Inversion of generalized V-line transforms of vector fields in ℝ^2
arxiv(2024)
摘要
This article studies the inverse problem of recovering a vector field
supported in 𝔻_R, the disk of radius R centered at the origin,
through a set of generalized broken ray/V-line transforms, namely longitudinal
and transverse V-line transforms. Geometrically, we work with broken lines that
start from the boundary of a disk and break at a fixed angle after traveling a
distance along the diameter. We derive two inversion algorithms to recover a
vector field in ℝ^2 from the knowledge of its longitudinal and
transverse V-line transforms over two different subsets of aforementioned
broken lines in ℝ^2.
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