Linear extrapolator for limited angle tomography

This paper considers the problem of limited angle tomography in which a complete sinogram is not available. This situation arises in many practical applications where tomographic projection over 180 degree is either physically unrealizable or infeasible. When a complete sinogram is not available, it is well known that the reconstructed images using common reconstruction algorithms, such as convolution back projection, will have severe streak artifacts. In this paper, a linear extrapolator to extrapolate the missing part of the sinogram is presented. 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. It is found that once designed, these parameters are data independent, especially for images of similar nature. For sinogram with 2N angular views, each having M raysum per view, if 2L views are available, the computational requirement of the extrapolator is 4MNL only. Hence, 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