Volume 14, no. 1Pages 104 - 118 Algorithm of Reconstructionof Three-Dimensional Images In X-Ray Computed Tomography with a Cone Beam
E. Simonov, A.V. ProkhorovAn algorithm for reconstructing three-dimensional images for X-ray computed tomography with a cone beam of radiation is developed. The algorithm is based on an
Full text- Keywords
- accurate analytical representation of the three-dimensional Radon transformation of the projection data. For this representation, an iteration-invariant point scattering function (FRT) is introduced. The proposed algorithm overcomes the main drawback of approximate algorithms-it provides a sufficiently high quality of the obtained images even at large angles of the radiation cone, which is manifested in a relatively small number of image artefacts. The quality of the reconstructed tomographic images was evaluated.
- References
- 1. Simonov E.N. Fizika vizualizacii izobrazhenij v rentgenovskoj komp'yuternoj tomografii [Physics of Image Visualization in X-Ray Computed Tomography]. Chelyabinsk, Publishing Center of SUSU, 2014. (in Russian)
2. Simonov E.N., Avramov M.V. [On the Development of Methods for Image Reconstruction in X-Ray Computed Tomography with a Cone Beam of Radiation]. Bulletin of the South Ural State University. Series: Computer Technology, Automatic Control, Radio Electronics, 2015, vol. 15, no. 4, pp. 58-66. DOI: 10.14529/ctcr150406 (in Russian)
3. Simonov E.N., Avramov M.V., Avramov D.V. [Analysis of Three-Dimensional Reconstruction Algorithms in X-Ray Computed Tomography]. Bulletin of the South Ural State University. Series: Computer Technology, Automatic Control, Radio Electronics, 2017, vol. 17, no. 2, pp. 24-32. (in Russian) DOI: 10.14529/ctcr170202
4. Kalender V. Kompyuternaya tomografiya osnovy, tekhnika, kachestvo izobrazhenij i oblasti klinicheskogo ispolzovaniya [Computed Tomography Fundamentals, Technique, Image Quality and Clinical Applications]. Moscow, Tekhnosfera, 2006. (in Russian)
5. Feldkamp L.A., Davis L.C., Kress J.W. Practicalcone-Beam Algorithm. Journal of the Optical Society of America A., 1984, no. 2, pp. 612-614.
6. Kachelrie M., Knaup M., Kalender W.A. Extended Parallel Backprojection for Standard Three-Dimensional and Phase-Correlated Four-Dimensional Axial and Spiral Cone-Beam Ct with Arbitrary Pitch, Arbitrary Cone-Angle, and 100 Dose Usage.MedicalPhysics, 2004, vol. 31, no. 1. pp. 1623–1641.
7. Kachelrie M., Shaller M., Kalender W.A. Advanced Single-Slice Rebinning in Cone-Beam Spiral CT. Medical Physics, 2001, vol. 27, no. 4. pp. 1033-1041.
8. Katsevich A. A General Scheme for Constructing Inversion Algorithms for Cone Beam CT. International Journal of Mathematics and Mathematical Sciences, 2003, no. 21, pp. 1305-1321.
9. Simonov E.N., Avramov D.V. K voprosu polucheniya ob''emnykh izobrazheniy v rentgenovskoy komp'yuternoy tomografii [On the Issue of Obtaining Volumetric Images in X-Ray Computed Tomography]. Bulletin of the South Ural State University. Series: Computer Technology, Automatic Control, Radio Electronics, 2015. vol. 15, no. 4, pp. 50-57. (in Russian)
10. Simonov E.N., Avramov M.V., Avramov D.V. [Volumetric Rendering Method for Visualizing Three-Dimensional Data in X-Ray Computed Tomography]. Bulletin of the South Ural State University. Series: Computer Technology, Automatic Control, Radio Electronics, 2016, vol. 16, no. 4, pp. 5-12. (in Russian) DOI: 10.14529/ctcr160401
11. Simonov E.N., Avramov M.V. Review of Image Reconstruction Methods in X-Ray Computed Tomography with Cone-Beam Geometry. Bulletin of the South Ural State University. Series: Computer Technology, Automatic Control, Radio Electronics, 2018, vol. 18, no. 2, pp. 29-37. DOI: 10.14529/ctcr180203 (in Russian)
12. Smith B.D. Cone-Beam Tomography: Recent Advances and Tutorial Review. Optical Engineering, 1991, no. 29, pp. 524-534.
13. Bronnikov V., Duifhuis G. Wavelet-Based Image Enhancementin X-Ray Imaging and Tomography. Applied Optics, 1998, no. 37, pp. 4437-4448.
14. Kirillov A. On a Problem of I.M. Gelfand. Doklady Akademii Nauk SSSR: Mathematics, 1961, no. 2, pp. 268-269.
15. Tuy Heang K. An Inversion Formula for Cone-Beam Reconstruction. SIAM Journal on Applied Mathematics, 1983, no. 43, pp. 546-552.
16. Bronnikov A.V. Cone-Beam Reconstruction by Backprojection and Filtering. Journal of the Optical Society of America A, 2000, vol. 17, no. 11, pp. 1993-2000.
17. Hermen G. Vosstanovlenie izobrazhenij po proekciyam: Osnovy rekonstruktivnoj tomografii [Reconstruction of Images from Projections: Fundamentals of Reconstructive Tomography]. Moscow, Mir, 1983. (in Russian)