Feature Reconstruction from Incomplete Tomographic Data without Detour

In this paper, we consider the problem of feature reconstruction from incomplete X-ray CT data. Such incomplete data problems occur when the number of measured X-rays is restricted either due to limit radiation exposure or due to practical constraints, making the detection of certain rays challengin...

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Vydané v:Mathematics (Basel) Ročník 10; číslo 8; s. 1318
Hlavní autori: Göppel, Simon, Frikel, Jürgen, Haltmeier, Markus
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Basel MDPI AG 01.04.2022
Predmet:
Algorithms
Computed tomography
Edge detection
Feature maps
feature reconstruction
Image processing
Image reconstruction
Image segmentation
limited data
Mathematics
Medical imaging
Radiation
Radiation effects
Radon transform
reconstruction
Regularization
Regularization methods
Robustness (mathematics)
sparse data
Tomography
ISSN:2227-7390, 2227-7390
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Shrnutí:In this paper, we consider the problem of feature reconstruction from incomplete X-ray CT data. Such incomplete data problems occur when the number of measured X-rays is restricted either due to limit radiation exposure or due to practical constraints, making the detection of certain rays challenging. Since image reconstruction from incomplete data is a severely ill-posed (unstable) problem, the reconstructed images may suffer from characteristic artefacts or missing features, thus significantly complicating subsequent image processing tasks (e.g., edge detection or segmentation). In this paper, we introduce a framework for the robust reconstruction of convolutional image features directly from CT data without the need of computing a reconstructed image first. Within our framework, we use non-linear variational regularization methods that can be adapted to a variety of feature reconstruction tasks and to several limited data situations. The proposed variational regularization method minimizes an energy functional being the sum of a feature dependent data-fitting term and an additional penalty accounting for specific properties of the features. In our numerical experiments, we consider instances of edge reconstructions from angular under-sampled data and show that our approach is able to reliably reconstruct feature maps in this case.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:2227-7390
2227-7390
DOI:10.3390/math10081318