari, To appear in Information and Inference: a Journal of the IMA.
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.
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.
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 Computational Resolution Limit in Multi-dimensional Spaces, Ping Liu, Hai Zhang*, Inverse Problems, 37(10):104001, 2021.
A Theory of Computational Resolution Limit for Line Spectral Estimation, Ping Liu, Hai Zhang*, IEEE Transactions on Information Theory, 67(7):4812-4827, 2021.
The non-Hermitian skin effect with three-dimensional long-range coupling, Habib Ammari, Silvio Barandun, Jinghao Cao, Bryn Davies, Erik Orvehed Hiltunen, Ping Liu, 2023, submitted to Journal of the European Mathematical Society.
Perturbed block Toeplitz matrices and the non-Hermitian skin effect in dimer systems of subwavelength resonators, Habib Ammari, Silvio Barandun, Ping Liu*, submitted to Journal de Mathematiques Pures et Appliquees.
Stability of the non-Hermitian skin effect, Habib Ammari, Silvio Barandun, Bryn Davies, Erik Orvehed Hiltunen, Ping Liu*, submitted to SIAM on Applied Mathematics.
A mathematical theory of super-resolution and diffraction limit, Ping Liu*, Habib Ammari, submitted to Forum of Mathematics Sigma.
A mathematical theory of resolution limits for super-resolution of positive sources, Ping Liu*, Yanchen He, Habib Ammari
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.
A measurement decoupling based fast algorithm for super-resolving point sources with multi-cluster structure, Ping Liu, Hai Zhang*, submitted to Inverse Problems.