A variational proximal alternating linearized minimization in a given metric for limited-angle CT image reconstruction

Abstract

• A nonconvex and nonsmooth optimization model is investigated for limited-angle CT imaging. • The proposed method can avoid computing the inverse of a large system matrix. • We show that each bounded sequence generated by our method globally converges to a critical point. • The results by our method are shown superior than some classical CT reconstruction methods by real data experiments. Due to the restriction of computed tomography (CT) scanning environment, the acquired projection data may be incomplete for exact CT reconstruction. Though some convex optimization methods, such as total variation minimization based method, can be used for incomplete data reconstruction, the edge of reconstruction image may be partly distorted for limited-angle CT reconstruction. To promote the quality of reconstruction image for limited-angle CT imaging, in this paper, a nonconvex and nonsmooth optimization model was investigated. To solve the model, a variational proximal alternating linearized minimization (VPALM) method based on proximal mapping in a given metric was proposed. The proposed method can avoid computing the inverse of a huge system matrix thus can be used to deal with the larger-scale inverse problems. What’s more, we show that each bounded sequence generated by VPALM globally converges to a critical point based on the Kurdyka–Lojasiewicz property . Real data experiments are used to demonstrate the viability and effectiveness of VPALM method, and the results show that the proposed method outperforms two classical CT reconstruction methods.