A springback TV algorithm for image reconstruction from sparse view data in CT

Abstract Objective. With the demand for reducing ray dose, image reconstruction from sparse-view projection data has become a hot research subject in computed tomography (CT). However, the traditional total variation (TV) algorithms based on ℓ 1 norm may lead to over-smoothing, especially when handling extremely sparse projections. To address this issue, we propose a new TV algorithm formulated by the springback penalty, named springback TV (STV) algorithm. Approach. The STV model replaces the simple ℓ 1 norm approximation with a weakly convex penalty to better approximate the ℓ 0 norm and enhance sparsity representation. Furthermore, we employ the difference of convex algorithm (DCA) and the fully linearized alternating direction method of multipliers (FL-ADMM) to efficiently solve the STV model, avoiding line search steps and accelerating internal iterations. Main Results. Experiments based on mathematical phantoms and clinical CT image demonstrate that the proposed STV algorithm outperforms standard TV, Total p-Variation (TpV) and weighted difference of anisotropic and isotropic TV (WDAI-TV) in terms of reconstruction quality. Significance. The proposed STV algorithm improves detail recovery while maintaining computational efficiency, providing a more robust and effective solution for sparse view CT image reconstruction under low-dose conditions.