One major challenge in computerized tomography is to image objects which change during the data acquisition and hence lead to inconsistent data sets. Motion artefacts in the reconstructions can be reduced by applying specially adapted algorithms which take the dynamic behaviour into account. Within this article, we analyse the achievable resolution in the dynamic setting in case of two-dimensional affine deformations. To this end, we characterize the null space of the operator describing the dynamic case, using its singular value decomposition and a necessary dynamic consistency condition. This shows that independent of any reconstruction method, the specimen's dynamics results in a loss of resolution compared to the stationary setting. Our theoretical results are illustrated at a numerical example.
%0 Journal Article
%1 hahn2016space
%A Hahn, B. N.
%D 2016
%J Inverse Problems
%K from:tobiasholicki
%N 2
%P 025006
%R 10.1088/0266-5611/32/2/025006
%T Null space and resolution in dynamic computerized tomography
%U http://dx.doi.org/10.1088/0266-5611/32/2/025006
%V 32
%X One major challenge in computerized tomography is to image objects which change during the data acquisition and hence lead to inconsistent data sets. Motion artefacts in the reconstructions can be reduced by applying specially adapted algorithms which take the dynamic behaviour into account. Within this article, we analyse the achievable resolution in the dynamic setting in case of two-dimensional affine deformations. To this end, we characterize the null space of the operator describing the dynamic case, using its singular value decomposition and a necessary dynamic consistency condition. This shows that independent of any reconstruction method, the specimen's dynamics results in a loss of resolution compared to the stationary setting. Our theoretical results are illustrated at a numerical example.
@article{hahn2016space,
abstract = {One major challenge in computerized tomography is to image objects which change during the data acquisition and hence lead to inconsistent data sets. Motion artefacts in the reconstructions can be reduced by applying specially adapted algorithms which take the dynamic behaviour into account. Within this article, we analyse the achievable resolution in the dynamic setting in case of two-dimensional affine deformations. To this end, we characterize the null space of the operator describing the dynamic case, using its singular value decomposition and a necessary dynamic consistency condition. This shows that independent of any reconstruction method, the specimen's dynamics results in a loss of resolution compared to the stationary setting. Our theoretical results are illustrated at a numerical example.},
added-at = {2020-04-22T18:01:53.000+0200},
author = {Hahn, B. N.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/24e2641b2d703468766a272dc99d4fbd1/oip},
doi = {10.1088/0266-5611/32/2/025006},
interhash = {da64af3edaa9076ea2def7faec53d53f},
intrahash = {4e2641b2d703468766a272dc99d4fbd1},
journal = {Inverse Problems},
keywords = {from:tobiasholicki},
number = 2,
pages = 025006,
timestamp = {2020-04-22T16:12:51.000+0200},
title = {Null space and resolution in dynamic computerized tomography},
url = {http://dx.doi.org/10.1088/0266-5611/32/2/025006},
volume = 32,
year = 2016
}
