Fourier-based approach to interpolation in single-slice helical computed tomography.
Fourier-based approach to interpolation in single-slice helical computed tomography.
复制标题
单层螺旋计算机断层扫描中基于傅立叶的插值方法。
作者：
LaRivière,PJ;Pan,X
最近的研究表明，在重建的单层螺旋计算机断层扫描 (CT) 体积中，纵向混叠可能是一个重要且有害的存在。出现这种混叠的原因是，螺旋 CT 中直接测量的数据通常在纵向上欠采样至少 2 倍，而且利用 360° 范围内采集的扇形束数据的冗余来生成额外的纵向样本并不能自动消除混叠。在本文中，我们证明，对于接近 1 或更低的音高，冗余扇形束数据如果使用得当，可以提供足够的信息来满足广义采样定理，从而消除混叠。我们开发并评估了一种基于傅里叶的算法，称为 180FT，可以实现这一目标。作为背景，我们提出了第二种基于傅里叶的方法，称为 360FT，它仅使用直接测量的数据。两种基于傅里叶的方法都利用快速傅里叶变换和傅里叶平移定理，从螺旋投影数据生成一组与等距横向切片相对应的扇束正弦图。然后使用二维扇束算法进行逐层重建。将所提出的方法与基于线性插值的对应方法（360LI 和 180LI 方法）进行比较。 180FT 方法的混叠抑制特性是该方法的一个明显优势，代表着朝着在重建螺旋 CT 体积中实现均匀纵向分辨率特性的理想目标迈出了一步。
It has recently been shown that longitudinal aliasing can be a significant and detrimental presence in reconstructed single‐slice helical computed tomography (CT) volumes. This aliasing arises because the directly measured data in helical CT are generally undersampled by a factor of at least 2 in the longitudinal direction and because the exploitation of the redundancy of fanbeam data acquired over 360° to generate additional longitudinal samples does not automatically eliminate the aliasing. In this paper we demonstrate that for pitches near 1 or lower, the redundant fanbeam data, when used properly, can provide sufficient information to satisfy a generalized sampling theorem and thus to eliminate aliasing. We develop and evaluate a Fourier‐based algorithm, called 180FT, that accomplishes this. As background we present a second Fourier‐based approach, called 360FT, that makes use only of the directly measured data. Both Fourier‐based approaches exploit the fast Fourier transform and the Fourier shift theorem to generate from the helical projection data a set of fanbeam sinograms corresponding to equispaced transverse slices. Slice‐by‐slice reconstruction is then performed by use of two‐dimensional fanbeam algorithms. The proposed approaches are compared to their counterparts based on the use of linear interpolation—the 360LI and 180LI approaches. The aliasing suppression property of the 180FT approach is a clear advantage of the approach and represents a step toward the desirable goal of achieving uniform longitudinal resolution properties in reconstructed helical CT volumes.