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We focus on an alignment-free method to estimate the underlying signal from a large number of noisy randomly shifted observations. Specifically, we recover the signal from the sample estimates of the invariant moments. We introduce a spectral method to recover the phase of the signal from the bispectrum matrix. The invariant moments approach is also applied to multi-segment reconstruction to recover a signal from noisy segments with unknown positions of the observation windows.
This presentation is part of Minisymposium “MS42 - Low dimensional structures in imaging science (3 parts)”
organized by: Wenjing Liao (Georgia Institute of Technology) , Haizhao Yang (Duke University) , Zhizhen Zhao (University of Illinois Urbana-Champaign) .