A linear sinogram extrapolator for limited angle tomography

This paper considers the problem of limited angle tomography in which a complete sinogram is not available and proposes a linear extrapolator to extrapolate the missing part of the sinogram. Once the complete sinogram is obtained via extrapolation, standard reconstruction techniques can be used to generate artifact free reconstructions. The linear extrapolator is designed using the sampling theory of signals with non-compact spectral support, the knowledge that complete sinograms have bowtie-shaped spectral support, and regularization. Once the extrapolator is designed, it can be used to extrapolate any incomplete sinogram. Since the sinogram is non-iterative, it is much more efficient than other iterative algorithms such as the method of projection onto convex sets, the Papoulis-Gerchberg´s algorithm and the Clark-Palmer-Lawrence interpolation method