Full Tomographic Reconstruction of 2D Vector Fields using Discrete Integral Data

Vector field tomography is a field that has received considerable attention in recent decades. It deals with the problem of the determination of a vector field from non-invasive integral data. These data are modelled by the vectorial Radon transform. Previous attempts at solving this reconstruction problem showed that tomographic data alone are insufficient for determining a 2D band-limited vector field completely and uniquely. This paper describes a method that allows one to recover both components of a 2D vector field based only on integral data, by solving a system of linear equations. We carry out the analysis in the digital domain and we take advantage of the redundancy in the projection data, since these may be viewed as weighted sums of the local vector field's Cartesian components. The potential of the introduced method is demonstrated by presenting examples of vector field reconstruction.