A Chambolle-Pock algorithm for sparse-view CT reconstruction via total generalized variation regularization and penalized weighted least-squares criterion

Total generalized variation (TGV) regularization effectively suppresses the staircase effect generated by the total variation (TV) regularization, while the penalized weighted least-squares (PWLS) criterion enhances image reconstruction accuracy by updating the projection data variance in each iteration. Consequently, these two terms are commonly employed to establish a computed tomography (CT) image reconstruction model. However, the traditional reconstruction algorithms solving this TGV-PWLS-based reconstruction model involve the nested loop structure, resulting in computational complexity and prolonged reconstruction time. To address this issue while maintaining the accuracy of the image to be reconstructed, the Chambolle-Pock (CP) algorithm was adopted to efficiently solve the TGV-PWLS-based reconstruction model, termed 'CP-TGV-PWLS' method. Firstly, by introducing three dual variables, the TGV-PWLS-based reconstruction model was reformulated as a saddle-point problem. Next, this saddle-point problem is transformed into a different equivalent form. Finally, this different equivalent form is solved to obtain the closed-form solution, yielding a single-loop iterative reconstruction algorithm for sparse-view CT. Qualitative and quantitative experimental analyses on the Shepp-Logan phantom and Mayo clinic dataset demonstrate the superior performance of the proposed method on detail preservation and structural features. Furthermore, our approach achieves faster iterative speed while outperforming other comparison methods in reconstruction accuracy.