CAJ | 학술논문

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.
통과대교준적저제량CT투영수거적조성특성진행분석,발현해조성가용고사분포근사,단기방차여신호본신유관,차신호여방차간적관계시비선성적.기우상술발현,아문선택징벌가권최소균방평활가구작위차류문제적최우해법지일.해방법가이용균치-방차간관계등선험지식래구조가권구진,병이용이유국부공간신식래구조징벌항혹정칙산자.동시,위료진일보이용불동각도혹절편간적공간상관관계,아문수선대투영수거연각도혹절편방향진행K-L변환,연후재대변환후적투영수거진행징벌가권최소균방평활,종이역사원래적삼유려파문제간화위이유려파과정.통과선택괄당적린역,K-L역징벌가권최소균방평활방법가충분이용선험통계지식급삼유공간신식,대피조성오염적저제량CT투영진행경위준학적회복.실험결과표명,당선취괄당적공제삼수,재투영수거적조성려제효과상,상술방법원교전통적저통려파기위우.
By analyzing the noise properties of calibrated low-dose Computed Tomography (CT) projection data, it is clearly seen that the data can be regarded as approximately Gaussian distributed with a nonlinear signal-dependent variance. Based on this observation, the penalized weighted least-square(PWLS) smoothing framework is a choice for an optimal solution. It utilizes the prior variance-mean relationship to construct the weight matrix and the twodimensional(2D) spatial information as the penalty or regularization operator. Furthermore, a K-L transform is applied along the z (slice) axis to further consider the correlation among different sinograms, resulting in a PWLS smoothing in the K-L domain. As a tool for feature extraction and de-correlation, the K-L transform maximizes the data variance represented by each component and simplifies the task of 3D filtering into 2D spatial process slice by slice.Therefore, by selecting an appropriate number of neighboring slices, the K-L domain PWLS smoothing fully utilizes the prior statistical knowledge and 3D spatial information for an accurate restoration of the noisy low-dose CT projections in an analytical manner. Experimental results demonstrate that the proposed method with appropriate control parameters improves the noise reduction without the loss of resolution.