The Identification Problem in Emission Computed Tomography

  • F. Natterer
Part of the Lecture Notes in Medical Informatics book series (LNMED, volume 8)


In (single photon) emission computed tomography one has to compute the activity distribution f(x) and the distribution of the attenuation coefficient μ (x) from the integral equation
$$\mathop \smallint \limits_{L(s,\omega )} f(x){e^{ - (M\mu )(x,\omega )}}dx = g(s,w)$$
where ω is a unit vector, L(s, ω) is the straight line perpendicular to a ω with (signed) distance s from the origin, and
$$(M\mu )(x,\omega ) = \mathop \smallint \limits_o^\infty \mu (x + t{\omega ^ - })dt$$
is the fan beam transform. We show that for finitely many sources, Mμ (x,ω) can be determined up to an additive constant for all sources x by the consistency conditions in the range of the attenuated Radon transform.


Single Photon Attenuation Coefficient Fourier Coefficient Consistency Condition Activity Distribution 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • F. Natterer
    • 1
  1. 1.Fachbereich 10Universität des SaarlandesSaarbrückenDeutschland

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