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.
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The work of the authors was supported by the Deutsche Forschungsgemeinschaft under grant Lo 310/2-4
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Louis, A.K., Rieder, A. Incomplete data problems in X-ray computerized tomography. Numer. Math. 56, 371–383 (1989). https://doi.org/10.1007/BF01396611
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DOI: https://doi.org/10.1007/BF01396611