Unrolled Algorithms for Group Synchronization

Noam Janco, Tamir Bendory

Research output: Contribution to journalArticlepeer-review


The group synchronization problem involves esti-mating a collection of group elements from noisy measurements of their pairwise ratios. This task is a key component in many computational problems, including the molecular reconstruction problem in single-particle cryo-electron microscopy (cryo-EM). The standard methods to estimate the group elements are based on iteratively applying linear and non-linear operators, and are not necessarily optimal. Motivated by the structural similarity to deep neural networks, we adopt the concept of algorithm unrolling, where training data is used to optimize the algorithm. We design unrolled algorithms for several group synchronization instances, including synchronization over the group of 3-D rota-tions: the synchronization problem in cryo-EM. We also apply a similar approach to the multi-reference alignment problem. We show by numerical experiments that the unrolling strategy outperforms existing synchronization algorithms in a wide variety of scenarios.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalIEEE Open Journal of Signal Processing
StateAccepted/In press - 2023


  • algorithm unrolling
  • Group synchronization
  • Maximum likelihood estimation
  • multi-reference alignment
  • Noise measurement
  • Signal processing algorithms
  • Signal to noise ratio
  • Standards
  • Synchronization
  • Training data


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