Feature Reconstruction from Incomplete Tomographic Data without Detour

Simon Göppel, Jürgen Frikel and Markus Haltmeier
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Simon Göppel: Department of Mathematics, University of Innsbruck, Technikerstraße 13, A-6020 Innsbruck, Austria
Jürgen Frikel: Faculty of Mathematics and Computer Sciences, OTH Regensburg, Galgenbergstraße 32, 93053 Regensburg, Germany
Markus Haltmeier: Department of Mathematics, University of Innsbruck, Technikerstraße 13, A-6020 Innsbruck, Austria

Mathematics, 2022, vol. 10, issue 8, 1-17

Abstract: 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.

Keywords: computed tomography; Radon transform; reconstruction; limited data; sparse data; feature reconstruction; edge detection (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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