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  • Electronic Resource  (6)
  • 1
    Electronic Resource
    Electronic Resource
    Incomplete data problems in x-ray computerized tomography (1986)
    Springer
    Numerische Mathematik 48 (1986), S. 251-262 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65R10 ; CR: G1.2
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The reconstruction of an object from its x-ray scans is achieved by the inverse Radon transform of the measured data. For fast algorithms and stable inversion the directions of the x rays have to be equally distributed. In the present paper we study the intrinsic problems arising when the directions are restricted to a limited range by computing the singular value decomposition of the Radon transform for the limited angle problem. Stability considerations show that parts of the spectrum cannot be reconstructed and the irrecoverable functions are characterized.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389474
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Acceleration of convergence for finite element solutions of the Poisson equation (1979)
    Springer
    Numerische Mathematik 33 (1979), S. 43-53 
    Details
    ISSN: 0945-3245
    Keywords: AMS (Mos): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Letu h be the finite element solution to−Δu=f with zero boundary conditions in a convex polyhedral domain Ω. Fromu h we calculate for eachz∈Ω and |α|≦1 an approximationu h −α (z) toD α u(z) with |D α u(z)−u h −α (z)|=O(h 2k−2) wherek is the order of the finite elements. The same superconvergence order estimates are obtained also for the boundary flux. We need not work on a regular mesh but we have to compute averages ofu h where the diameter of the domain of integration must not depend onh.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396494
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  • 3
    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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  • 4
    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
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  • 5
    Electronic Resource
    Electronic Resource
    Nonuniqueness in inverse radon problems: The frequency distribution of the ghosts (1984)
    Springer
    Mathematische Zeitschrift 185 (1984), S. 429-440 
    Details
    ISSN: 1432-1823
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01215050
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  • 6
    Electronic Resource
    Electronic Resource
    On the mathematical foundations of hyperthermia therapy (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 467-479 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Hyperthermia is an aid to standard cancer therapy. The aim is to heat up a tumour region inside the patient's body with the help of microwave radiation. The microwayes are generated by some suitable antenna array. Here we investigate the control properties of such antenna configurations and determine their resolution capabilities. We will define the hyperthermia operator, which can produce every field of any antenna array up to any degree of accuracy. We shall see that this operator is compact and we are able to compute a singular system under general assumptions explicitly. This, together with a detailed knowledge of the decay of the singular values, constitutes the tools with which we treat the previously stated problems. We examine the propagation of microwave radiation in homogeneous media and then carry over the results obtained to the case of inhomogeneous media.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670130603
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