Abstract
We present two methods that combine image reconstruction and edge detection in computed tomography (CT) scans. Our first method is as an extension of the prominent filtered backprojection algorithm. In our second method we employ \(\mathcal{l}^{1}\)-regularization for stable calculation of the gradient. As opposed to the first method, we show that this approach is able to compensate for undersampled CT data.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Natterer F. The mathematics of computerized tomography. Stuttgart: B. G. Teubner; 1986.
Frikel J, Quinto ET. Characterization and reduction of artifacts in limited angle tomography. Inverse Probl. 2013;29(12):125007.
Canny J. A computational approach to edge detection. IEEE Trans Pattern Anal Mach Intell. 1986;PAMI-8(6):679–698.
Louis AK. Combining image reconstruction and image analysis with an application to two-dimensional tomography. SIAM J Imaging Sci. 2008;1:188–208.
Natterer F, Wübbeling F. Mathematical methods in image reconstruction. SIAM Monographs on Mathematical Modeling and Computation. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM); 2001.
Candés EJ, Romberg JK, Tao T. Stable signal recovery from incomplete and inaccurate measurements. Comm Pure Appl Math. 2006;59(8):1207–1223.
Bubba TA, Hauptmann A, Huotari S, et al. Tomographic X-ray data of a lotus root filled with attenuating objects. 2016; p. 111. arXiv:1609.07299 [physics.data-an].
Daubechies I, Defrise M, De Mol C. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Comm Pure Appl Math. 2004;57(11):1413–1457.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Der/die Autor(en), exklusiv lizenziert durch Springer Fachmedien Wiesbaden GmbH, ein Teil von Springer Nature
About this paper
Cite this paper
Frikel, J., Göppel, S., Haltmeier, M. (2021). Combining Reconstruction and Edge Detection in Computed Tomography. In: Palm, C., Deserno, T.M., Handels, H., Maier, A., Maier-Hein, K., Tolxdorff, T. (eds) Bildverarbeitung für die Medizin 2021. Informatik aktuell. Springer Vieweg, Wiesbaden. https://doi.org/10.1007/978-3-658-33198-6_37
Download citation
DOI: https://doi.org/10.1007/978-3-658-33198-6_37
Published:
Publisher Name: Springer Vieweg, Wiesbaden
Print ISBN: 978-3-658-33197-9
Online ISBN: 978-3-658-33198-6
eBook Packages: Computer Science and Engineering (German Language)