Sampling Bounds for 2-D Vector Field Tomography
The tomographic mapping of a 2-D vector field from line-integral data in the discrete domain requires the uniform sampling of the continuous Radon domain parameter space. In this paper we use sampling theory and derive limits for the sampling steps of the Radon parameters, so that no information is lost. It is shown that if Delta x is the sampling interval of the reconstruction region and x(max) is the maximum value of domain parameter x, the steps one should use to sample Radon parameters rho and theta should be: Delta rho <= Delta x/root 2 and Delta theta <= Delta x/((root 2 + 2)vertical bar x(max)vertical bar). Experiments show that when the proposed sampling bounds are violated, the reconstruction accuracy of the vector field deteriorates. We further demonstrate that the employment of a scanning geometry that satisfies the proposed sampling requirements also increases the resilience to noise.
vector field tomography scanning geometry radon transform sampling theorem inverse problems