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Astrid Kousholt

Reconstruction of convex bodies from moments

Publikation: Working paper/Preprint › Working paper › Forskning

Standard

Reconstruction of convex bodies from moments. / Hörrmann, Julia; Kousholt, Astrid.
Aarhus University: Centre for Stochastic Geometry and advanced Bioimaging, Aarhus University, 2016.

Publikation: Working paper/Preprint › Working paper › Forskning

Harvard

Hörrmann, J & Kousholt, A 2016 'Reconstruction of convex bodies from moments' CSGB Research Reports, nr. 7, Centre for Stochastic Geometry and advanced Bioimaging, Aarhus University, Aarhus University.

APA

Hörrmann, J., & Kousholt, A. (2016). Reconstruction of convex bodies from moments. Centre for Stochastic Geometry and advanced Bioimaging, Aarhus University. CSGB Research Reports Nr. 7

CBE

Hörrmann J, Kousholt A. 2016. Reconstruction of convex bodies from moments. Aarhus University: Centre for Stochastic Geometry and advanced Bioimaging, Aarhus University.

MLA

Hörrmann, Julia og Astrid Kousholt Reconstruction of convex bodies from moments. Aarhus University: Centre for Stochastic Geometry and advanced Bioimaging, Aarhus University. (CSGB Research Reports; Journal nr. 7). 2016., 28 s.

Vancouver

Hörrmann J, Kousholt A. Reconstruction of convex bodies from moments. Aarhus University: Centre for Stochastic Geometry and advanced Bioimaging, Aarhus University. 2016.

Author

Hörrmann, Julia ; Kousholt, Astrid. / Reconstruction of convex bodies from moments. Aarhus University : Centre for Stochastic Geometry and advanced Bioimaging, Aarhus University, 2016. (CSGB Research Reports; Nr. 7).

Bibtex

@techreport{6ba3bc4d998c416f81b197ae7fda5771,
title = "Reconstruction of convex bodies from moments",
abstract = "We investigate how much information about a convex body can be retrievedfrom a finite number of its geometric moments. We give a sufficient conditionfor 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 areuniquely determined by a finite number of moments form a dense set. Further,we derive a stability result for convex bodies based on geometric moments. Itturns out that the stability result is improved considerably by using anotherset of moments, namely Legendre moments. We present a reconstruction algo-rithm that approximates a convex body using a finite number of its Legendremoments. The consistency of the algorithm is established using the stabil-ity result for Legendre moments. When only noisy measurements of Legendremoments are available, the consistency of the algorithm is established undercertain assumptions on the variance of the noise variables.",
author = "Julia H{\"o}rrmann and Astrid Kousholt",
year = "2016",
language = "English",
series = "CSGB Research Reports",
number = "7",
publisher = "Centre for Stochastic Geometry and advanced Bioimaging, Aarhus University",
type = "WorkingPaper",
institution = "Centre for Stochastic Geometry and advanced Bioimaging, Aarhus University",

}

RIS

TY - UNPB

T1 - Reconstruction of convex bodies from moments

AU - Hörrmann, Julia

AU - Kousholt, Astrid

PY - 2016

Y1 - 2016

N2 - We investigate how much information about a convex body can be retrievedfrom a finite number of its geometric moments. We give a sufficient conditionfor 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 areuniquely determined by a finite number of moments form a dense set. Further,we derive a stability result for convex bodies based on geometric moments. Itturns out that the stability result is improved considerably by using anotherset of moments, namely Legendre moments. We present a reconstruction algo-rithm that approximates a convex body using a finite number of its Legendremoments. The consistency of the algorithm is established using the stabil-ity result for Legendre moments. When only noisy measurements of Legendremoments are available, the consistency of the algorithm is established undercertain assumptions on the variance of the noise variables.

AB - We investigate how much information about a convex body can be retrievedfrom a finite number of its geometric moments. We give a sufficient conditionfor 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 areuniquely determined by a finite number of moments form a dense set. Further,we derive a stability result for convex bodies based on geometric moments. Itturns out that the stability result is improved considerably by using anotherset of moments, namely Legendre moments. We present a reconstruction algo-rithm that approximates a convex body using a finite number of its Legendremoments. The consistency of the algorithm is established using the stabil-ity result for Legendre moments. When only noisy measurements of Legendremoments are available, the consistency of the algorithm is established undercertain assumptions on the variance of the noise variables.

UR - http://math.au.dk/en/research/publications/publication-series/publication/publid/1070/

M3 - Working paper

T3 - CSGB Research Reports

BT - Reconstruction of convex bodies from moments

PB - Centre for Stochastic Geometry and advanced Bioimaging, Aarhus University

CY - Aarhus University

ER -