Ji W G, Zhao W, Rowlands J A
Department of Medical Imaging, University of Toronto, Sunnybrook, Canada.
Med Phys. 1998 Nov;25(11):2148-62. doi: 10.1118/1.598411.
Alias reduction is analyzed with the concept of an equivalent presampling filter, and a mathematical approach is established to find the equivalent presampling filter corresponding to specific digital image processing algorithms. The effects of different sampling period T and sampling aperture tau on aliasing artifacts and on the resultant detective quantum efficiency (DQE) for a self-scanned, flat-panel, amorphous selenium detector are obtained. Different effective apertures can be obtained from the same detector by averaging signals over adjacent pixels. It is shown that adding outputs from M adjacent pixels is equivalent to introducing an equivalent presampling filter with special properties. Appropriate selection of the averaging parameters (M and weights) is shown to reduce the aliasing artifact in the resultant image. The effect of incomplete charge collection due to geometrical effects (fill factor) is examined. It is shown that a large fill factor is desirable for aliasing reduction. The relationship between a digital filter applied to the sampled signal and its equivalent presampling analog filter is also established. Analytical formulas for the sampled spectrum of white signal and for the sampled power spectrum of white noise are obtained for aperture functions with a spatially uniform response. These formulas take into accounts aliasing artifacts, signal correlation and aperture function response, and demonstrate the dependence of sampled spectra on T and tau. With these formulas the detective quantum efficiency DQE is derived. It is shown that the resultant DQE depends only on the fill factor and the size of readout electrode tau 0, but is completely independent of the degree or type of pixel averaging. That is, even though the pixel averaging method reduces aliasing it leaves DQE (omega) unchanged. When significant amplifier noise is present the DQE obtained with the pixel averaging method can be better than those obtained with an analog presampling filter. Finally, it is pointed out that the requirement of reducing aliasing artifacts conflicts with other requirements for a detector such as maximizing modulation transfer function (MTF). A careful and practical compromise has to be made by a detector designer in choosing the extent to which the aliasing artifacts are eliminated.
利用等效预采样滤波器的概念分析了混叠减少问题，并建立了一种数学方法来找到与特定数字图像处理算法相对应的等效预采样滤波器。获得了不同采样周期T和采样孔径τ对自扫描平板非晶硒探测器的混叠伪像以及所得探测量子效率（DQE）的影响。通过对相邻像素的信号进行平均，可以从同一探测器获得不同的有效孔径。结果表明，对M个相邻像素的输出进行相加等效于引入具有特殊特性的等效预采样滤波器。结果表明，适当选择平均参数（M和权重）可减少所得图像中的混叠伪像。研究了几何效应（填充因子）导致的电荷收集不完全的影响。结果表明，大的填充因子有利于减少混叠。还建立了应用于采样信号的数字滤波器与其等效预采样模拟滤波器之间的关系。对于具有空间均匀响应的孔径函数，获得了白信号采样频谱和白噪声采样功率谱的解析公式。这些公式考虑了混叠伪像、信号相关性和孔径函数响应，并证明了采样频谱对T和τ的依赖性。利用这些公式推导出探测量子效率DQE。结果表明，所得DQE仅取决于填充因子和读出电极的尺寸τ0，但与像素平均的程度或类型完全无关。也就是说，即使像素平均方法减少了混叠，它也不会改变DQE（ω）。当存在显著的放大器噪声时，采用像素平均方法获得的DQE可能优于采用模拟预采样滤波器获得的DQE。最后，指出减少混叠伪像的要求与探测器的其他要求（如最大化调制传递函数（MTF））相冲突。探测器设计者在选择消除混叠伪像的程度时必须做出谨慎而实际的折衷。
