Super-resolution on the sphere using convex optimization

Tamir Bendory, Shai Dekel, Arie Feuer

Research output: Contribution to journalArticlepeer-review


This paper considers the problem of recovering an ensemble of Diracs on a sphere from its low resolution measurements. The Diracs can be located at any location on the sphere, not necessarily on a grid. We show that under a separation condition, one can recover the ensemble with high precision by a three-stage algorithm, which consists of solving a semi-definite program, root finding and least-square fitting. The algorithm's computation time depends solely on the number of measurements, and not on the required solution accuracy. We also show that in the special case of non-negative ensembles, a sparsity condition is sufficient for recovery. Furthermore, in the discrete setting, we estimate the recovery error in the presence of noise as a function of the noise level and the super-resolution factor.

Original languageEnglish
Article number7029667
Pages (from-to)2253-2262
Number of pages10
JournalIEEE Transactions on Signal Processing
Issue number9
StatePublished - 1 May 2015
Externally publishedYes


  • Harmonic analysis
  • compressed sensing
  • signal resolution


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