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中文摘要：
基于全变分正则化构造了重构CT图像的动力系统方法。相比于传统的迭代反演方法，在对算子施加较弱的假设条件下，证明解的存在性，并用Lyapunov稳定性理论证明方法是稳定的。通过具体的数值模拟，分别重构了全角、半角的Shepp—Logan和人体腹部CT图像，并将所提方法与基于水平集的重构方法做了比较。
英文摘要：
Based on total variational regularization, the dynamical system methods for the image reconstruction in computed tomography is proposed. Compared with classical iterative methods, the exist- ence of the solution and the stability of dynamical systems are proven by using Lyapunov stability theorem under weaker restrictions on the operator. In numerical experiment, the Shepp-Logan phantom and CT image of abdomen with full angle and limited angle are reconstructed, respectively. Moreover, the reconstruction based on dynamical system methods and based on level set are compared. This kind of problem is widely applied in the field of medicine.
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