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Speaker: Weilin Li, City College of New York, CUNY

Title: Super-resolution: theory and algorithms

Abstract: Super-resolution refers to stable recovery of closely spaced point sources given noisy Fourier measurements. We study the fundamental limits of super-resolution and stability of subspace methods. Under a sparsity and grid assumption, we derive sharp bounds for the min-max error in terms of the model parameters. The error can be improved if the support satisfies additional geometric properties beyond just sparsity. To this end, we introduce a clumps model for the support and derive a novel lower bound for the minimum singular value of Fourier/Vandermonde matrices. Employing this bound, we derive a perturbation bound for subspace algorithms, including MUSIC and ESPRIT, which depends on the cardinality of the clumps as opposed to the sparsity.

Bio: Weilin Li conducts research in computational harmonic analysis and its applications to data science. He has worked on the mathematics of Fourier imaging, on the analysis of scattering transforms with applications to remote sensing, and on constrained approximation problems that arise in machine learning. Prior to joining CUNY City College as an assistant professor, he was a Courant Instructor at New York University and received his PhD from the University of Maryland, College Park.