On constrained Kaczmarz algorithm with momentum for image reconstruction

Summary The Kaczmarz algorithm is widely used in image reconstruction. In this paper, we propose an enhanced version of the Kaczmarz algorithm by integrating Nesterov momentum into the Kaczmarz algorithm, denoted as the Kaczmarz algorithm with momentum. Our innovation offers a novel approach to accelerate the convergence rate of the Kaczmarz algorithm significantly. Based on greedy rules for selecting work row, we prove that the Kaczmarz method with momentum can achieve global linear convergence rates. Furthermore, we extend a constrained version of the Kaczmarz algorithm with Nesterov momentum for improved image reconstruction and prove its convergence. Numerical experiments show that the proposed algorithm outperforms the original Kaczmarz algorithm in terms of efficiency for image reconstruction.