On artifacts in limited data spherical Radon transform: curved observation surface. (18th December 2015)

• Record Type: Journal Article
• Authors: Barannyk, Lyudmyla L; Frikel, Jürgen; Nguyen, Linh V
• Is Part Of: Inverse problems. Volume 32:Number 1(2016:Jan.)
• Publication Date: 2015-12-18
• Subjects: spherical Radon transform -- limited data problem -- microlocal analysis -- tomography -- singularities -- artifacts -- pseudodifferential and Fourier integral operators; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/1/015012
• Languages: English
• ISSNs: 0266-5611

Abstract

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 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.