• Corpus ID: 248512879

Rates of estimation for high-dimensional multi-reference alignment

  title={Rates of estimation for high-dimensional multi-reference alignment},
  author={Zehao Dou and Zhou Fan and Harrison H. Zhou},
We study the continuous multi-reference alignment model of estimating a periodic function on the circle from noisy and circularly-rotated observations. Motivated by analogous high-dimensional problems that arise in cryo-electron microscopy, we establish minimax rates for estimating generic signals that are explicit in the dimension K . In a high-noise regime with noise variance σ 2 & K , the rate scales as σ 6 and has no further dependence on the dimension. This rate is achieved by a bispectrum… 

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