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  • AMS(MOS): 65J10  (1)
  • CR: 61.2  (1)
  • 1
    Electronic Resource
    Electronic Resource
    The instability of some gradient methods for ill-posed problems (1990)
    Springer
    Numerische Mathematik 58 (1990), S. 129-134 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65J10 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary For the solution of linear ill-posed problems some gradient methods like conjugate gradients and steepest descent have been examined previously in the literature. It is shown that even though these methods converge in the case of exact data their instability makes it impossible to base a-priori parameter choice regularization methods upon them.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385614
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Incomplete data problems in X-ray computerized tomography (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 371-383 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 R 10 ; CR: 61.2
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In the present paper we study truncated projections for the fanbeam geometry in computerized tomography. First we derive consistency conditions for the divergent beam transform. Then we study a singular value decomposition for the case where only the interior rays in the fan are provided, as for example in region-of-interest tomography. We show that the high angular frequency components of the searched-for densities are well determined and we present reconstructions from real data where the missing information is approximated based on the singular value decomposition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396611
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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