We improve data extrapolation for truncated computed tomography (CT) projections by using Helgason-Ludwig (HL) consistency\nconditions thatmathematically describe the overlap of information between projections. First, we theoretically derive a 2D Fourier\nrepresentation of the HL consistency conditions from their original formulation (projection moment theorem), for both parallelbeam\nand fan-beam imaging geometry.The derivation result indicates that there is a zero energy region forming a double-wedge\nshape in 2D Fourier domain. This observation is also referred to as the Fourier property of a sinogram in the previous literature.\nThe major benefit of this representation is that the consistency conditions can be efficiently evaluated via 2D fast Fourier transform\n(FFT). Then, we suggest a method that extrapolates the truncated projections with data from a uniform ellipse of which the\nparameters are determined by optimizing these consistency conditions. The forward projection of the optimized ellipse can be\nused to complete the truncation data. The proposed algorithm is evaluated using simulated data and reprojections of clinical data.\nResults show that the root mean square error (RMSE) is reduced substantially, compared to a state-of-the-art extrapolation method.
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