Sunnybrook Research Institute, Toronto, M4N 3M5, ON, Canada.
Med Phys. 2019 Nov;46(11):4792-4802. doi: 10.1002/mp.13734. Epub 2019 Sep 9.
A method was developed to obtain three-dimensional (3D) point spread functions (PSFs) of reconstructed x-ray volumetric images using spheres of known diameters. The algorithm consists of a sphere localization step using template matching applied to the entire volume. Richardson Lucy (RL) deconvolution is used atypically to determine the PSF from the reconstructed x-ray image and a model of the sphere. The resulting PSF is arbitrary, that is, there are no assumptions of separability or symmetry. Oversampling is not used, and sample spacing matches the image. The effect of sphere radius on PSF estimate reproducibility is investigated.
Phantoms were constructed by suspending five polytetrafluoroethylene (PTFE) spheres having known radii equal to 4.77, 7.95, 9.52, 12.68, and 19.53 mm in an agar solution. The phantom included a 25 μm steel wire to calculate a line spread function (LSF). The phantom was imaged and reconstructed with a Medtronic surgical O-Arm 23 times and a Toshiba Aquilion One computed tomography (CT) 20 times. A sharp reconstruction kernel exhibiting a nonmonotonic PSF was used with the Toshiba CT. PSFs and LSFs were computed for all of the images and repeated estimates were used to compute mean and standard deviation values for every point of the PSFs and LSFs. The PSFs from spheres were converted to LSFs and compared to the wire LSF.
The standard deviations of the PSF estimates exhibit a decreasing trend as the sphere radius is increased. The PSF from the smallest 4.77 mm sphere is the least reproducible. The normalized root mean square difference between the mean LSF derived from the 4.77 mm radius sphere and the mean wire LSF is 2.0% for the O-arm and 1.2% for the CT.
Richardson Lucy (RL) deconvolution provides a method to estimate generalized (no separability or other simplifying assumptions) 3D PSFs from spheres. X-ray noise in images acquired with typical clinical protocols cause noticeable variations in PSF estimates which can be mitigated by selecting larger spheres and combining PSF estimates from different images.
开发了一种使用已知直径的球体获取重建 X 射线体图像三维（3D）点扩散函数（PSF）的方法。该算法由使用模板匹配对整个体积进行球体定位步骤组成。Richardson Lucy（RL）反卷积通常用于从重建的 X 射线图像和球体模型确定 PSF。得到的 PSF是任意的，也就是说，没有可分离性或对称性的假设。不使用过采样，并且采样间距与图像匹配。研究了球体半径对 PSF 估计可重复性的影响。
通过将五个具有已知半径的聚四氟乙烯（PTFE）球体悬浮在含有已知半径为 4.77、7.95、9.52、12.68 和 19.53mm 的琼脂溶液中构建了一个体模。该体模包括一根 25μm 的钢丝，用于计算线扩散函数（LSF）。使用 Medtronic 手术 O-Arm 对该体模进行了 23 次成像和重建，使用 Toshiba Aquilion One 计算机断层扫描（CT）进行了 20 次成像和重建。使用 Toshiba CT 采用锐化重建核，该重建核具有非单调 PSF。计算了所有图像的 PSF 和 LSF，并使用重复估计来计算 PSF 和 LSF 每个点的平均值和标准偏差值。将球体的 PSF 转换为 LSF，并将其与钢丝的 LSF 进行比较。
随着球体半径的增加，PSF 估计的标准偏差呈下降趋势。最小的 4.77mm 球体的 PSF 最不可重复。O-arm 和 CT 的 4.77mm 半径球的平均 LSF 与平均钢丝 LSF 之间的归一化均方根差分别为 2.0%和 1.2%。
Richardson Lucy（RL）反卷积提供了一种从球体估计广义（无可分离性或其他简化假设）3D PSF 的方法。典型临床方案采集的图像中的 X 射线噪声会导致 PSF 估计值发生明显变化，可以通过选择更大的球体并结合来自不同图像的 PSF 估计值来减轻这种变化。
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