Multi-Target detection with application to cryo-electron microscopy

Tamir Bendory, Nicolas Boumal, William Leeb, Eitan Levin, Amit Singer

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


We consider the multi-Target detection problem of recovering a set of signals that appear multiple times at unknown locations in a noisy measurement. In the low noise regime, one can estimate the signals by first detecting occurrences, then clustering and averaging them. In the high noise regime, however, neither detection nor clustering can be performed reliably, so that strategies along these lines are destined to fail. Notwithstanding, using autocorrelation analysis, we show that the impossibility to detect and cluster signal occurrences in the presence of high noise does not necessarily preclude signal estimation. Specifically, to estimate the signals, we derive simple relations between the autocorrelations of the observation and those of the signals. These autocorrelations can be estimated accurately at any noise level given a sufficiently long measurement. To recover the signals from the observed autocorrelations, we solve a set of polynomial equations through nonlinear least-squares. We provide analysis regarding well-posedness of the task, and demonstrate numerically the effectiveness of the method in a variety of settings. The main goal of this work is to provide theoretical and numerical support for a recently proposed framework to image 3D structures of biological macromolecules using cryo-electron microscopy in extreme noise levels.

Original languageEnglish (US)
Article number104003
JournalInverse Problems
Issue number10
StatePublished - Sep 4 2019

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics


  • Autocorrelation analysis
  • Blind deconvolution
  • Cryo-electron microscopy
  • Detection


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