Virtual sensors for 2D vector field tomography

We consider the application of tomography to the reconstruction of 2-D vector fields. The most convenient sensor configuration in such problems is the regular positioning along the domain boundary. However, the most accurate reconstructions are obtained by sampling uniformly the Radon parameter domain rather than the border of the reconstruction domain. This dictates a prohibitively large number of sensors and impractical sensor positioning. In this paper, we propose uniform placement of the sensors along the boundary of the reconstruction domain and interpolation of the measurements for the positions that correspond to uniform sampling in the Radon domain. We demonstrate that when the cubic spline interpolation method is used, a 60 times reduction in the number of sensors may be achieved with only about 10% increase in the error with which the vector field is estimated. The reconstruction error by using the same sensors and ignoring the necessity of uniform sampling in the Radon domain is in fact higher by about 30%. The effects of noise are also examined.