A numerical solver based on \(B\)-splines for 2D vector field tomography in a refracting medium. (English) Zbl 1499.65047
Summary: Efficient and stable numerical solvers for vector tomography problems taking refractions into account are subject of current research. This article is concerned with the problem of reconstructing a 2D-vector field in a refracting medium from its known longitudinal or transverse ray transform. The refraction is modeled using a Riemannian metric in the domain under consideration. We propose a numerical solver that is based on the least squares method where we use a finite basis consisting of \(B\)-splines as basis functions. In that sense the method can be seen as a projection method for minimizing an \(L^2\)-data fitting term. Numerical simulations show a good performance of that method, also compared to methods relying on exact inversion formulas.
Publisher’s note: Incorrect inclusion of this article in [Math. Comput. Simulation 94, 15–32 (2013)].
Publisher’s note: Incorrect inclusion of this article in [Math. Comput. Simulation 94, 15–32 (2013)].
MSC:
| 65D07 | Numerical computation using splines |
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