Phase retrieval for characteristic functions of convex bodies and reconstruction from covariograms

@article{Bianchi2010PhaseRF,
  title={Phase retrieval for characteristic functions of convex bodies and reconstruction from covariograms},
  author={Gabriele Bianchi and Richard J. Gardner and Markus Kiderlen},
  journal={Journal of the American Mathematical Society},
  year={2010},
  volume={24},
  pages={293-343}
}
We propose strongly consistent algorithms for reconstructing the characteristic function 1K of an unknown convex body K in R n from possibly noisy measurements of the modulus of its Fourier transform c 1K. This represents a complete theoretical solution to the Phase Retrieval Problem for characteristic functions of convex bodies. The approach is via the closely related problem of reconstructing K from noisy measurements of its covariogram, the function giving the volume of the intersection of K… 

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