Rational approximations for tomographic reconstructions
Rational approximations for tomographic reconstructions
复制标题
断层扫描重建的有理近似
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Lucas Monzón
中科院分区：
文献类型：
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作者：
Matthew J. Reynolds;G. Beylkin;Lucas Monzón
我们使用最佳的合理近似的投影数据收集在X射线断层扫描，以提高图像分辨率。在假设感兴趣的对象是由跳跃不连续的函数描述的情况下，对于每个投影，我们构造其有理近似，对于给定的精度阈值，具有少量（接近最优）的项。这使我们能够增加测量数据，即，使每个投影中的可用样本的数量加倍，或者等效地，扩展（加倍）它们的傅立叶变换的域。我们还开发了一种新的、快速的极坐标傅里叶域算法，该算法以自然的方式使用我们对投影数据的非线性近似。使用增强投影的Shepp-Logan体模，我们提供了一个新的算法和标准的过滤反投影算法之间的比较。我们证明，重建图像具有提高的分辨率，而没有额外的伪影附近的图像中的急剧过渡。
We use optimal rational approximations of projection data collected in x-ray tomography to improve image resolution. Under the assumption that the object of interest is described by functions with jump discontinuities, for each projection we construct its rational approximation with a small (near optimal) number of terms for a given accuracy threshold. This allows us to augment the measured data, i.e., double the number of available samples in each projection or, equivalently, extend (double) the domain of their Fourier transform. We also develop a new, fast, polar coordinate Fourier domain algorithm which uses our nonlinear approximation of projection data in a natural way. Using augmented projections of the Shepp–Logan phantom, we provide a comparison between the new algorithm and the standard filtered back-projection algorithm. We demonstrate that the reconstructed image has improved resolution without additional artifacts near sharp transitions in the image.