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  • AMS(MOS)  (1)
  • Secondary: 44A 15  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    On the inversion of the attenuated Radon transform (1979)
    Springer
    Numerische Mathematik 32 (1979), S. 431-438 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65R05 ; CR ; 5.18
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We given an inversion formula for the attenuated Radon transform $$\bar \omega _L $$ for constant attenuation μ which is accurate up toO(µ 4) We also derive an integral equation of the second kind for the solution ofR μf=g. The implementation of both methods for the inversion ofR μ consists basically of a generalized filtered backprojection algorithm. Numerical examples are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01401046
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Numerical inversion of the Radon transform (1978)
    Springer
    Numerische Mathematik 30 (1978), S. 81-91 
    Details
    ISSN: 0945-3245
    Keywords: Primary: 65JR05 ; Secondary: 44A 15 ; 45L 10 ; 45H05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The problem of inverting the Radon transform, i.e. the reconstruction of a function inR 2 from its line integrals arises e.g. in computerized tomography and in nondestructive testing. In the present paper the least squares method with piecewise constant trial functions is investigated. An error estimate is derived. An implementation using the fast Fourier transform is described and numerical results are reported.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01403908
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    Paper (German National Licenses)
    Fulltext
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