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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 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 datafitting 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.

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Metadaten
Author:Simon GöppelORCiD, Jürgen FrikelORCiD, Markus HaltmeierORCiD
DOI:https://doi.org/10.3390/math10081318
Parent Title (English):Mathematics
Publisher:MDPI
Document Type:Article
Language:English
Year of first Publication:2022
Release Date:2022/04/25
Tag:Computed tomography; Radon transform; edge detection; feature reconstruction,; limited data; reconstruction; sparse data
Volume:10
Issue:8
Article Number:1318
Institutes:Fakultät Informatik und Mathematik
Begutachtungsstatus:peer-reviewed
OpenAccess Publikationsweg:Gold Open Access- Erstveröffentlichung in einem/als Open-Access-Medium
research focus:Information und Kommunikation
Licence (German):Creative Commons - CC BY - Namensnennung 4.0 International
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