@article{BarannykFrikelNguyen, author = {Barannyk, Lyudmyla L. and Frikel, J{\"u}rgen and Nguyen, Linh V.}, title = {On artifacts in limited data spherical Radon transform: Curved observation surface}, series = {Inverse Problems}, volume = {32}, journal = {Inverse Problems}, number = {1}, publisher = {Institute of Physics}, address = {Bristol [u.a.]}, issn = {1361-6420}, doi = {10.1088/0266-5611/32/1/015012}, abstract = {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.}, language = {de} }