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Super-resolution of positive near-colliding point sources

by P. Liu and H. Ammari

(Report number 2023-03)

Abstract
In this paper, we analyze the capacity of super-resolution of one-dimensional positive sources. We consider resolving of positive point sources where some nodes are closely spaced and forming a cluster, while the rest of the nodes are well separated. For both the cluster and the non-cluster nodes, we estimate the minimax error rates for reconstructing the nodes and recovering the corresponding amplitudes. Our numerical experiments show that the Matrix Pencil method achieves the above optimal bounds when resolving the positive sources.

Keywords: super-resolution, positive sources, near-colliding sources, clusters, minimax error rate

@Techreport{LA23_1040,
  author = {P. Liu and H. Ammari},
  title = {Super-resolution of positive near-colliding point sources},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2023-03},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2023/2023-03.pdf },
  year = {2023}
}

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