反射型衍射CT中的迭代法图像重构(英文)

Iterative Image Reconstruction in Reflection Mode Diffraction Tomography

基于衍射的计算机层析成像术是建立在Fourier衍射投影定理基础上的。衍射CT图象重构可看作由非均匀频率样点重建信号的问题。提出一种用于反射型衍射CT的图像重构算法,此方法利用反向散射数据进行 2D非均匀 Fourier反变换。由于直接的非均匀Fourier反变换不易实现,所以采用基于min max优化准则的非均匀快速 Fourier正变换,通过迭代实现非均匀Fourier逆变换的快速有效计算。为了减少迭代次数加快收敛速度,首先用频域插值法得到重构图像的初值,然后根据min max准则,每经过一次迭代得到重构图像的一个更新版本,重复多次迭代直至得到可接受的重构结果。给出了数值实验结果。与传统重构算法如Gridding方法相比,该算法计算复杂度相当而重构精度较高。

It proposed a reconstruction algorithm for the reflection mode diffraction tomography (RMDT), which uses back-scattered data and treats image reconstruction as a two-dimensional non-uniform inverse Fourier transform problem. As it is difficult to implement a direct non-uniform inverse Fourier transform, a non-uniform forward Fourier transform is performed based upon a min-max optimization criterion, and fast computation of the inverse transform is obtained through iteration. In order to reduce the number of iterations and speed up convergence, an initial estimate of the image by frequency domain interpolation is used. Updated versions are generated with iteration until an acceptable result is obtained. Experimental results are presented. Compared to the traditional methods such as gridding, the proposed algorithm has the advantage of better reconstruction accuracy with similar computational complexity.