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The Approximate Inverse in Action with an Application to Computerized Tomography

Andreas Rieder and Thomas Schuster
SIAM Journal on Numerical Analysis
Vol. 37, No. 6 (2000), pp. 1909-1929
Stable URL: http://www.jstor.org/stable/2587353
Page Count: 21
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The Approximate Inverse in Action with an Application to Computerized Tomography
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Abstract

The approximate inverse is a scheme to obtain stable numerical inversion formulae for linear operator equations of the first kind. Yet, in some applications the computation of a crucial ingredient, the reconstruction kernel, is time-consuming and instable. It may even happen that the kernel does not exist for a particular semidiscrete system. To cure this dilemma we propose and analyze a technique that is based on a singular value decomposition of the underlying operator. The results are applied to the reconstruction problem in 2D-computerized tomography where they enable the design of reconstruction filters and lead to a novel error analysis of the filtered backprojection algorithm.

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