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通过对校准的低剂量CT投影数据的噪声特性进行分析,发现该噪声可用高斯分布近似,但其方差与信号本身有关,且信号与方差间的关系是非线性的。基于上述发现,我们选择惩罚加权最小均方平滑架构作为此类问题的最优解法之一。该方法可利用均值-方差间关系等先验知识来构造加权矩阵,并利用二维局部空间信息来构造惩罚项或正则算子。同时,为了进一步利用不同角度或切片间的空间相关关系,我们首先对投影数据沿角度或切片方向进行K-L变换,然后再对变换后的投影数据进行惩罚加权最小均方平滑,从而亦使原来的三维滤波问题简化为二维滤波过程。通过选择适当的邻域,K-L域惩罚加权最小均方平滑方法可充分利用先验统计知识及三维空间信息,对被噪声污染的低剂量CT投影进行更为准确的恢复。实验结果表明,当选取适当的控制参数,在投影数据的噪声滤除效果上,上述方法远较传统的低通滤波器为优。
By analyzing the noise characteristics of the calibrated low-dose CT projection data, the noise can be approximated by a Gaussian distribution, but the variance is related to the signal itself, and the relationship between the signal and the variance is nonlinear. Based on the above findings, we choose to penalize the weighted least mean square smoothing architecture as one of the optimal solutions to such problems. This method can construct the weighted matrix by a priori knowledge such as mean-variance relationship, and construct the penalty or regular operator by using two-dimensional local space information. At the same time, in order to further utilize the spatial correlation between different angles or slices, we first KL transform the projection data along the angle or the slice direction, and then penalize the transformed projection data with the weighted least mean square smooth, so that the original Three-dimensional filtering problem reduced to two-dimensional filtering process. By choosing appropriate neighborhoods, the K-L penalty-weighted least-mean-square smoothing method can make full use of prior knowledge of statistics and three-dimensional spatial information to more accurately recover low-dose CT images contaminated by noise. The experimental results show that the proposed method is superior to the traditional low-pass filter in selecting the appropriate control parameters for the noise filtering effect of projection data.