Efficient and robust 3D CT image reconstruction based on total generalized variation regularization using the alternating direction method

Iterative reconstruction algorithms for computed tomography (CT) through total variation regularization based on piecewise constant assumption can produce accurate, robust, and stable results. Nonetheless, this approach is often subject to staircase artefacts and the loss of fine details. To overcome these shortcomings, we introduce a family of novel image regularization penalties called total generalized variation (TGV) for the effective production of high-quality images from incomplete or noisy projection data for 3D reconstruction. We propose a new, fast alternating direction minimization algorithm to solve CT image reconstruction problems through TGV regularization. Based on the theory of sparse-view image reconstruction and the framework of augmented Lagrange function method, the TGV regularization term has been introduced in the computed tomography and is transformed into three independent variables of the optimization problem by introducing auxiliary variables. This new algorithm applies a local linearization and proximity technique to make the FFT-based calculation of the analytical solutions in the frequency domain feasible, thereby significantly reducing the complexity of the algorithm. Experiments with various 3D datasets corresponding to incomplete projection data demonstrate the advantage of our proposed algorithm in terms of preserving fine details and overcoming the staircase effect. The computation cost also suggests that the proposed algorithm is applicable to and is effective for CBCT imaging. Theoretical and technical optimization should be investigated carefully in terms of both computation efficiency and high resolution of this algorithm in application-oriented research.