Abstract
We compare three cone-beam reconstruction algorithms called and implemented as RADON, LINCON and DC respectively. In a first phase all three algorithms compute the derivative of the 3D Radon transform. In a second phase RADON and LINCON employ the inversion formula for the 3D Radon transform. RADON uses line-integration and 2D backprojections for the first and second phase, respectively, while LINCON employs linogram techniques in both phases of the algorithm. During the second phase in DC, filtered cone-beam projections are generated, which are then backprojected into the reconstructed 3D-volume.
This study is mainly concerned with quality measures such as the Modulation Transfer Function (MTF) and noise sensitivity. We have found that the image quality in RADON is improved with extra zeropadding in the Fourier domain. Introduction of linogram techniques in the DC-method seems very beneficial. The resolution is improved, the distortions are reduced as well as the reconstruction time.
RADON with zeropadding and LINCON yield the best MTF. Ringing and noise sensitivity follow the MTF rather closely. Less smoothing improves the resolution but increase the ringing and the noise sensitivity. For reconstruction of an N 3 volume from N 3 data values LINCON has the theoretical complexity O(N 3 logN), while both RADON and DC have complexity O(N 4). In practise we have found that for equivalent image quality when reconstructing a 1283-volume LINCON is twice as fast as RADON and DC. DC requires considerably less memory than the other two. Due to the 3D backprojection reconstruction one 2D-projection can be processed in full while the next one is detected.
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References
Axelsson, C. and Danielsson, P.E. (1994) 3D Reconstruction from Cone-Beam Data in O(N31ogN) time, Physics in Medicine and Biology, Vol. 39, pp. 477–491.
Defrise, M. and Clack, R. (1994) A Cone-Beam Reconstruction Algorithm Using Shift-Variant Filtering and Cone-Beam Backprojection, IEEE Transactions in Medical Imaging, Vol. 13, No. 1, pp. 186–195.
Defrise, M. and Clack, R. (1995) Filtered backprojection reconstruction of combined parallel beam and cone beam SPECT data, Phys. Med. Biol. 40, pp. 1517–1537.
Edholm, P.R. and Herman, G.T. (1987) Linograms in image reconstructions from projections, IEEE Transaction on medical imaging, Vol. MI-6, pp. 301–307.
Feldkamp, L.A. and Davis, L.C. and Kress, J.0. (1984) Practical cone-beam algorithms, J. Opt. Soc. Am, vol. A6, No. 10, pp. 612–619.
Grangeat, P. (1991) Mathematical framework of cone beam 3D reconstruction via the first derivative of the Radon transform, in G.T. Herman and A.K. Louis and F. Natterer (eds.), Mathematical Methods in Tomography, Springer Verlag, Lecture notes in Mathematics No. 1497, pp. 66–97.
Kudo, H. and Saito, T. (1994) Derivation and implementation of a cone-beam reconstruction algorithm for non-planar orbits, IEEE Transactions on medical imaging, Vol. 13, No. 1, pp. 196–211.
Magnusson, M. (1993) Linogram and Other Direct Fourier Methods for Tomographic Reconstruction, Dissertations No. 320, Linköping studies in Science and Technology, S-581 83 Linköping, Sweden.
Marr, R.B. and Chen, C. and Lauterbur, P.C. (1981) On two approaches to 3D reconstruction onstruction in NMR zeugmatography, Proc. of Mathematical Aspect of Computerized Tomography, Oberwolfach (FRG), 1980, G.T. Herman, F. Natterer (eds.), SpringerVerlag.
Rabiner, L.R. and Schafer, R.W. and Rader, C.M. (1969) The Chirp z-transform Algorithm, No. 2, pp. 86 rithm, IEEE Transactions on audio and electroacoustics, vol. AU-17 No 86–92.
Rizo, P. and Grangeat, P. and Sire, P. and Lemasson, P. and Melennec, P. (1991) Comparison of two three-dimensional X-ray cone-beam reconstruction algorithms with circular source trajectories, J. Opt. Soc. Am. A, vol. 8, No. 10.
Smith, B.D. (1985) Image reconstruction from Cone-Beam Projections: Necessary and Sufficient Conditions and Reconstruction Methods, IEEE Transactions on medical imaging, vol. MI-4, No. 1.
Tuy, H.K. (1983) An inversion formula for cone-beam reconstruction, SIAM J. Appl. Math., vol. 43, No. 3.
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© 1996 Springer Science+Business Media Dordrecht
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Axelsson-Jacobson, C., Guillemaud, R., Danielsson, PE., Grangeat, P., Defrise, M., Clack, R. (1996). Comparison of three 3D-Reconstruction Methods from Cone-Beam Data. In: Grangeat, P., Amans, JL. (eds) Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine. Computational Imaging and Vision, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8749-5_1
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DOI: https://doi.org/10.1007/978-94-015-8749-5_1
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