Skip to main content

Methods for Improving the Quality of Image Reconstruction in Computerized Tomography

  • Chapter
  • First Online:
Models and Theories in Social Systems

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 179))

  • 419 Accesses

Abstract

Appeared in early 50s in medical applications, but essentially developed since early 70s Computerized Tomography (CT) has became nowadays one of the most powerful investigation tool in science and technology. In this chapter we present several classes of methods which can rise the efficiency and/or robustness of classical projection-based algorithms (as Kaczmarz and Cimmino type algorithms) for algebraic reconstruction of images in Computerized Tomography.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Bautu, A., Bautu, E., Popa, C.: Evolutionary algorithms in image reconstruction from limited data. In: Proceedings of the 4th Workshop on Mathematical Modelling on Environmental and Life Sciences Problems, 7–10 Sept 2005. Constanta, Romania, Publishing House of the Romanian Academy, Bucharest, Romania, pp. 15–26 (2006)

    Google Scholar 

  • Butz F., Fügenschuh, Wood J.N., Breuer M.: Particle-image velocimetry and the assignement problem. In: Fink, A., Fgenschuh, A., Geiger, M. (eds.), Operations Research Proceedings (GOR (Gesellschaft fr Operations Research e.V.)). Springer, Cham, pp. 243–249 (2016)

    Google Scholar 

  • Censor, Y., Stavros, A.Z.: Parallel optimization: theory, algorithms and applications. In: Numerical Mathematics and Scientific Computation Series. Oxford Univ. Press, New York (1997)

    Google Scholar 

  • Censor, Y., Gordon, D., Gordon, R.: Component averaging: an efficient iterative parallel algorithm for large and sparse unstructured problems. Parallel Comput. 27, 777–808 (2001)

    Article  MathSciNet  Google Scholar 

  • Censor, Y., Pantelimon, I., Popa, C.: Family constraining of iterative algorithms. Numer. Alg. 66(2), 323–338 (2014)

    Article  MathSciNet  Google Scholar 

  • Cimmino, G.: Calcolo approssiomatto per le soluzioni dei sistemi di equazioni lineari. Ric. Sci. progr. tecn. econom. naz. 1, 326–333 (1938)

    MATH  Google Scholar 

  • Herman, G.T.: Image reconstruction from projections. In: The Fundamentals of Computerized Tomography. Academic Press, New York (1980)

    Google Scholar 

  • Kaczmarz, S.: Angenaherte Auflosung von Systemen linearer Gleichungen. Bull. Acad. Polonaise Sci. et Lettres A , 355–357 (1937)

    Google Scholar 

  • Kaczmarz, S.: Approximate solution of systems of linear equations. Int. J. Control. 57(6), 1269–1271 (1993)

    Article  MathSciNet  Google Scholar 

  • Koltracht, I., Lancaster, P.: Constraining strategies for linear iterative processes. IMA J. Numer. Anal. 10, 555–567 (1990)

    Article  MathSciNet  Google Scholar 

  • Köstler, H., Popa, C., Preclik, T., Rüde, U.: On Kaczmarz’s projection iteration as a direct solver for linear least squares problems. Linear Alg. Appl. 436(2), 389–404 (2012)

    Article  MathSciNet  Google Scholar 

  • Natterer, F.: The Mathematics of Computerized Tomography. Wiley, New York (1986)

    Google Scholar 

  • Nicola, A., Petra, S., Popa, C., Schnörr, C.: A general extending and constraining procedure for linear iterative methods. Int. J. Comput. Math. 89(2), 231–253 (2012)

    Article  MathSciNet  Google Scholar 

  • Pantelimon, I., Popa, C.: Constraining by a family of strictly nonexpansive idempotent functions with applications in image reconstruction. BIT Numer. Math. 53, 527–544 (2013)

    MathSciNet  MATH  Google Scholar 

  • Petra, S., Popa, C., Schnörr, C.: Accelerating Constrained SIRT with Applications in Tomographic Particle Image Reconstruction (2009). http://www.ub.uni-heidelberg.de/archiv/9477

  • Popa, C., Zdunek, R.: Kaczmarz extended algorithm for tomographic image reconstruction from limited-data. Math. Comput. Simul. 65, 579–598 (2004)

    Article  MathSciNet  Google Scholar 

  • Popa, C.: Constrained Kaczmarz extended algorithm for image reconstruction. Linear Alg. Appl. 429(8–9), 2247–2267 (2008)

    Article  MathSciNet  Google Scholar 

  • Popa, C.: A hybrid Kaczmarz—conjugate gradient algorithm for image reconstruction. Math. Comput. Simul. 80(12), 2272–2285 (2010)

    Article  MathSciNet  Google Scholar 

  • Popa, C.: Extended and constrained diagonal weighting algorithm with application to inverse problems in image reconstruction. Inv. Probl. 26(6), 17p (2010)

    Article  MathSciNet  Google Scholar 

  • Tanabe, K.: Projection method for solving a singular system of linear equations and its applications. Numer. Math. 17, 203–214 (1971)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Constantin Popa .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Carp, D., Popa, C., Şerban, C. (2019). Methods for Improving the Quality of Image Reconstruction in Computerized Tomography. In: Flaut, C., Hošková-Mayerová, Š., Flaut, D. (eds) Models and Theories in Social Systems. Studies in Systems, Decision and Control, vol 179. Springer, Cham. https://doi.org/10.1007/978-3-030-00084-4_5

Download citation

Publish with us

Policies and ethics