Image reconstruction for cone-beam computed tomography using total p-variation plus Kullback–Leibler data divergence

Accurate reconstruction from a reduced data set is highly essential for computed tomography in fast and/or low dose imaging applications. Conventional total variation (TV)-based algorithms apply the L1 norm-based penalties, which are not as efficient as Lp ($0<p<1$) quasi-norm-based penalties. TV with a p-th power-based norm can serve as a feasible alternative of the conventional TV, which is referred to as total p-variation (TpV). This paper proposes a TpV-based reconstruction model and develops an efficient algorithm. The total p-variation and Kullback–Leibler (KL) data divergence, which has better noise suppression capability compared with the often-used quadratic term, are combined to build the reconstruction model. The proposed algorithm is derived by the alternating direction method (ADM) which offers a stable, efficient, and easily coded implementation. We apply the proposed method in the reconstructions from very few views of projections (7 views evenly acquired within 180°). The images reconstructed by the new method show clearer edges and higher numerical accuracy than the conventional TV method. Both the simulations and real CT data experiments indicate that the proposed method may be promising for practical applications. (paper)