Numerical inversion and uniqueness of a spherical radon transform restricted with a fixed angular span
作者：
Highlights：
• Spherical Radon transforms arises in medical imaging and geophysical applications.
• Spherical Radon transforms assigns to a given function its integral over the sphere.
• Under some limitation, the measurement data can be modeled integrals of functions along sphere with a fixed angular span.
• We show uniqueness results for function recovery from spherical Radon transform data.
• An efficient numerical inversion is implemented using a truncated SVD algorithm.
摘要
•Spherical Radon transforms arises in medical imaging and geophysical applications.•Spherical Radon transforms assigns to a given function its integral over the sphere.•Under some limitation, the measurement data can be modeled integrals of functions along sphere with a fixed angular span.•We show uniqueness results for function recovery from spherical Radon transform data.•An efficient numerical inversion is implemented using a truncated SVD algorithm.
论文关键词：Spherical radon transform,Spherical harmonics,Volterra integral equations,Truncated singular value decomposition
论文评审过程：Received 31 July 2020, Revised 1 April 2021, Accepted 28 April 2021, Available online 24 May 2021, Version of Record 24 May 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.126338
