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Astrid Kousholt

Reconstruction of convex bodies from surface tensors

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

Standard

Reconstruction of convex bodies from surface tensors. / Kousholt, Astrid; Kiderlen, Markus.
I: Advances in Applied Mathematics, Bind 76, 2016, s. 1-33.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

Harvard

Kousholt, A & Kiderlen, M 2016, 'Reconstruction of convex bodies from surface tensors', Advances in Applied Mathematics, bind 76, s. 1-33. https://doi.org/10.1016/j.aam.2016.01.001

APA

Kousholt, A., & Kiderlen, M. (2016). Reconstruction of convex bodies from surface tensors. Advances in Applied Mathematics, 76, 1-33. https://doi.org/10.1016/j.aam.2016.01.001

CBE

Kousholt A, Kiderlen M. 2016. Reconstruction of convex bodies from surface tensors. Advances in Applied Mathematics. 76:1-33. https://doi.org/10.1016/j.aam.2016.01.001

MLA

Kousholt, Astrid og Markus Kiderlen. "Reconstruction of convex bodies from surface tensors". Advances in Applied Mathematics. 2016, 76. 1-33. https://doi.org/10.1016/j.aam.2016.01.001

Vancouver

Kousholt A, Kiderlen M. Reconstruction of convex bodies from surface tensors. Advances in Applied Mathematics. 2016;76:1-33. doi: 10.1016/j.aam.2016.01.001

Author

Kousholt, Astrid ; Kiderlen, Markus. / Reconstruction of convex bodies from surface tensors. I: Advances in Applied Mathematics. 2016 ; Bind 76. s. 1-33.

Bibtex

@article{ef1582e0df1b4e4d84addfd8d0ba11c1,
title = "Reconstruction of convex bodies from surface tensors",
abstract = "We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. When only measurements subject to noise of surface tensors are available for reconstruction, we recommend to use certain values of the surface tensors, namely harmonic intrinsic volumes instead of the surface tensors evaluated at the standard basis. The second algorithm we present is based on harmonic intrinsic volumes and allows for noisy measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based on measurements subject to noise is established under certain assumptions on the noise variables.",
keywords = "Generalized Wirtinger's inequality, Harmonic intrinsic volume, Surface tensor, Reconstruction algorithm, Convex body",
author = "Astrid Kousholt and Markus Kiderlen",
year = "2016",
doi = "10.1016/j.aam.2016.01.001",
language = "English",
volume = "76",
pages = "1--33",
journal = "Advances in Applied Mathematics",
issn = "0196-8858",
publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - Reconstruction of convex bodies from surface tensors

AU - Kousholt, Astrid

AU - Kiderlen, Markus

PY - 2016

Y1 - 2016

N2 - We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. When only measurements subject to noise of surface tensors are available for reconstruction, we recommend to use certain values of the surface tensors, namely harmonic intrinsic volumes instead of the surface tensors evaluated at the standard basis. The second algorithm we present is based on harmonic intrinsic volumes and allows for noisy measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based on measurements subject to noise is established under certain assumptions on the noise variables.

AB - We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. When only measurements subject to noise of surface tensors are available for reconstruction, we recommend to use certain values of the surface tensors, namely harmonic intrinsic volumes instead of the surface tensors evaluated at the standard basis. The second algorithm we present is based on harmonic intrinsic volumes and allows for noisy measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based on measurements subject to noise is established under certain assumptions on the noise variables.

KW - Generalized Wirtinger's inequality

KW - Harmonic intrinsic volume

KW - Surface tensor

KW - Reconstruction algorithm

KW - Convex body

U2 - 10.1016/j.aam.2016.01.001

DO - 10.1016/j.aam.2016.01.001

M3 - Journal article

VL - 76

SP - 1

EP - 33

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

SN - 0196-8858

ER -