﻿ 东南大学学报(自然科学版)

(1南京航空航天大学机械结构力学及控制国家重点实验室, 南京210016)

Direct iterative basis material decomposition method for dual-energy CT based on MAP-EM algorithm
Zhou Zhengdong1，Zhang Xuling1，Xin Runchao1,2，Jia Junshan1，Wei Shisong 1，Mao Ling1
(1State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China)(2Department of Nuclear Science and Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China)

To improve the accuracy of basis material decomposition and reduce the noise in the basis material images for dual-energy CT(computed tomography), a direct iterative basis material decomposition method based on the MAP-EM(maximum a posteriori expectation-maximization)algorithm was proposed. Combined with the MAP-EM algorithm, the direct iterative formulas for basis material decomposition were derived. The basis material decomposition images were directly reconstructed from the dual-energy projection data set. The performance of the method was evaluated and analyzed. The simulation results show that the proposed method can significantly reduce the error of decomposition and the noise of basis material images, and improve the contrast-to-noise ratio. Compared with the image domain basis material decomposition method based on the FBP(filtered back projection)algorithm, the proposed method can reduce the noise of each material region in the basis material images by 57.42% to 63.64%. The decomposition error levels of each material region in the basis material images can be reduced by 31.72% to 62.14%. The contrast-to-noise ratios of each material region in the basis material images can be improved by 1.37% to 223.17%.

1976年Alvarez和Macovski[1]首次提出双能CT(dual-energy CT, DECT)的概念,利用2种不同管电压下的X射线对目标进行扫描成像.利用双能CT可获得伪单能图像,降低射束硬化伪影的影响[2].双能CT通过识别2个能谱下的能量信息,可以提供更多的物质属性,在物质识别方面远远优于传统CT.

1 材料与方法1.1 MAP-EM统计重建算法

yk～possion(Zk+ek)(1)

Zk=AkI=∑Ni=1akiIi i=1, 2, …, N; k=1,2,...,K(2)

P(Ι〖JB<1|〗y)=(P(y〖JB<1|〗I)P(I))/(P(y))(3)

P(I)=(exp(-βU(I)))/c(4)

Is+1i=(Isi)/(∑kaki+β(∂U(Is))/(∂Ii))∑k(ykaki)/(∑i'aki'Isi')(5)

1.2 直接迭代基材料分解方法

μ(E,l)≈∑nfm-1xm(l)μm(E)(6)

P(E,l)=∑nfm=1μm(E)Bm(l)(7)

P(u,l)=∑Qq=1w(Eq)P(Eq,l)=

Qq=1nfm=1w(Eqm(Eq)Bm(l)=∑nfm=1μm(u)Bm(l)(8)

Bm(l)=Axm(l)m=1,2,…,nf(9)

P=JRx(10)

J=J1CK,J1=[μ1(u1)… μnf(u1)

 

μ1(uNe)… μnf(uNe)](11)

R=CnfA(12)

P=JRx=[μ1(uL)A μ2(uL)A

μ1(uH)A μ2(uH)A][x1

x2](13)

xs+11i=(xs1i)/(∑kcki+β(∂U(xs1))/(∂x1i))∑k(y1kcki)/(∑i'cki'xs1i')

xs+12i=(xs2i)/(∑kcki+β(∂U(xs2))/(∂x2i))∑k(y2kcki)/(∑i'cki'xs2i')(14)

1.3 性能评估指标

σ=(1/(N-1)∑Ni=1(zi-z-)2)1/2(15)

R=(|z-c-z-b|)/(σb)(16)

M=(∑Ni=1(zreci-zrefi)2)/N(17)

δ=1/(E2-E1)∫E2E1(|μ(E)-[b1μ1(E)+b2μ2(E)]|)/(μ(E))dE(18)

1.4 模拟实验装置

1.5 基材料分解理论值计算

[b1

b2]=[μ1L μ2L

μ1H μ2H]-1L

μH](19)

2 实验结果与分析2.1 正则化参数评价

MAP-EM算法在迭代过程中加入了惩罚项,相当于在重建过程中施加一定的先验约束条件来达到抑制噪声的目的.迭代过程中,正则化参数β的选择对重建图像质量具有较大影响.为了评价正则化参数对分解结果的影响,引入如下2个指标:①重建图像与参考图像的近似程度,通过均方误差M来确定; ②重建图像的噪声水平,通过各模体材料的对比噪声比R来确定.M越小,重建图像越接近于参考图像; R越大则图像的噪声越小.计算均方误差M时,将理论分解图像作为参考图像; 计算R时,将PE设置为背景材料.

2.2 基材料分解图像重建结果

2.3 结果分析2.3.1 噪声水平分析

2.3.2 对比噪声比分析

2.3.3 误差水平分析

3 结论

1)针对双能CT,提出了基于MAP-EM算法的直接迭代基材料分解方法, 将基材料分解问题转化为基材料图像重建问题,推导出MAP-EM-DIBMD方法的迭代求解公式,有效提高基材料分解的精度和鲁棒性.

2)仿真实验结果表明,MAP-EM-DIBMD算法显著降低了基材料分解图像的噪声水平和误差水平, 提高了基材料分解图像的对比噪声比,具有重要的实际应用价值.

3)MAP-EM-DIBMD算法采用迭代的方法重建分解图像,耗时较长,可采用有序子集的方法对算法进行加速,在实际应用中还可采用GPU提高算法的计算效率.下一步可将所提方法拓展到光子计数能谱CT并应用于临床研究,对其性能进行进一步评估和改进,为临床精确诊断提供服务.