We consider the application of tomography to the reconstruction of two-dimensional vector fields. The most practical sensor configuration in such problems is the regular positioning along the boundary of the reconstruction domain. However, such a configuration does not result in uniform distribution in the Radon parameter space, which is a necessary requirement to achieve accurate reconstruction results. On the other hand, sampling the projection space uniformly imposes serious constraints on space or time. In this paper, we propose to place the sensors regularly along the boundary of the reconstruction domain and employ probabilistic weights with the purpose of compensating for the lack of uniformity in the distribution of projection space parameters. Simulation results demonstrate that, when the proposed probabilistic weights are employed, an average 27% decrease in the reconstruction error may be achieved, over the case that projection measurements are not weighed (e.g., in one case the error reduces from 3.7% to 2.6%). When compared with the case where actual uniform sampling of the projection space is employed, the proposed method achieves a 90 times reduction in the number of the required sensors or 180 times reduction in the total scanning time, with only 7% increase in the error with which the vector field is estimated.
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