Constrained SART algorithm for inverse problems in image reconstruction (Q1951304)

The authors investigate the simultaneous algebraic reconstruction technique (SART) algorithm for solving iteratively least squares problems arising in image reconstruction problems. For the convergence proof results for a general projection method presented by \textit{A.~Nicola, S.~Petra, C.~Popa} and \textit{C.~Schnörr} [Int. J. Comput. Math. 89, No. 2, 231-253 (2012; Zbl 1256.65027)] are used. Additionally, the convergence of a constrained version of the SART algorithm is proved. For two special constraining functions it is shown that they satisfy the assumptions made for the constrained algorithm considered. Finally, the SART algorithm with and without constraints is compared with some versions of the Kaczmarz algorithm. An advantage of the SART algorithm is that it is parallelizable.