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中文摘要：
The order of the projection in the algebraic reconstruction technique(ART)method has great influence on the rate of the convergence.Although many scholars have studied the order of the projection,few theoretical proofs are given.Thomas Strohmer and Roman Vershynin introduced a randomized version of the Kaczmarz method for consistent,and over-determined linear systems and proved whose rate does not depend on the number of equations in the systems in 2009.In this paper,we apply this method to computed tomography(CT)image reconstruction and compared images generated by the sequential Kaczmarz method and the randomized Kaczmarz method.Experiments demonstrates the feasibility of the randomized Kaczmarz algorithm in CT image reconstruction and its exponential curve convergence.
英文摘要：
The order of the projection in the algebraic reconstruction technique （ART） method has great influence on the rate of the convergence. Although many scholars have studied the order of the projection, few theoretical proofs are given. Tho-mas Strohmer and Roman Vershynin introduced a randomized version of the Kaczmarz method for consistent, and over-de- termined linear systems and proved whose rate does not depend on the number of equations in the systems in 2009. In this paper, we apply this method to computed tomography （CT） image reconstruction and compared images generated by the se-quential Kaczmarz method and the randomized Kaczmarz method. Experiments demonstrates the feasibility of the random-ized Kaczmarz algorithm in CT image reconstruction and its exponential curve convergence.
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