Convergence analysis of SART: optimization and statistics

Simultaneous algebraic reconstruction technique (SART) [1, 2] is an iterative method for solving inverse problems of form Ax(+n) = b. This type of problems arises for example in computed tomography reconstruction, in which case A is obtained from discrete Radon transform. In this paper, we provide several methods for derivation of SART and connections between SART and other methods. Using these connections, we also prove the convergence of SART in different ways. These approaches are from optimization and statistical points of view and can be applied to other Landweber-like schemes such as Cimmino’s algorithm and component averaging (CAV). Furthermore, the noisy case is considered and error estimation is given. Several numerical experiments for computed tomography reconstruction are provided to demonstrate the convergence results in practice.