Random Action of Compact Lie Groups and Minimax Estimation of a Mean Pattern

@article{Bigot2012RandomAO,
  title={Random Action of Compact Lie Groups and Minimax Estimation of a Mean Pattern},
  author={J{\'e}r{\'e}mie Bigot and Claire Christophe and S{\'e}bastien Gadat},
  journal={IEEE Transactions on Information Theory},
  year={2012},
  volume={58},
  pages={3509-3520}
}
This paper considers the problem of estimating a mean pattern in the setting of Grenander's pattern theory. Shape variability in a dataset of curves or images is modeled by the random action of elements in a compact Lie group on an infinite dimensional space. In the case of observations contaminated by an additive Gaussian white noise, it is shown that estimating a reference template in the setting of Grenanders pattern theory falls into the category of deconvolution problems over Lie groups… 
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