Coifman Ronald R, Shkolnisky Yoel, Sigworth Fred J, Singer Amit
Department of Mathematics, Program in Applied Mathematics, Yale University, New Haven, CT 06520-8283, USA.
IEEE Trans Image Process. 2008 Oct;17(10):1891-9. doi: 10.1109/TIP.2008.2002305.
We introduce a graph Laplacian-based algorithm for the tomographic reconstruction of a planar object from its projections taken at random unknown directions. A Laplace-type operator is constructed on the data set of projections, and the eigenvectors of this operator reveal the projection orientations. The algorithm is shown to successfully reconstruct the Shepp-Logan phantom from its noisy projections. Such a reconstruction algorithm is desirable for the structuring of certain biological proteins using cryo-electron microscopy.
我们介绍一种基于图拉普拉斯算子的算法，用于从在随机未知方向上获取的投影重建平面物体的断层图像。在投影数据集上构建一个拉普拉斯型算子，该算子的特征向量揭示投影方向。结果表明，该算法能从有噪声的投影中成功重建出Shepp-Logan体模。这种重建算法对于使用冷冻电子显微镜对某些生物蛋白质进行结构分析是很有必要的。
