A sampling theorem for deconvolution in two dimensions

Joseph McDonald, Brett Bernstein, Carlos Fernandez-Granda

Research output: Contribution to journalArticlepeer-review


This work studies the problem of estimating a two-dimensional superposition of point sources or spikes from samples of their convolution with a Gaussian kernel. Our results show that minimizing a continuous counterpart of the ℓ1-norm exactly recovers the true spikes if they are sufficiently separated, and the samples are sufficiently dense. In addition, we provide numerical evidence that our results extend to non-Gaussian kernels relevant to microscopy and telescopy.

Original languageEnglish (US)
Pages (from-to)1754-1780
Number of pages27
JournalSIAM Journal on Imaging Sciences
Issue number4
StatePublished - 2020


  • Convex optimization
  • Deconvolution
  • Dual certificate
  • Gaussian convolution
  • Sampling theory
  • Sparsity
  • Super-resolution

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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