TV or not TV? That is the Question

Iterative reconstruction methods with regularization become more and more popular. In the literature, amazing results are reported that are able to reconstruct images from very few views and from trajectories that do not acquire complete data sets such as would be required for analytical reconstruction methods. A large disadvantage of iterative methods is their high computational demand. Bruder et al. have shown that if the reconstruction is accurate enough, the regularization can be performed in the reconstructed image only which allows for much faster application of the regularization term. In this paper, we present a heuristic compensation weight that corrects for the loss of mass in a filtered back-projection type reconstruction given a limited angle problem. Although the reconstruction contains artifacts, we show that the application of a bilateral filter in the reconstruction domain is able to recover almost the same signal as a TV-regularized iterative reconstruction. The reconstruction error is reduced from 0.130 to 0.057 which is the same as for the iterative case.