Tang Xiangyang, Hsieh Jiang
Applied Science Laboratory, GE Healthcare, P.O. Box 414, W1190, Milwaukee, Wisconsin 53201, USA.
Med Phys. 2007 Jun;34(6):1989-98. doi: 10.1118/1.2736789.
A cone-angle-based window function is defined in this manuscript for image reconstruction using helical cone beam filtered backprojection (CB-FBP) algorithms. Rather than defining the window boundaries in a two-dimensional detector acquiring projection data for computed tomographic imaging, the cone-angle-based window function deals with data redundancy by selecting rays with the smallest cone angle relative to the reconstruction plane. To be computationally efficient, an asymptotic approximation of the cone-angle-based window function is also given and analyzed in this paper. The benefit of using such an asymptotic approximation also includes the avoidance of functional discontinuities that cause artifacts in reconstructed tomographic images. The cone-angle-based window function and its asymptotic approximation provide a way, equivalent to the Tam-Danielsson-window, for helical CB-FBP reconstruction algorithms to deal with data redundancy, regardless of where the helical pitch is constant or dynamically variable during a scan. By taking the cone-parallel geometry as an example, a computer simulation study is conducted to evaluate the proposed window function and its asymptotic approximation for helical CB-FBP reconstruction algorithm to handle data redundancy. The computer simulated Forbild head and thorax phantoms are utilized in the performance evaluation, showing that the proposed cone-angle-based window function and its asymptotic approximation can deal with data redundancy very well in cone beam image reconstruction from projection data acquired along helical source trajectories. Moreover, a numerical study carried out in this paper reveals that the proposed cone-angle-based window function is actually equivalent to the Tam-Danielsson-window, and rigorous mathematical proofs are being investigated.
本文定义了一种基于锥角的窗函数，用于使用螺旋锥束滤波反投影（CB-FBP）算法进行图像重建。基于锥角的窗函数不是在获取计算机断层成像投影数据的二维探测器中定义窗边界，而是通过选择相对于重建平面具有最小锥角的射线来处理数据冗余。为了提高计算效率，本文还给出并分析了基于锥角的窗函数的渐近近似。使用这种渐近近似的好处还包括避免在重建的断层图像中产生伪影的函数不连续性。基于锥角的窗函数及其渐近近似为螺旋CB-FBP重建算法提供了一种与Tam-Danielsson窗等效的方法，用于处理数据冗余，无论扫描过程中螺旋间距是恒定的还是动态变化的。以锥平行几何为例，进行了计算机模拟研究，以评估所提出的窗函数及其渐近近似在螺旋CB-FBP重建算法中处理数据冗余的能力。在性能评估中使用了计算机模拟的Forbild头部和胸部体模，结果表明，所提出的基于锥角的窗函数及其渐近近似能够很好地处理沿螺旋源轨迹采集的投影数据在锥束图像重建中的数据冗余。此外，本文进行的数值研究表明，所提出的基于锥角的窗函数实际上与Tam-Danielsson窗等效，目前正在研究严格的数学证明。
