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• W2397553202 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 algorithm that approximates a convex body using a finite number of its Legendre moments. The consistency of the algorithm is established using the stability 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." @default.
• W2397553202 created "2016-06-24" @default.
• W2397553202 creator A5003989557 @default.
• W2397553202 creator A5076304752 @default.
• W2397553202 date "2016-05-20" @default.
• W2397553202 modified "2023-09-27" @default.
• W2397553202 title "Reconstruction of convex bodies from moments" @default.
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• W2397553202 hasPublicationYear "2016" @default.
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