Abstract
Tomographic reconstruction algorithms perform reconstruction on a discrete grid, assuming a discrete projection model. However, such discrete assumptions bring artifacts into the reconstructed results, we call interpolation error. We compared eight projection models including the Joseph, Siddon or box-beam-integrated methods for analyzing their interpolation errors. We found that by selecting the proper projection model, one can gain significantly better reconstruction quality.
We are grateful to the Nvidia Hardware Grant program for providing a GPU for the research. Ministry of Human Capacities, Hungary, grant 20391-3/2018/FEKUSTRAT is acknowledged. This research was supported by the project “Integrated program for training new generation of scientists in the fields of computer science”, no EFOP-3.6.3-VEKOP-16-2017-0002. The project has been supported by the European Union and co-funded by the European Social Fund.
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References
Dataset. https://urlzs.com/y1UG3
Matlab r2017b. The MathWorks Inc, Natick, Massachusetts, United States
van Aarle, W., et al.: Fast and flexible x-ray tomography using the astra toolbox. Opt. Express 24(22), 25129–25147 (2016)
Andersen, A., Kak, A.: Simultaneous algebraic reconstruction technique (SART): a superior implementation of the art algorithm. Ultrason. Imaging 6(1), 81–94 (1984)
Danielsson, P.E., Magnusson, M., Cvl, S.: Combining fourier and iterative methods in computer tomography: analysis of an iteration scheme. the 2D-case 49 (2004)
Flores, L., Vidal, V., Verdu, G.: System matrix analysis for computed tomography imaging. PLoS ONE 10, 1252–1255 (2015)
Foi, A., Trimeche, M., Katkovnik, V., Egiazarian, K.: Practical poissonian-gaussian noise modeling and fitting for single-image raw-data. IEEE Trans. Image Process. 17(10), 1737–1754 (2008)
Hahn, K., Schondube, H., Stierstorfer, K., Hornegger, J., Noo, F.: A comparison of linear interpolation models for iterative CT reconstruction. Med. Phys. 43(12), 6455–6473 (2016)
Hanson, K.M., Wecksung, G.W.: Local basis-function approach to computed tomography. Appl. Opt. 24, 4028 (1985)
Haralick, R., Shanmugam, K., Dinstein, I.: Textural features for image classification. IEEE Trans. Syst. Man Cybern. SMC 3(6), 610–621 (1973)
Herman, G.: Fundamentals of Computerized Tomography: Image Reconstruction from Projections, 2nd edn. Springer, London (2009). https://doi.org/10.1007/978-1-84628-723-7
Joseph, P.: An improved algorithm for reprojecting rays through pixel images. IEEE Trans. Med. Imaging 1(3), 192–196 (1982)
Kak, A., Slaney, M.: Principles of Computerized Tomographic Imaging. IEEE Press, New York (1999)
Shepp, L.A., Logan, B.F.: The fourier reconstruction of a head section. IEEE Trans. Nucl. Sci. 21(3), 21–43 (1974)
Lewitt, R.: Alternatives to voxels for image representation in iterative reconstruction algorithms. Phys. Med. Biol. 37(3), 705–716 (1992)
Man, B.D., Basu, S.: Distance-driven projection and backprojection in three dimensions. Phys. Med. Biol. 49, 2463–2475 (2004)
Siddon, R.: Fast calculation of the exact radiological path for a three-dimensional ct array. Med. Phys. 12, 252–255 (1985)
van der Sluis, A., van der Vorst, H.: SIRT- and CG-type methods for the iterative solution of sparse linear least-squares problems. Linear Algebra Appl. 130, 257–303 (1990)
Wang, Z., Bovik, A., Sheikh, H., Simoncelli, E.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)
Xu, F., Mueller, K.: A comparative study of popular interpolation and integration methods for use in computed tomography. In: 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, vol. 4, pp. 1252–1255 (2006)
Yu, Z., Noo, F., Dennerlein, F., Wunderlich, A., Lauritsch, G., Hornegger, J.: Simulation tools for two-dimensional experiments in x-ray computed tomography using the for bild head phantom. Phys. Med. Biol. 57(13), 237–252 (2012)
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Olasz, C., Varga, L.G., Nagy, A. (2019). Evaluation of the Interpolation Errors of Tomographic Projection Models. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2019. Lecture Notes in Computer Science(), vol 11845. Springer, Cham. https://doi.org/10.1007/978-3-030-33723-0_32
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DOI: https://doi.org/10.1007/978-3-030-33723-0_32
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