Journal article · Preprint article
On artifacts in limited data spherical Radon transform: curved observation surface
We study the limited data problem of the spherical Radon transform in two and three-dimensional spaces with general acquisition surfaces. In such situations, it is known that the application of filtered-backprojection reconstruction formulas might generate added artifacts and degrade the quality of reconstructions.
In this article, we explicitly analyze a family of such inversion formulas, depending on a smoothing function that vanishes to order k on the boundary of the acquisition surfaces. We show that the artifacts are k orders smoother than their generating singularity. Moreover, in two-dimensional space, if the generating singularity is conormal satisfying a generic condition then the artifacts are even orders smoother than the generating singularity.
Our analysis for three-dimensional space contains an important idea of lifting up space. We also explore the theoretical findings in a series of numerical experiments. Our experiments show that a good choice of the smoothing function leads to a significant improvement of reconstruction quality.
Language: | English |
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Publisher: | IOP Publishing |
Year: | 2015 |
Pages: | 015012 |
ISSN: | 13616420 and 02665611 |
Types: | Journal article and Preprint article |
DOI: | 10.1088/0266-5611/32/1/015012 |
Artifacts Limited data problem Microlocal analysis Pseudodifferential and Fourier integral operators Singularities Spherical Radon transform Tomography