Skip to main content
Top

2018 | OriginalPaper | Chapter

An Improvement of Iterative Algebraic Reconstruction Technique by Using Bisectors: An Illustration in Computerized Tomography

Authors : Mohamad Soubra, Ömer Özgür Tanrıöver

Published in: Computational Vision and Bio Inspired Computing

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This paper proposes the utilization of bisectors for iterative algebraic reconstruction techniques to attain better image reconstruction. We use bisector hyperplanes and the average of the multiple solutions for beam equations. We also discussed why bisector hyperplanes may improve the approximate solution for pixel intensities and how they are obtained. Then, we defined the ART procedure with bisector hyperplanes and implemented the algorithm. Through an application, we compared the solution points obtained with other ART based methods and our ART procedure. As closer solution points may be obtained at each iteration; the images formed by pixels intensities based on these solutions may have higher quality.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Appendix
Available only for authorised users
Literature
1.
go back to reference Anton, H., Rorres, C.: Elementary Linear Algebra Applications, pp. 685–697. Wiley, New York (1994) Anton, H., Rorres, C.: Elementary Linear Algebra Applications, pp. 685–697. Wiley, New York (1994)
3.
go back to reference Kak, A.C., Slaney, M.: Principles of Computerized Tomographic Imaging, pp. 276–294. SIAM, New York, (2001) Kak, A.C., Slaney, M.: Principles of Computerized Tomographic Imaging, pp. 276–294. SIAM, New York, (2001)
4.
go back to reference Sakas, G.: Trends in medical imaging: from 2D to 3D. Comput. Graph. 577–587 (2002) Sakas, G.: Trends in medical imaging: from 2D to 3D. Comput. Graph. 577–587 (2002)
5.
go back to reference Jiri, J.: Medical Image Processing, Reconstruction an Restoration, pp. 374–400. Taylor and Francis, New York (2006) Jiri, J.: Medical Image Processing, Reconstruction an Restoration, pp. 374–400. Taylor and Francis, New York (2006)
7.
go back to reference Kesidis, A.L., Papamarkos, N.: Exact image reconstruction from a limited number of projections. J. Vis. Commun. Image Represent. 285–298 (2008) Kesidis, A.L., Papamarkos, N.: Exact image reconstruction from a limited number of projections. J. Vis. Commun. Image Represent. 285–298 (2008)
8.
go back to reference Dai, X.B., Shua, H.Z., Luoa, L.M., Hanb, G.N., Coatrieux, J.L.: Reconstruction of tomographic images from limited range projections using discrete Radon transform and Tchebichef moments. Pattern Recogn. 1152–1164 (2010) Dai, X.B., Shua, H.Z., Luoa, L.M., Hanb, G.N., Coatrieux, J.L.: Reconstruction of tomographic images from limited range projections using discrete Radon transform and Tchebichef moments. Pattern Recogn. 1152–1164 (2010)
11.
go back to reference Cengiz, K., Kamasak, M.: Comparison of algebraic reconstruction techniques for tomosynthesis. In: IWSSIP 2014 Proceedings, Dubrovnik, pp. 15–18 (2014) Cengiz, K., Kamasak, M.: Comparison of algebraic reconstruction techniques for tomosynthesis. In: IWSSIP 2014 Proceedings, Dubrovnik, pp. 15–18 (2014)
12.
go back to reference Li, Z., Song, Y.: Improving algebraic reconstruction techniques with nonlinear iterating algorithms. In: 2009 Fifth International Conference on Natural Computation, Tianjin, pp. 387–391 (2009) Li, Z., Song, Y.: Improving algebraic reconstruction techniques with nonlinear iterating algorithms. In: 2009 Fifth International Conference on Natural Computation, Tianjin, pp. 387–391 (2009)
13.
go back to reference Chetih, N., Messali, Z.: Tomographic image reconstruction using filtered back projection (FBP) and algebraic reconstruction technique (ART). In: 2015 3rd International Conference on Control, Engineering & Information Technology (CEIT), Tlemcen, pp. 1–6 (2015) Chetih, N., Messali, Z.: Tomographic image reconstruction using filtered back projection (FBP) and algebraic reconstruction technique (ART). In: 2015 3rd International Conference on Control, Engineering & Information Technology (CEIT), Tlemcen, pp. 1–6 (2015)
14.
go back to reference Wan, X., Zhang, F., Liu, Z.: Modified simultaneous algebraic reconstruction technique and its parallelization in cryo-electron tomography. In: 2009 15th International Conference on Parallel and Distributed Systems (ICPADS), Shenzhen, pp. 384–390 (2009) Wan, X., Zhang, F., Liu, Z.: Modified simultaneous algebraic reconstruction technique and its parallelization in cryo-electron tomography. In: 2009 15th International Conference on Parallel and Distributed Systems (ICPADS), Shenzhen, pp. 384–390 (2009)
15.
go back to reference Kim, J.H., Kang, B.C., Choi, B.Y., Lee, S.H., Kim, K.Y.: On-line directional algebraic reconstruction technique for electrical capacitance tomography. In: 2006 5th IEEE Conference on Sensors, Daegu, pp. 923–926 (2006) Kim, J.H., Kang, B.C., Choi, B.Y., Lee, S.H., Kim, K.Y.: On-line directional algebraic reconstruction technique for electrical capacitance tomography. In: 2006 5th IEEE Conference on Sensors, Daegu, pp. 923–926 (2006)
16.
go back to reference Jiang, M., Wang, G.: Convergence of the simultaneous algebraic reconstruction technique (SART). IEEE Trans. Image Process. 12(8), 957–961 (2003)MathSciNetCrossRefMATH Jiang, M., Wang, G.: Convergence of the simultaneous algebraic reconstruction technique (SART). IEEE Trans. Image Process. 12(8), 957–961 (2003)MathSciNetCrossRefMATH
17.
go back to reference Saha, S., Tahtali, M., Lambert, A., Pickering, M.: Compressed sensing inspired rapid algebraic reconstruction technique for computed tomography. In: IEEE International Symposium on Signal Processing and Information Technology, Athens, pp. 000398–000403 (2013) Saha, S., Tahtali, M., Lambert, A., Pickering, M.: Compressed sensing inspired rapid algebraic reconstruction technique for computed tomography. In: IEEE International Symposium on Signal Processing and Information Technology, Athens, pp. 000398–000403 (2013)
18.
go back to reference Oliveira, N., Mota, A.M., Matela, N., Janeiro, L., Almeida, P.: Dynamic relaxation in algebraic reconstruction technique (ART) for breast tomosynthesis imaging. Comput. Methods Programs Biomed. 132, 189–196 (2016)CrossRef Oliveira, N., Mota, A.M., Matela, N., Janeiro, L., Almeida, P.: Dynamic relaxation in algebraic reconstruction technique (ART) for breast tomosynthesis imaging. Comput. Methods Programs Biomed. 132, 189–196 (2016)CrossRef
Metadata
Title
An Improvement of Iterative Algebraic Reconstruction Technique by Using Bisectors: An Illustration in Computerized Tomography
Authors
Mohamad Soubra
Ömer Özgür Tanrıöver
Copyright Year
2018
DOI
https://doi.org/10.1007/978-3-319-71767-8_66