# 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}
}
• Published 23 March 2010
• Mathematics
• Journal of the American Mathematical Society
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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