Journal
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume 38, Issue 2, Pages 681-692Publisher
SIAM PUBLICATIONS
DOI: 10.1137/050637492
Keywords
thermoacoustic tomography; Radon transform; range description
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The transform considered in the paper integrates a function supported in the unit disk on the plane over all circles centered at the boundary of this disk. Such a circular Radon transform arises in several contemporary imaging techniques, as well as in other applications. As is common for transforms of Radon type, its range has infinite codimension in standard function spaces. Range descriptions for such transforms are known to be very important for computed tomography for instance, when dealing with incomplete data, error correction, and other issues. A complete range description for the circular Radon transform is obtained. Range conditions include the recently found set of moment-type conditions, which happens to be incomplete, as well as other conditions that have less standard form. In order to explain the procedure better, a similar (nonstandard) treatment of the range conditions is described first for the usual Radon transform on the plane.
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