Ehrhardt J C
Med Phys. 1986 Sep-Oct;13(5):658-62. doi: 10.1118/1.595869.
The images formed by many radiological systems are difficult to sample at spatial intervals small enough to avoid aliasing in the calculation of the system's modulation transfer function. However, if a system's response can be assumed to be symmetrical, this assumption can be used to effectively double the sampling density and to double the frequency limit before aliasing occurs. To accomplish this, a more complex algorithm is required. In this work, the formula for the calculation of the modulation transfer function from a symmetrical, one-dimensional line spread function is derived and a similar result for a symmetrical, two-dimensional point spread function is presented. The effect of noisy data and errors in the estimation of the offset of the center of the line spread function from a sampling point are investigated by simulation studies. For low noise (relative standard deviation of 1%) and an offset error of no more than 2% or 3% of a sampling interval, reasonable precision is obtained. These conditions appear to be achievable, especially when the noise is Poisson distributed.
许多放射成像系统所形成的图像难以按照足够小的空间间隔进行采样，以避免在计算系统调制传递函数时出现混叠现象。然而，如果可以假定一个系统的响应是对称的，那么这一假设可用于有效地将采样密度提高一倍，并在混叠发生之前将频率极限提高一倍。要实现这一点，需要一种更复杂的算法。在这项工作中，推导了根据对称的一维线扩展函数计算调制传递函数的公式，并给出了对称二维点扩展函数的类似结果。通过模拟研究，探讨了噪声数据以及线扩展函数中心相对于采样点的偏移估计误差的影响。对于低噪声（相对标准偏差为1%）且偏移误差不超过采样间隔的2%或3%的情况，可以获得合理的精度。这些条件似乎是可以实现的，尤其是当噪声呈泊松分布时。
