2021/08/26 by Mathias Hockmann, Stefan Kunis, Hockmann, Mathias +1 · 1 citation
Computer Science · Engineering · Mathematics · #49Q22 (Secondary) #65T40 (Primary) 42B05 #Advanced Image Processing Techniques #Advanced Numerical Analysis Techniques #Applied mathematics #Cluster analysis #Computer science #Dimension (graph theory) #FOS: Mathematics #Lipschitz continuity #Mathematical analysis #Mathematics #Measure (data warehouse) #Numerical Analysis (math.NA) #Pure mathematics #Sparse and Compressive Sensing Techniques #Statistics #Trigonometry #cs.NA #math.NA #msc:42B05 #msc:49Q22 #msc:65T40
paper · pdf · doi:10.48550/arxiv.2108.11925
published in arXiv (Cornell University) (Cornell University) · 27 pages, 6 figures
arxiv created 2021/08/26 · openalex publication_date 2021/08/26 · arxiv updated 2021/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by the application of neural networks in super resolution microscopy, this paper considers super resolution as the mapping of trigonometric moments of a discrete measure on [0,1)d to its support and weights. We prove that this map satisfies a local Lipschitz property where we give explicit estimates for the Lipschitz constant depending on the dimension d and the sampling effort. Moreover, this local Lipschitz estimate allows to conclude that super resolution with the Wasserstein distance as the metric on the parameter space is even globally Lipschitz continuous. As a byproduct, we improve an estimate for the smallest singular value of multivariate Vandermonde matrices having pairwise clustering nodes.