Reconstruction of convex bodies from moments

Julia Hörrmann, Astrid Kousholt

Publikation: Working paper/Preprint Working paperForskning

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Abstract

We investigate how much information about a convex body can be retrieved
from a finite number of its geometric moments. We give a sufficient condition
for a convex body to be uniquely determined by a finite number of its geometric moments, and we show that among all convex bodies, those which are
uniquely determined by a finite number of moments form a dense set. Further,
we derive a stability result for convex bodies based on geometric moments. It
turns out that the stability result is improved considerably by using another
set of moments, namely Legendre moments. We present a reconstruction algo-
rithm that approximates a convex body using a finite number of its Legendre
moments. The consistency of the algorithm is established using the stabil-
ity result for Legendre moments. When only noisy measurements of Legendre
moments are available, the consistency of the algorithm is established under
certain assumptions on the variance of the noise variables.
OriginalsprogEngelsk
UdgivelsesstedAarhus University
UdgiverCentre for Stochastic Geometry and advanced Bioimaging, Aarhus University
Antal sider28
StatusUdgivet - 2016
NavnCSGB Research Reports
Nummer7

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