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Analyzing reconstruction artifacts from arbitrary incomplete X-ray CT data. (English) Zbl 1439.44004
This article studies nonsmooth artifacts in the reconstruction of a two-dimensional function by a filtered backprojection algorithm for X-ray computed tomography with arbitrary incomplete data.
It is shown that all singular artifacts arise from points on the boundary of the data set. They can only be one of two types.
Object-dependent artifacts are generated by singularities of the object being scanned; these artifacts extend along lines, and generalize the streak artifacts observed in limited-angle tomography. Object-independent artifacts take one of two forms: streaks or lines if the boundary of the data set is not smooth at a point, and curved artifacts if the boundary is locally smooth.
The results are interpreted and illustrated numerically in various settings, including the motivating example: a synchrotron data set in which artifacts appear on lines that have no relation to the object.

MSC:
44A12 Radon transform
92C55 Biomedical imaging and signal processing
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