Projected gradient and conjugate gradient methods for image reconstruction using preconditioning matrix

This paper describes fast image reconstruction methods for computed tomography. These methodologies employ convex programming techniques with box constraints. To accelerate these algorithms, the preconditioning matrix is introduced through the filtered back projection method. Additionally, we present the convergence theorem of the projected gradient method, which is based on a proximal gradient method, a sparse modeling technique. We show the fundamental numerical characteristics of the proposed methods and demonstrate superior image reconstruction capabilities compared to previous works in the same setting.