Work

On the Reconstruction of Planar Vector Fields From Its Longitudinal and Transverse Ray Transform

Year: 2026

Type: article

Abstract: ABSTRACT We consider a planar vector tomography problem of reconstructing a complex‐valued vector field from the (complete and partial) information of its longitudinal and transverse ray transforms, as well as from one of those transforms and its first moment. The method is based on solving an inverse boundary value problem for a system of inhomogeneous Beltrami‐like equations associated with ‐analytic and ‐anti‐analytic maps. In the partial data setting, the available data are only provided on a subset of lines, specifically those intersecting a prescribed arc. We present reconstruction methods for recovering the vector field within the convex hull of the given arc.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.71053

Author: Kamran Sadiq

Institution: Johann Radon Institute for Computational and Applied Mathematics

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $5,000

OpenAlex ID: W7224091326

FWCI:

Cites: 42

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Related to: 10