On the Convergence of Generalized Simultaneous Iterative Reconstruction Algorithms

In this paper, we generalize the widely used simultaneous block iterative reconstruction algorithm and show that it converges, at a linear rate, to a weighted least-squares and weighted minimum-norm reconstruction. Our theoretical result provides a much simpler proof of the convergence properties obtained by Jiang and Wang and covers a much more general class of algorithms. The frequency domain iterative reconstruction algorithm is then introduced as a special application of our theory.