Abstract
The paper describes an original algorithm for reconstructing tomographic images from a few views. The algorithm is based on the known iterative Simultaneous Multiplicative Algebraic Reconstruction Technique (SMART). It is peculiar in that corrections for different zones of the reconstruction area are calculated differently with allowance for the distribution of shadows from contrast structures. The algorithm we call SMART-SA (SMART with Shadow Allowance) is implemented in 2D and tested for two numerical models with an air cavity and a material interface with 10% contrast. Reconstruction results are evaluated visually and quantitatively with such characteristics as correlation coefficient and deviation factor. It is shown that SMART-SA is capable of reconstructing the images that are free of artifacts typical of few-views tomography, and it performs especially well in combination with the MART-AP algorithm we published earlier.
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References
Herman, G.T.: Fundamentals of Computerized Tomography: Image Reconstruction from Projections. Springer-Verlag, London (2009)
Scott, D.M., Williams, R.A. (eds.) Frontiers in Industrial Process Tomography. Engineering Foundation, New York (1996)
Pickalov, V.V., Melnikova, T.S.: Plasma Tomography. Nauka, Novosibirsk (1995). (in Russian)
Batenburg, K.J., Bals, S., Sijbers, J., Kübel, C., Midgley, P.A., Hernandez, J.C., Kaiser, U., Encina, E.R., Coronado, E.A., Van Tendeloo, G.: 3D Imaging of Nanomaterials by Discrete Tomography. Ultramicroscopy 109, 730–740 (2009)
Konovalov, A.B., Mogilenskikh, D.V., Kozlov, E.A., Vlasov, V.V., Kiselev, A.N., Kovalev, E.V., Zakharov, M.N., Povyshev, V.N., Stavrietskii, V.I.: Few-View Gamma Tomography Used to Monitor Scabbing and Shear Fracture in a Spherical Iron Shell Compressed by Explosion. Russ. J. Nondestruct. Testing 44(1), 15–24 (2008)
Pang, T.F.: AWE multi-axis radiographic facility: a review of 3D-reconstructions from limited data. In: Mohammad-Djafari, A. (ed.) AIP Conference Proceedings, vol. 568, pp. 521–530. AIP Publ., New York (2001)
Gordon, R., Bender, R., Herman, G.T.: Algebraic Reconstruction Techniques (ART) for Three-Dimensional Electron Microscopy and X-Ray Photography. J. Theor. Biol. 29, 471–481 (1970)
Anderson, A., Kak, A.: Simultaneous Algebraic Reconstruction Technique (SART): A Superior Implementation of the ART Algorithm. Ultrason. Imaging 6, 81–94 (1984)
Byrne, C.L.: Iterative Image Reconstruction Algorithms Based on Cross-Entropy Minimization. IEEE Trans. Image Process. 2, 96–103 (1993)
Minerbo, G.: MENT: A Maximum Entropy Algorithm for Reconstructing a Source from Projection Data. Comput. Graph. Image Process. 10, 48–68 (1979)
Rangayyan, R.M., Gordon, R.: Streak Preventive Image Reconstruction with ART and Adaptive Filtering. IEEE Trans. Med. Imaging 1, 173–178 (1982)
Konovalov, A.B., Vlasov, V.V., Kalintsev, A.G., Kravtsenyuk, O.V., Lyubimov, V.V.: Time-Domain Diffuse Optical Tomography Using Analytic Statistical Characteristics of Photon Trajectories. Quantum Electronics 36, 1048–1055 (2006)
Konovalov, A.B., Mogilenskikh, D.V., Vlasov, V.V., Kiselev, A.N.: Algebraic reconstruction and post-processing in incomplete data computed tomography: from X-rays to laser beams. In: Obinata, G., Dutta, A. (eds.) Vision Systems: Applications, pp. 487–518. I-Tech Education and Publishing, Vienna (2007)
Siltanen, S., Kolehmainen, V., Jaervenpaa, S., Kaipio, J.P., Koistinen, P., Lassas, M., Pirttila, J., Somersalo, E.: Statistical Inversion for X-Ray Tomography with Few Radiographs. I. General Theory. Phys. Med. Biol. 48, 1437–1463 (2003)
Herman, G.T., Kuba, A. (eds.): Discrete Tomography: Foundations, Algorithms and Applications. Birkhauser, Boston (1999)
Herman, G.T., Kuba, A. (eds.): Advances in Discrete Tomography and its Applications. Birkhauser, Boston (2007)
Batenburg, K.J., Sijbers, J.: DART: A Practical Reconstruction Algorithm for Discrete Tomography. IEEE Trans. Image Process. 20, 2542–2553 (2011)
Batenburg, K.J., Sijbers, J., Poulsen, H.F., Knudsen, E.: DART: A Robust Algorithm for Fast Reconstruction of Three-Dimensional Grain Maps. J. Appl. Crystalogr. 43, 1464–1473 (2010)
Vlasov, V.V., Konovalov, A.B., Uglov, A.S.: An a priori information based algorithm for artifact preventive reconstruction in few-view computed tomography. In: 5th International Symposium on Communications, Control and Signal Processing, paper 042. University Roma Tre, Roma (2012)
Konovalov, A.B., Vlasov, V.V.: Spatial Resolution Analysis for Few-Views Discrete Tomography Based on MART-AP Algorithm. ISRN Sign. Process. 2013, 356291 (2013)
Konovalov, A.B.: Time-Domain Diffuse Optical Mammotomography. The Photon Average Trajectory Method. Lambert Academic Publishing, Saarbrüken (2014). (in Russian)
Zucker, S.W.: Region Growing: Childhood and Adolescence. Comput. Graphics Image Process. 5, 382–399 (1976)
Gonzalez, R.C., Woods, R.E.: Digital Image Processing. Prentice-Hall, New Jersey (2002)
Klose, A.D., Hielscher, A.H.: Quasi-Newton Methods in Optical Tomographic Image Reconstruction. Inverse Problems 19, 387–409 (2003)
Batenburg, K.J., Van Aarle, W., Sijbers, J.: A Semi-Automatic Algorithm for Grey Level Estimation in Tomography. Pattern Recognit. Lett. 32, 1395–1405 (2011)
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Vlasov, V.V., Konovalov, A.B., Uglov, A.S. (2015). Few-Views Image Reconstruction with SMART and an Allowance for Contrast Structure Shadows. In: Azzopardi, G., Petkov, N. (eds) Computer Analysis of Images and Patterns. CAIP 2015. Lecture Notes in Computer Science(), vol 9256. Springer, Cham. https://doi.org/10.1007/978-3-319-23192-1_56
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DOI: https://doi.org/10.1007/978-3-319-23192-1_56
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