A regularization method for unfolding the measured data of different X-ray spectrometers in Compton scattering tomography

  • C. Bonifazzi
  • G. Maino
  • A. Tartari
Poster Session D: Biomedical Applications, Detection, Control & Surveillance, Inspection, Optical Character Recognition
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1311)


Radiation imaging techniques are important tools in many fields of basic and applied sciences, from medical analyses to industrial applications. In addition to the conventional photon transmission tomography, methods based on the Compton scattering and X-ray diffraction have been developed in the last ten years. In this paper, we discuss some inverse problems relevant to the image recovering of scattering and diffraction tomography. In particular, the problem of recovering the X-ray spectrum from measured data is discussed in detail and it is shown that the original signal from both NaI(Tl) and HP-Ge spectrometers characterized by very different energy resolution, can be uniquely reconstructed.


Pulse Height Compton Scattering HPGe Detector Sommable Function Intrinsic Resolution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    H.H.Barret and W.Swindell, Radiological Imaging. The Theory of Image Formation, Detection and Processing, Academic Press, New York (1981).Google Scholar
  2. 2.
    S.R.Gautam, F.F.Hopkins, R.Kliksiek and I.L.Morgan, IEEE Trans. Nucl. Sci. NS-30 (1983) 1680.Google Scholar
  3. 3.
    G.Harding and R.Tischler, Phys. Med. Biol. 31 (1986) 477.CrossRefPubMedGoogle Scholar
  4. 4.
    J.Hadamard, Bull. Univ. Princeton 13 (1902); Le probléme de Cauchy et les équations aux dérivées partielles linéaires hyperboliques, Hermann, Paris (1932).Google Scholar
  5. 5.
    B.Hofmann, Regularization for Applied Inverse and Ill-Posed Problems. A Numerical Approach, Teubner — Texte zur Mathematik 85, Leipzig (1986).Google Scholar
  6. 6.
    A.N.Tikhonov and V.Arsenine, Méthodes de resolution de problémes mal posées, MIR Publ., Moscow (1976).Google Scholar
  7. 7.
    D.L.Phillips, ACM J. 9 (1962) 84.CrossRefGoogle Scholar
  8. 8.
    M.Bertero, Regularization Methods for Linear Inverse Problems, in Inverse Problems, Lecture Notes in Mathematics, Springer-Verlag (1986) p.1125.Google Scholar
  9. 9.
    A.Tartari, E.Casnati, C.Bonifazzi, J.Felsteiner and J.E.Fernandez, in Proc. Int. Conf. on Röntgen Centennial, Würsburg, Oct. 23–27 (1995) p.C30.Google Scholar
  10. 10.
    A.Tartari, C.Bonifazzi, J.Felsteiner and E.Casnati, Nucl. Instr. Meth. Phys. Res. B 117 (1996) 325.CrossRefGoogle Scholar
  11. 11.
    S.J.Norton, J. Appl. Phys. 76 (1994) 2007.CrossRefGoogle Scholar
  12. 12.
    J.A.Grant, M.J.Morgan, D.R.Davis and P.Wels, Meas. Sci. Technol. 4 (1993) 83.CrossRefGoogle Scholar
  13. 13.
    G.Harding, J.Kosanetky and U.Neitzel, Med. Phys. 14 (1987) 515.CrossRefPubMedGoogle Scholar
  14. 14.
    U.Neitzel, J.Kosanetky and G.Harding, Phys. Med. Biol. 30 (1985) 1289.CrossRefPubMedGoogle Scholar
  15. 15.
    J.Kosanetky, B.Knoerr, G.Harding and U.Neitzel, Med. Phys. 14 (1987) 526.CrossRefPubMedGoogle Scholar
  16. 16.
    G.Harding, M.Newton and J.Kosanetzky, Phys. Med. Biol. 35 (1990) 33.CrossRefGoogle Scholar
  17. 17.
    D.A.Bradley, D.R.Dance, S.H.Evans and C.H.Jones, Med. Phys. 16 (1989) 851.CrossRefPubMedGoogle Scholar
  18. 18.
    S.H.Evans, D.A.Bradley, D.R.Dance, J.E.Bateman and C.H.Jones, Phys. Med. Biol. 35 (1991) 33.Google Scholar
  19. 19.
    A.N.Tikhonov and A.V.Goncharsky, eds., Ill-Posed Problems in the Natural Sciences, MIR Publ., Moscow (1987).Google Scholar
  20. 20.
    C.Bonifazzi, G.Maino and A.Tartari, to be submitted for publ., Inv. Problems.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • C. Bonifazzi
    • 1
  • G. Maino
    • 2
  • A. Tartari
    • 3
  1. 1.Istituto di Fisiologia UmanaUniversitá di FerraraFerraraItaly
  2. 2.Dipartimento Innovazione, Divisione Fisica ApplicataENEABologna
  3. 3.Dipartimento di FisicaUniversitá di FerraraFerraraItaly

Personalised recommendations