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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。
Diffraction-based computed tomography is based on the Fourier diffraction projection theorem. Diffraction CT image reconstruction can be viewed as a problem of reconstructing signals from non-uniform frequency samples. An image reconstruction algorithm for reflective diffraction CT is proposed. This method uses backscattering data to inverse 2D inhomogeneous Fourier transform. Because direct inhomogeneous Fourier inverse transform is not easy to implement, non-uniform fast Fourier transform based on min max optimization criterion is adopted to realize fast and efficient computation of non-uniform Fourier inverse transform through iteration. In order to reduce the number of iterations to speed up the convergence, the initial value of the reconstructed image is first obtained by using the frequency-domain interpolation method. Then, an updated version of the reconstructed image is obtained after each iteration according to the min max criterion, and iterations are repeated until an acceptable Reconstruction of the results. Numerical experiments are given. Compared with the traditional reconstruction algorithm such as Gridding method, the proposed algorithm has the same computational complexity and high reconstruction accuracy.