Improving Analytical Tomographic Reconstructions Through Consistency Conditions

• Autorzy: Arcadu F. , Vogel J. , Stampanoni M. , Marone F.

Identyfikatory

DOI

10.3233/FI-2017-1589

• Języki publikacji: EN

Abstrakty

EN

This work introduces and characterizes a fast parameterless filter based on the Helgason- Ludwig consistency conditions, used to improve the accuracy of analytical reconstructions of tomographic undersampled datasets. The filter, acting in the Radon domain, extrapolates intermediate projections between those existing. The resulting sinogram, doubled in views, is then reconstructed by a standard analytical method. Experiments with simulated and real data prove that the peak-signal-to-noise ratio of the results computed by filtered backprojection is improved up to 5–6 dB, if the filter is used prior to reconstruction.

Słowa kluczowe

EN

tomography; analytical reconstruction algorithms; consistency conditions

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2017
• Tom: Vol. 155, nr 4
• Strony: 341--361
• Opis fizyczny: Bibliogr. 22 poz., rys., tab., wykr.

Twórcy

autor

Arcadu F.

• Institute for Biomedical Engineering, ETH Zurich, 8092 Zurich, Switzerland, Swiss Light Source, Paul Scherrer Institute, 5232 Villigen, Switzerland

autor

Vogel J.

• Institute for Biomedical Engineering, ETH Zurich, 8092 Zurich, Switzerland, Swiss Light Source, Paul Scherrer Institute, 5232 Villigen, Switzerland

autor

Stampanoni M.

• Institute for Biomedical Engineering, ETH Zurich, 8092 Zurich, Switzerland, Swiss Light Source, Paul Scherrer Institute, 5232 Villigen, Switzerland

autor

Marone F.

• Institute for Biomedical Engineering, ETH Zurich, 8092 Zurich, Switzerland, Swiss Light Source, Paul Scherrer Institute, 5232 Villigen, Switzerland

Bibliografia

• [1] Radon J. Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten. Akad. Wiss., 1917. 69:262–277.
• [2] Ludwig D. The radon transform on euclidean space. Communications on Pure and Applied Mathematics, 2010. 19(1):49–81. doi:10.1002/cpa.3160190105. URL http://dx.doi.org/10.1002/cpa.3160190105.
• [3] Heyn E. Helgason, S., The Radon Transform. Progress in Mathematics 5. Boston-Basel-Stuttgart, Birkhäuser Verlag 1980. VII, 192 S., sFr. 15–ISBN 3-7643-3006-6. ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, 1981. 61(8):411–411. doi:10.1002/zamm.19810610835. URL http://dx.doi.org/10.1002/zamm.19810610835.
• [4] Prince J, Willsky A. Constrained sinogram restoration for limited-angle tomography. Optical Engineering, 1990. 29(5):535–544.
• [5] Kudo H, Saito T. Sinogram recovery with the method of convex projections for limited-data reconstruction in computed tomography. Journal of the Optical Society of America A, 1991. 8(7):1148. doi:10.1364/josaa.8.001148. URL http://dx.doi.org/10.1364/JOSAA.8.001148.
• [6] Gompel GV, Defrise M, Dyck DV. Elliptical extrapolation of truncated 2D CT projections using Helgason-Ludwig consistency conditions. In: Flynn MJ, Hsieh J (eds.), Medical Imaging 2006: Physics of Medical Imaging. SPIE-Intl Soc Optical Eng, 2006 doi:10.1117/12.653293. URL http://dx.doi.org/10.1117/12.653293.
• [7] Xu J, Taguchi K, Tsui BMW. Statistical Projection Completion in X-ray CT Using Consistency Conditions. IEEE Transactions on Medical Imaging, 2010. 29(8):1528–1540. doi:10.1109/tmi.2010.2048335. URL http://dx.doi.org/10.1109/TMI.2010.2048335.
• [8] Yu H, Wang G. Data Consistency Based Rigid Motion Artifact Reduction in Fan-Beam CT. IEEE Transactions on Medical Imaging, 2007. 26(2):249–260. doi:10.1109/tmi.2006.889717. URL http: //dx.doi.org/10.1109/TMI.2006.889717.
• [9] Liu Z, Yau SF. A sinogram restoration technique for the hollow projection problem in computer tomography. In: Proceedings of the 20th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. Vol.20 Biomedical Engineering Towards the Year 2000 and Beyond (Cat. No.98CH36286). Institute of Electrical and Electronics Engineers (IEEE) doi:10.1109/iembs.1998.745502. URL https://doi.org/10.1109%2Fiembs.1998.745502.
• [10] Alessio AM, Kinahan PE, Champley KM, Caldwell JH. Attenuation-emission alignment in cardiac PET/CT based on consistency conditions. Med. Phys., 2010. 37(3):1191. doi:10.1118/1.3315368. URL http://dx.doi.org/10.1118/1.3315368.
• [11] Herman G. Image Reconstruction from Projections: Implementation and Applications (Topics in Applied Physics). Springer, 1979. ISBN 3540094172.
• [12] Kak AC, Slaney M. Principles of Computerized Tomographic Imaging (Classics in Applied Mathematics). Society for Industrial and Applied Mathematics, 2001. ISBN 089871494X.
• [13] Chen GH, Leng S. A new data consistency condition for fan-beam projection data. Med. Phys., 2005. 32(4):961. doi:10.1118/1.1861395. URL http://dx.doi.org/10.1118/1.1861395.
• [14] Clackdoyle R, Desbat L. Full data consistency conditions for cone-beam projections with sources on a plane. Physics in Medicine and Biology, 2013. 58(23):8437–8456. doi:10.1088/0031-9155/58/23/8437. URL http://dx.doi.org/10.1088/0031-9155/58/23/8437.
• [15] Bortfeld T, Oelfke U. Fast and exact 2D image reconstruction by means of Chebyshev decomposition and backprojection. Physics in Medicine and Biology, 1999. 44(4):1105. URL http://stacks.iop.org/0031-9155/44/i=4/a=020.
• [16] Poularikas A. The Transforms and Applications Handbook, Second Edition (Electrical Engineering Handbook). CRC Press, 2000. ISBN 0849385954.
• [17] Shepp LA, Logan BF. The Fourier reconstruction of a head section. IEEE Trans. Nucl. Sci., 1974. 21(3):21–43. doi:10.1109/tns.1974.6499235. URL http://dx.doi.org/10.1109/TNS.1974.6499235.
• [18] Toft P. The Radon Transform. Theory and Implementation. Department of Mathematical Modelling, Section for Digital Signal Processing, Technical University of Denmark, 1996. URL https://books.google.ch/books?id=s7EPYAAACAAJ.
• [19] Lyra M, Ploussi A. Filtering in SPECT Image Reconstruction. International Journal of Biomedical Imaging, 2011. 2011:1–14. doi:10.1155/2011/693795. URL http://dx.doi.org/10.1155/2011/693795.
• [20] Telea A. An Image Inpainting Technique Based on the Fast Marching Method. Journal of Graphics Tools, 2004. 9(1):23–34. doi:10.1080/10867651.2004.10487596. URL https://doi.org/10.1080%2F10867651.2004.10487596.
• [21] Huynh-Thu Q, Ghanbari M. Scope of validity of PSNR in image/video quality assessment. Electron. Lett., 2008. 44(13):800. doi:10.1049/el:20080522. URL http://dx.doi.org/10.1049/el:20080522.
• [22] Schomberg H, Timmer J. The gridding method for image reconstruction by Fourier transformation. IEEE Transactions on Medical Imaging, 1995. 14(3):596–607. doi:10.1109/42.414625. URL http://dx.doi.org/10.1109/42.414625.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).