基于Abel变换的图像重建自适应方法

本文论述了利用轴对称物体的单幅投影信息进行密度重建的一种自适应正则化模型。所提模型基于全变分正则项与高阶全变分正则项的联合使用,主要的优点是在保持清晰的界面及恢复平稳变化区域的同时减弱了阶梯效应。并且使用自适应方法,提高了效果的同时简化了所使用的参数。对于其中涉及的最优化问题,我们采用增广拉格朗日方法来解。数值结果表明,这一模型提高了关于密度界面位置及密度值的准确度,具有较好的抗噪性。 

Abel Transformation Based Adaptive Regularization Approach for Image Reconstruction

In this paper, we discuss an adaptive regularization approach for density reconstruction of axially symmetric object whose tomography comes from a single X-ray projection. The method we proposed is based on the combination of total variation regularization and high-order total variation regularization. Its main advantage is to reduce the staircase effect while keeping sharp edges and recovering smoothly varying regions. Moreover, it simplifies the use of parameters. We apply the augmented Lagrangian method to solve the optimization involved. Numerical results show that the proposed method has improved the accuracy of density edges and values. Besides, the method is not sensitive to the measured data noise.