Publications:
Super-resolution of positive near-colliding point sources, Ping Liu*, Habib Ammari, Information and Inference: a Journal of the IMA, 12(4):iaad048, 2023.
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.
Preprints:
Spectra and pseudo-spectra theory of tridiagonal k-Toeplitz operators and the topological origin of the non-Hermitian skin effect, Habib Ammari, Silvio Barandun, Yannick De Bruijn, Ping Liu*, Clemens Thalhammer, 2024.
Exponentially localised interface eigenmodes in finite chains of resonators,Habib Ammari, Silvio Barandun, Bryn Davies, Erik Orvehed Hiltunen, Thea Kosche, Ping Liu*, 2023.
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.