Fast fully 3-D image reconstruction in PET using planograms.
Fast fully 3-D image reconstruction in PET using planograms.
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使用货架图在 PET 中快速进行全 3D 图像重建。
DOI：
10.1109/tmi.2004.824231
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
Townsend,DW
中科院分区：
文献类型：
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作者：
Brasse,D;Kinahan,PE;Clackdoyle,R;Defrise,M;Comtat,C;Townsend,DW
我们提出了一种方法来执行快速和准确的三维（3-D）反投影仅使用傅里叶变换操作的线积分数据获得的平面探测器阵列在正电子发射断层扫描。这种方法是Edholm二维（2-D）线性图技术的三维扩展。通过使用特殊的参数选择来索引一对平面探测器的响应线（LOR），而不是用于索引圆形层析仪的响应线的常规参数，所有通过视场（FOV）中的点的响应线都位于四维（4-D）数据空间中的二维平面上。因此，所有通过视场点的LORs的反向投影对应于通过4-D“平面图”的二维平面的积分。关键的一步是，沿着一组平行的二维平面通过平面图进行积分，即点平面的反投影，可以通过数据的四维傅里叶变换的原点来替换为二维截面。反向投影可以作为傅里叶变换操作的序列来执行，以便更快地实现。此外，我们还推导了平面格式数据的中心截面定理，并推导了用于反投影-滤波和滤波-反投影重建算法的重建滤波器。通过基于软件的傅里叶变换计算，我们提供了平面反投影与标准3d反投影的初步比较，并证明计算时间减少了大约15倍。
We present a method of performing fast and accurate three-dimensional (3-D) backprojection using only Fourier transform operations for line-integral data acquired by planar detector arrays in positron emission tomography. This approach is a 3-D extension of the two-dimensional (2-D) linogram technique of Edholm. By using a special choice of parameters to index a line of response (LOR) for a pair of planar detectors, rather than the conventional parameters used to index a LOR for a circular tomograph, all the LORs passing through a point in the field of view (FOV) lie on a 2-D plane in the four-dimensional (4-D) data space. Thus, backprojection of all the LORs passing through a point in the FOV corresponds to integration of a 2-D plane through the 4-D "planogram." The key step is that the integration along a set of parallel 2-D planes through the planogram, that is, backprojection of a plane of points, can be replaced by a 2-D section through the origin of the 4-D Fourier transform of the data. Backprojection can be performed as a sequence of Fourier transform operations, for faster implementation. In addition, we derive the central-section theorem for planogram format data, and also derive a reconstruction filter for both backprojection-filtering and filtered-backprojection reconstruction algorithms. With software-based Fourier transform calculations we provide preliminary comparisons of planogram backprojection to standard 3-D backprojection and demonstrate a reduction in computation time by a factor of approximately 15.