Hilbert transform based FBP algorithm for fan-beam CT full and partial scans.
Hilbert transform based FBP algorithm for fan-beam CT full and partial scans.
复制标题
基于希尔伯特变换的 FBP 算法，适用于扇束 CT 完整和部分扫描。
DOI：
10.1109/tmi.2006.889705
复制
发表时间：
2007
影响因子：
10.6
通讯作者：
Zeng,GengshengL
中科院分区：
文献类型：
--
作者：
You,Jiangsheng;Zeng,GengshengL
本文提出了一种用于扇束全扫描和部分扫描的新型滤波反投影（FBP）算法。滤波相对于角度变量是平移不变的。反投影不包括通过希尔伯特变换以及扇形光束坐标和平行光束坐标之间的一维变换实现的位置相关权重。滤波投影的强对称性直接导致部分数据的精确重建。希尔伯特变换的使用避免了基于斜坡滤波器的FBP算法中所需的非均匀截止频率引入的近似。方差分析表明该算法可以使重建图像的分辨率和噪声具有更好的均匀性。提供数值模拟来评估具有无噪声和噪声投影的算法。我们的仿真结果表明，该算法确实比基于斜坡滤波器的 FBP 和圆谐波重构算法具有更好的稳定性。这可能有助于提高具有单行探测器的就地计算机断层扫描仪的图像质量
This paper presents a new type of filtered backprojection (FBP) algorithm for fan-beam full- and partial-scans. The filtering is shift-invariant with respect to the angular variable. The backprojection does not include position-dependent weights through the Hilbert transform and the one-dimensional transformation between the fan- and parallel-beam coordinates. The strong symmetry of the filtered projections directly leads to an exact reconstruction for partial data. The use of the Hilbert transform avoids the approximation introduced by the nonuniform cutoff frequency required in the ramp filter-based FBP algorithm. Variance analysis indicates that the algorithm might lead to a better uniformity of resolution and noise in the reconstructed image. Numerical simulations are provided to evaluate the algorithm with noise-free and noisy projections. Our simulation results indicate that the algorithm does have better stability over the ramp-filter-based FBP and circular harmonic reconstruction algorithms. This may help improve the image quality for in place computed tomography scanners with single-row detectors