An Extrapolation Method for Image Reconstruction from a Straight-line Trajectory

In this paper, we present an extrapolation method for compensation of missing data in image reconstruction from a straight-line trajectory (LCT scan). We adopt the idea for band-limited signal extrapolation. The missing data are estimated and updated during each iteration by a reprojection from the reconstructed image, in which the reconstruction and reprojection steps are implemented by the linogram technique and its inverse, respectively. The convergence condition of this extrapolation is studied. Our method has some benefits. First, the linogram reconstruction does not need any interpolation at all. Second, only O(N² log N) arithmetic operations are required in each iteration when the projection and the reconstruction are both of size NtimesN. Third, prior knowledge on the image and the Fourier spaces such as non-negativity can be introduced to improve the convergence efficiency. The performances of this approach are compared with the iterative reconstruction reprojection (IRR) method.