Cone-beam and fan-beam image reconstruction algorithms based on spherical and circular harmonics.
Cone-beam and fan-beam image reconstruction algorithms based on spherical and circular harmonics.
复制标题
基于球谐波和圆谐波的锥束和扇束图像重建算法。
DOI：
10.1088/0031-9155/49/11/009
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发表时间：
2004
影响因子：
3.5
通讯作者：
Gullberg,GrantT
中科院分区：
文献类型：
--
作者：
Zeng,GengshengL;Gullberg,GrantT
提出了一种利用球谐展开的锥束图像重建算法。重建算法采用每个锥束采集点处的两个离散球谐展开系数阵列的内积求和的形式。这种形式不同于常见的滤波反投影算法和直接傅立叶重建算法。没有对数据进行重新采样，并且使用球谐展开而不是傅立叶展开。作为一种特殊情况，还根据圆谐波展开推导了一种新的扇束图像重建算法。给出了圆形平面轨道采集的锥束和扇束算法的计算机模拟结果。该算法提供准确的重建；然而，锥束重建算法的实现需要大量计算。当使用圆形扫描轨道时，提出了一种相对有效的算法来重建图像的中心切片。
A cone-beam image reconstruction algorithm using spherical harmonic expansions is proposed. The reconstruction algorithm is in the form of a summation of inner products of two discrete arrays of spherical harmonic expansion coefficients at each cone-beam point of acquisition. This form is different from the common filtered backprojection algorithm and the direct Fourier reconstruction algorithm. There is no re-sampling of the data, and spherical harmonic expansions are used instead of Fourier expansions. As a special case, a new fan-beam image reconstruction algorithm is also derived in terms of a circular harmonic expansion. Computer simulation results for both cone-beam and fan-beam algorithms are presented for circular planar orbit acquisitions. The algorithms give accurate reconstructions; however, the implementation of the cone-beam reconstruction algorithm is computationally intensive. A relatively efficient algorithm is proposed for reconstructing the central slice of the image when a circular scanning orbit is used.