Electronic Resource
Chichester, West Sussex
:
Wiley-Blackwell
Mathematical Methods in the Applied Sciences
10 (1988), S. 397-406
ISSN:
0170-4214
Keywords:
Mathematics and Statistics
;
Applied Mathematics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
We examine here the problem of reconstructing an X-ray attenuation function from measurements of its integrals. The approach that is taken is to maximize the difference of the entropy and the residual error in meeting the measurements. The solution of this optimization problem is constrained by requiring that the solution lie in a certain weakly compact subset of L2, to be determined by physical information.We show that the constrained optimization problem is well-posed: there exists a unique solution (even when the measured data are inconsistent) and the solution depends continuously on the measurements. In the course of proving this, we show that the entropy functional is continuous on L2. We further demonstrate that the solution of the optimization problem for a special case, must be piecewise constant.
Additional Material:
1 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/mma.1670100405
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