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Algebraic Reconstruction Techniques

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Abstract

The group of algorithms known by their initials algebraic reconstruction techniques (ARTs) is the second most popular family of reconstruction methods. However, ART techniques belong in turn to a broader methodology, which makes use of finite series expansion [4, 5, 15, 16, 18].

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References

  1. Andersen AH, Kak AC (1984) Simultaneous algebraic reconstruction technique: a new implementation of the ART algorithm. Ultrason Imaging 6:81–94

    Article  Google Scholar 

  2. Bouman C, Sauer K (1993) A generalized Gaussian image model for edge-preserving MAP estimation. IEEE Trans Image Process 2(3):296–310

    Article  Google Scholar 

  3. Bouman C, Sauer K (1996) A unified approach to statistical tomography using coordinate descent optimization. IEEE Trans Image Process 5(3):480–492

    Article  Google Scholar 

  4. Censor Y (1981) Row-action methods for huge and sparse systems and their applications. SIAM Rev 23(3):444–464

    Article  MATH  MathSciNet  Google Scholar 

  5. Censor Y (1983) Finite series-expansion reconstruction methods. Proc IEEE 71:409–419

    Article  Google Scholar 

  6. Chazan D, Miranker W (1969) Chaotic relaxation. Linear Algebra Appl 2:199–222

    Article  MATH  MathSciNet  Google Scholar 

  7. DeMan B, Basu S (2004) Distance-driven projection and backprojection in three dimensions. Phys Med Biol 49:2463–2475

    Article  Google Scholar 

  8. Eggermont PPB, Herman GT, Lent A (1981) Iterative algorithms for large partitioned linear systems, with application to image reconstruction. Linear Algebra Appl 40:37–67

    Article  MATH  MathSciNet  Google Scholar 

  9. Geman S, McClure D (1985) Bayesian image analysis: an application to single photon emission tomography. in: Proceedings of the statistical computing section. American statistical association, pp 12–18

    Google Scholar 

  10. Geman S, McClure D (1987) Statistical methods for tomographic image reconstruction. Bull Int Stat Inst LII-4 5–21

    Google Scholar 

  11. Gordon R, Bender R, Herman GT (1970) Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. J Theor Biol 29:471–481

    Article  Google Scholar 

  12. Grimmett GR (1973) A theorem about random fields. Bull London Math Soc 5:81–84

    Article  MATH  MathSciNet  Google Scholar 

  13. Gubarieny N (1999) Generalized model of asynchronous iterations for image reconstruction. Proc Confer PPAM’99, Kazimierz Dolny

    Google Scholar 

  14. Hara AK, Paden RG, Silva AC, Kujak J, Lawder HJ, Pavlicek W (2010) Iterative reconstruction technique for reducing body radiation dose at CT: feasibility study. Am J Roentgenol 193(9):764–771

    Google Scholar 

  15. Herman GT, Lent A (1976) Iterative reconstruction algorithms. Comput Biol Med 6:273–294

    Article  Google Scholar 

  16. Herman GT (1980) Image reconstruction from projections: the fundamentals of computerized tomography. Academic Press, New York

    MATH  Google Scholar 

  17. Jähne B (1991) Digital image processing: concepts, algorithms and scientific applications. Springer, Berlin

    Google Scholar 

  18. Jain AK (1989) Fundamentals of digitals image processing. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  19. Kak AC, Slanley M (1988) Principles of computerized tomographic imaging. IEEE Press, New York

    MATH  Google Scholar 

  20. Kaczmarz S (1937) Angenäherte Auflösung von Systemen linearer Gleichungen. Bull Acad Polon Sci Lett 35:355–357

    Google Scholar 

  21. Saquib SS, Bouman CA, Sauer K,(1998) ML parameter estimation for Markov random fields with application to Bayesian tomography. IEEE Trans Image Process 7(7):1029–1044

    Article  Google Scholar 

  22. Sauer K, Bouman C (1992) Bayesian estimation of transmission tomograms using segmentation based otimization. IEEE Trans Nucl Sci 39(4):1144–1152

    Article  Google Scholar 

  23. Sauer K, Bouman C (1993) A local update strategy for iterative reconstruction from projections. IEEE Trans Signal Process 41(2):534–548

    Article  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  25. Thibault J-B, Sauer K, Bouman C (2000) Newton-style optimization for emission tomographic estimation. J Electron Imag 9(3):269–282

    Article  Google Scholar 

  26. Thibault J-B, Sauer KD, Bouman CA, Hsieh J (2006) A recursive filter for noise reduction in statistical iterative tomographic imaging. SPIE 6065

    Google Scholar 

  27. Thibault J-B, Sauer KD, Bouman CA, Hsieh J (2007) A three-dimensional statistical approach to improved image quality for multislice helical CT. Med Phys 34(11):4526–4544

    Article  Google Scholar 

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Correspondence to Robert Cierniak .

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Cierniak, R. (2011). Algebraic Reconstruction Techniques. In: X-Ray Computed Tomography in Biomedical Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-027-4_8

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  • DOI: https://doi.org/10.1007/978-0-85729-027-4_8

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