Presampling, algorithm factors, and noise: Considerations for CT in particular and for medical imaging in general
Presampling, algorithm factors, and noise: Considerations for CT in particular and for medical imaging in general
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DOI：
10.1118/1.1897083
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发表时间：
2005-05-01
期刊：
影响因子：
3.8
通讯作者：
Kalender, WA
中科院分区：
文献类型：
--
作者：
Kachelriess, M;Kalender, WA
CT扫描仪在离散样本位置采集噪声数据。通常，在处理过程中必须应用如何将这些数据从离散整数位置延续到连续域的惯例。本文研究了三种典型的一维空间域插值算法的性能。品质因数Q是空间分辨率、数据噪声和剂量的函数，用于优化探测器设计。空间分辨率R被定义为均方宽度Delta或点扩展函数（PSF）的半峰全宽W。我们的研究结果表明，梯形插值算法是最佳的高分辨率域（相对于检测器孔径大小g），并应取代三角形或高斯插值函数的空间分辨率约为1.3g或更大，这些结果在钟形的PSF。假设采用这样的混合算法，与最高分辨率重建相比，当将数据平滑到3g或更高的空间分辨率时，我们发现Q（2）增加了1.5倍--这相当于剂量使用提高了50%。因此，建议使用所需空间分辨率W的三分之一大小的探测器，并通过减少33%的剂量来补偿Q（2）的1.5倍增加。在存在中等大小的隔膜的情况下（例如，空间分辨率元件尺寸的10%），优化的益处仍然在于改进剂量使用的30%的量级;在这种情况下，探测器尺寸g应该是W/2的量级，并且可以实现23%的剂量减少。同样，对于给定剂量，钟形PSF显示出比矩形PSF更好的噪声和分辨率之间的折衷。我们的研究结果的一般解释是，对于一个给定的分辨率选择的加权或插值函数的自由度是大的小探测器和小的大探测器。因此，与具有大g的系统相比，具有小g的系统具有更高的优化潜力。类似地，应避免检测器合并，其对应于用2g替换g。请注意，报告的数字对应于一维插值。二维检测器通常是分离的，并且所得到的品质因子可以通过乘法容易地获得。然后，Q2预计将在无隔片的情况下提高1.5（2）倍，在有隔片的情况下提高1.3（2）倍。这表明剂量可分别减少约56%和约41%。我们的发现是普遍的，并不局限于CT。它们可以很容易地应用于医学或非医学成像设备和数字探测器，它们也可能在其他领域中有用。(c)2005年美国医学物理学家协会。
CT scanners acquire noisy data at discrete sample positions. Typically, a convention of how to continue these data from discrete integer positions to the continuous domain must be applied during processing. We study the properties of three typical one-dimensional spatial domain interpolation algorithms in terms of a cost or quality factor Q. This figure of merit Q is a function of spatial resolution, data noise, and dose and is used to optimize detector design. Spatial resolution R is defined as either mean square width Delta or as the full width at half maximum W of the point spread function (PSF). Our results show that a trapezoidal interpolation algorithm is optimal for the high resolution domain (relative to the detector aperture size g) and should be replaced by a triangular or Gaussian interpolation function for spatial resolutions of about 1.3g or larger; these result in bell-shaped PSFs. Assuming such a hybrid algorithm we find a 1.5-fold increase of Q(2)-this is equivalent to 50% improved dose usage-when smoothing the data to a spatial resolution of 3g or more compared to a highest resolution reconstruction. Therefore it is advisable to use detectors of one-third of the size of the desired spatial resolution W and to compensate for the 1.5-fold increase in Q(2) by reducing dose by 33%. Under the presence of moderately sized septa (e.g., 10% of the spatial resolution element size) the benefit of optimizing still lies in the order of 30% improved dose usage; in that case the detector size g should be on the order of W/2 and a dose reduction of 23% can be achieved. Again, bell-shaped PSFs show a better tradeoff between noise and resolution for a given dose than rectangular-shaped PSFs. The general interpretation of our results is that the degree of freedom of choosing the weighting or interpolation function for a given resolution is large for small detectors and small for large detectors. Thus systems with small g have a higher potential of optimization compared to systems with large g. Similarly, detector binning, which corresponds to replacing g by 2g, should be avoided. Note that the figures reported correspond to a one-dimensional interpolation. Two-dimensional detectors typically separate and resulting quality factors can be easily obtained by multiplication. Then, Q2 is expected to improve by a factor of 1.5(2) without septa and by a factor of 1.3(2) with septa. This indicates that dose can be reduced by about 56% and about 41%, respectively. Our findings are general and not restricted to CT. They can be readily applied to medical or nonmedical imaging devices and digital detectors and they may also turn out to be useful in other fields. (c) 2005 American Association of Physicists in Medicine.