Convergence of the simultaneous algebraic reconstruction technique (SART) (invited talk

Abstract—Computed tomography (CT) has been extensively studied for years and widely used in the modern society. Although the filtered back-projection algorithm is the method of choice by manufacturers, efforts are being made to revisit iterative methods due to their unique advantages, such as superior performance with incomplete noisy data. In 1984, the simultaneous algebraic reconstruction technique (SART) was developed as a major refine-ment of the algebraic reconstruction technique (ART). However, the convergence of the SART has never been established since then. In this paper, the convergence is proved under the condition that coefficients of the linear imaging system are nonnegative. It is shown that from any initial guess the sequence generated by the SART converges to a weighted least square solution. Index Terms—Algebraic reconstruction technique (ART), computed tomography (CT), emission tomography, expectation maximization (EM), inverse problem, simultaneous algebraic reconstruction technique (SART). I