Adaptive Landweber image reconstruction with an optimal presetting method

An optimal presetting method is proposed to improve the adaptation of the Landweber algorithm. The Armijo-like search rule for accelerating the CQ (nonempty closed convex sets C and Q) algorithm is introduced. The proposed method firstly calculates the error at each step of iterations. Then it presets the optimal number of iterations. Afterward it combines with the result of the Armijo-like search method. A new step-size with better adaptive property can be obtained. It not only emphasizes the rate at the beginning stages, but also still working at the later. Both methods were applied to reconstruct the Shepp-Logan image from the sparse view projection data. The results demonstrated the proposed method has faster convergence rate and lower errors.