Year: 2025
Type: article
Abstract: In two dimensions, we consider the problem of reconstructing a vector field from partial knowledge of its zeroth and first moment ray transforms. Different from existing works the data is known on a subset of lines, namely the ones intersecting a given arc. The problem is non-local and, for partial data, severely ill-posed. We present a reconstruction method which recovers the vector field in the convex hull of the arc. An algorithm based on this method is implemented on some numerical experiments. While still ill-posed the discretization stabilizes the numerical reconstruction.
Source: Inverse Problems
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4411443352