Robust Recovery of Positive Stream of Pulses

Tamir Bendory*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The problem of estimating the delays and amplitudes of a positive stream of pulses appears in many applications, such as single-molecule microscopy. This paper suggests estimating the delays and amplitudes using a convex program, which is robust in the presence of noise (or model mismatch). Particularly, the recovery error is proportional to the noise level. We further show that the error grows exponentially with the density of the delays and also depends on the localization properties of the pulse.

Original languageEnglish
Article number7829411
Pages (from-to)2114-2122
Number of pages9
JournalIEEE Transactions on Signal Processing
Issue number8
StatePublished - 15 Apr 2017
Externally publishedYes


  • Convex optimization
  • Dual certificate
  • Rayleigh regularity
  • Sparse deconvolution
  • Stream of pulses
  • Super-resolution


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