针对计算机层析成像(CT)偏置扫描滤波反投影(FBP)重建算法中加权函数形式复杂、抑噪性能不足的问题,该文提出了一种形式简洁、连续光滑的Sigmoid指数型加权函数。通过对偏置重建过程进行Fourier变换,推导得到加权函数对白噪声的频域响应余项,相较Parker、Wang这2种加权函数,该文函数频域响应余项的高频部分幅度更低。该文分别进行了扇形束与锥形束几何在无噪声和有噪声情况下的偏置扫描仿真实验,重建图像采取主客观相结合的方法进行评价。结果表明:在理想无噪声条件下,3种加权函数重建图像无显著差异;在有噪声条件下,该文函数重建图像整体平滑、边缘锐利、对比度突出;F-范数、均方差(MSE)、对比度噪声比(CNR)这3项指标均有改善。相较Parker与Wang函数,该文函数形式简洁且抑噪性能更为优异。

For computed tomography (CT) with a displaced detector array, projections should be weighted by a weighting function to fit the filtered-backprojection (FBP) image reconstruction algorithm. Existing weighting functions have complicated piecewise forms and do not give good noise suppression. This study uses Sigmoid-like exponential weighting function, which is continuous, differentiable, and simple. Fourier transforms are used for the weighted FBP algorithm to obtain the residual terms of the frequency response for white noise. The residuals of this function are lower than those of wary function at high frequencies. The fan-beam and cone-beam geometries with displaced detector arrays were simulated with the images reconstructed using the FBP weighted by the Parker function, Wang function, and the present function. Subjective and objective evaluations show that for ideal noise-free conditions, the image qualities for the three functions are quite close; while with noisy conditions, the images given by the present function are smoother with sharper edges and higher contrast with improved F-norm, and mean squared error (MSE), contrast noise ratio (CNR) indices. Thus, this function is simpler and gives better noise suppression than the existing Parker and Wang functions.