TY - JOUR A1 - Barannyk, Lyudmyla L. A1 - Frikel, Jürgen A1 - Nguyen, Linh V. T1 - On artifacts in limited data spherical Radon transform: Curved observation surface T2 - Inverse Problems N2 - 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 k+1/2 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. Y1 - 2016 UR - https://opus4.kobv.de/opus4-oth-regensburg/frontdoor/index/index/docId/5093 SN - 1361-6420 SN - 0266-5611 VL - 32 IS - 1 PB - Institute of Physics CY - Bristol [u.a.] ER -