Conditioning of partial nonuniform Fourier matrices with clustered nodes

Dmitry Batenkov, Laurent Demanet, Gil Goldman, Yosef Yomdin

Research output: Contribution to journalArticlepeer-review


We prove sharp lower bounds for the smallest singular value of a partial Fourier matrix with arbitrary "off the grid" nodes (equivalently, a rectangular Vandermonde matrix with the nodes on the unit circle) in the case when some of the nodes are separated by less than the inverse bandwidth. The bound is polynomial in the reciprocal of the so-called superresolution factor, while the exponent is controlled by the maximal number of nodes which are clustered together. As a corollary, we obtain sharp minimax bounds for the problem of sparse superresolution on a grid under the partial clustering assumptions.

Original languageEnglish
Pages (from-to)199-220
Number of pages22
JournalSIAM Journal on Matrix Analysis and Applications
Issue number1
Early online date30 Jan 2020
StatePublished - 2020


  • Decimation
  • Partial Fourier matrix
  • Prolate matrix
  • Singular values
  • Superresolution
  • Vandermonde matrix with nodes on the unit circle

All Science Journal Classification (ASJC) codes

  • Analysis


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