TY - JOUR
T1 - Numerical inversion and uniqueness of a spherical radon transform restricted with a fixed angular span
AU - Gouia-Zarrad, Rim
AU - Roy, Souvik
AU - Moon, Sunghwan
N1 - Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2021/11/1
Y1 - 2021/11/1
N2 - In this paper, we study a spherical Radon transform that maps a function to its surface integrals over spheres restricted with a fixed angular span. Such transform is relevant for various image reconstruction problems arising in medical, radar and sonar imaging. This paper contains uniqueness results for the spherical Radon transform in the case of a fixed angular span, valid when the support of the image function is inside or outside the data acquisition sphere. Furthermore, we present simulation results for the numerical inversion in the special case of the spherical cap Radon transform.
AB - In this paper, we study a spherical Radon transform that maps a function to its surface integrals over spheres restricted with a fixed angular span. Such transform is relevant for various image reconstruction problems arising in medical, radar and sonar imaging. This paper contains uniqueness results for the spherical Radon transform in the case of a fixed angular span, valid when the support of the image function is inside or outside the data acquisition sphere. Furthermore, we present simulation results for the numerical inversion in the special case of the spherical cap Radon transform.
KW - Spherical harmonics
KW - Spherical radon transform
KW - Truncated singular value decomposition
KW - Volterra integral equations
UR - http://www.scopus.com/inward/record.url?scp=85106360752&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2021.126338
DO - 10.1016/j.amc.2021.126338
M3 - Article
AN - SCOPUS:85106360752
SN - 0096-3003
VL - 408
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
M1 - 126338
ER -