Papoulis-Gerchberg Algorithms for Limited Angle Tomography Using Data Consistency Conditions

Huang Y, Taubmann O, Huang X, Lauritsch G, Maier A (2018)

Publication Language: English

Publication Type: Conference contribution, Original article

Publication year: 2018

City/Town: Salt Lake City, Utah, the USA

Pages Range: 189-192

Conference Proceedings Title: Proceedings of the 5th International Conference on Image Formation in X-ray Computed Tomography

Event location: Salt Lake City, Utah, the USA

URI: https://www5.informatik.uni-erlangen.de/Forschung/Publikationen/2018/Huang18-PAF.pdf

Abstract

The Papoulis-Gerchberg (P-G) algorithm is widely used for extrapolation of band-limited signals. It is applicable to limited angle tomography as well since typical imaged objects in computed tomography have a limited spatial extent, which means that the Fourier transforms of the objects can be considered band-limited signals. In computed tomography, some other bandlimitation properties have been discovered as well, which are referred to as data consistency conditions. For example, the Fourier transform of a parallel-beam sinogram has an empty double-wedge region. The Chebyshev-Fourier transform of a parallel-beam sinogram only has nonzero values inside a wedge region and these values form a checkerboard pattern, which is Helgason-Ludwig consistency condition. In this paper, we propose two P-G algorithms to restore missing data in limited angle tomography using the above two consistency conditions. Numerical experiments on the Shepp-Logan phantom demonstrate that they can reduce streaks better than the conventional P-G algorithm. 

Authors with CRIS profile

Involved external institutions

Siemens AG, Healthcare Sector Germany (DE)

How to cite

APA:

Huang, Y., Taubmann, O., Huang, X., Lauritsch, G., & Maier, A. (2018). Papoulis-Gerchberg Algorithms for Limited Angle Tomography Using Data Consistency Conditions. In Proceedings of the 5th International Conference on Image Formation in X-ray Computed Tomography (pp. 189-192). Salt Lake City, Utah, the USA: Salt Lake City, Utah, the USA.

MLA:

Huang, Yixing, et al. "Papoulis-Gerchberg Algorithms for Limited Angle Tomography Using Data Consistency Conditions." Proceedings of the the 5th International Conference on Image Formation in X-ray Computed Tomography, Salt Lake City, Utah, the USA Salt Lake City, Utah, the USA, 2018. 189-192.

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