The x-ray transform maps a compactly supported function in R n to its integrals over all the straight lines in R n . A singular value decomposition (SVD) for this operator is given in arbitrary dimensions. The proof uses results from the representation theory of Lie groups. This paper addresses questions concerning the stability of the inversion problem. The SVD shows which parts of a reconstructed function are affected by data errors and by how much. The resolution in the reconstruction is determined if only a finite set of data is available.
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A 1987 study studied this question.