缺少投影角度与时变物体断层重建的外推恢复正弦图方法

Sinogram Extrapolator for Limited Angle and Time-Varying Object Tomography

本文针对缺少投影角度及物体时变这两类缺损投影数据问题，在分析了限空间区域及限频域图像的雷当变换的若干性质基础上，分别导出基于最小均方误差准则的外推公式，从而得到完整的正弦图的最佳估计.基于这一外推所得的正弦图，可以利用传统的断层重建方法对物体进行重建本文给出了外推公式的推导过程及其求解的迭代算法。计算机模拟结果显示了这一技术的有效性.

This paper considers the following two cases of missing cone problem: the limited angle tomography and time-varying object tomography.Based on the spatial and Fourier domain properties of Radon transform, a sinogram extrapolation technique is proposed.The missing data in sinogram is extrapolated using a novel least mean square error criterion and a complete sinogram can be restored. This complete sinogram is then used for image reconstruction by standard methods. The derivation of the sinogram extrapolation formulations is given. An iterative algorithm for solving these formulations is also given. Computer simulation results are presented to demonstrate the efficiency of the proposed technique.