Magnetic Induction Tomography of IntraCerebral Hemorrhage Based on Improved Newton-Raphson Algorithm
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摘要: 针对脑出血磁感应断层成像(MIT)中正问题模型过于简化、图像重建质量较低、算法收敛效率低、病变与背景间伪影较大、耗时较长等问题，该文提出一种用于脑出血MIT的改进牛顿-拉夫逊(NR)算法。将线性反投影(LBP)算法计算结果作为改进NR算法的迭代初值，在目标函数中加入自适应加速惩罚项和L2范数惩罚项，提高算法每一步迭代的效率，减少重建图像的伪影。引入投影算子P施加物理意义上的约束，提高收敛速度并改善成像质量。利用Comsol Multiphysics构建了包含头皮、颅骨、脑脊液和脑实质的真实3维颅脑模型。仿真计算了相位差检测值和灵敏度矩阵用于后续的图像重建。利用所提改进NR算法与5种图像重建算法分别对3个位置出血量分别为24 ml, 14 ml, 2 ml的脑出血进行磁感应断层成像。实验结果表明，所提算法相比其他5种算法重建图像的质量更高，成像时间平均只需NR算法的1/3。使用更少的迭代次数重建出更高质量的图像，并且能实现2 ml脑出血的图像重建，为脑出血的MIT检测提供一种新的有效算法。Abstract: To solve the problems of over-simplified positive problem model, low image reconstruction quality, low algorithm convergence efficiency, large artifacts between lesion and background, and long time consuming in IntraCerebral Hemorrhage (ICH) Magnetic Induction Tomography (MIT), an improved Newton-Raphson (NR) algorithm for MIT of intracerebral hemorrhage is proposed. The calculation results of Linear Back Projection (LBP) algorithm are used as the iterative initial values of the improved NR algorithm, the adaptive acceleration penalty term and the L2 norm penalty term are added to the objective function to improve the efficiency of each iteration of the algorithm and reduce the artifacts of the reconstructed image. A real three-dimensional brain model including scalp, skull, cerebrospinal fluid and brain parenchyma is constructed by Comsol Multiphysics. The phase difference detection value and sensitivity matrix are simulated and calculated for subsequent image reconstruction. The proposed improved NR algorithm and five image reconstruction algorithms are used to perform magnetic induction tomography on intracerebral hemorrhage with blood loss of 24 ml, 14 ml and 2 ml at three locations, respectively. The experimental results show that the proposed algorithm has higher quality of reconstructed images than the other five algorithms. The average imaging time is only 1/3 of the NR algorithm. The higher quality image is reconstructed with fewer iterations, the image reconstruction of 2 ml intracerebral hemorrhage can be realized, which provides a new and effective algorithm for MIT detection of intracerebral hemorrhage.
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表 1 1 MHz下的脑组织电磁特性
脑组织 头皮 颅骨 脑脊液 脑实质 脑出血 电导率(S/m) 0.044 0.024 2.000 0.102 0.822 介电常数(F/m) 50.8 145 109 480 3030 
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表 2 相关系数
脑出血分布 Tikhonov Landweber CGLS NR NR (优化迭代策略) 改进NR (无投影算子) 改进NR 位置A：24 ml 0.505 0.355 0.490 0.483 0.512 0.513 0.676 位置A：14 ml 0.437 0.306 0.422 0.416 0.443 0.441 0.595 位置A： 2 ml 0.269 0.209 0.255 0.253 0.275 0.267 0.377 位置B：24 ml 0.455 0.311 0.449 0.416 0.468 0.448 0.590 位置B：14 ml 0.378 0.282 0.380 0.342 0.388 0.367 0.401 位置B： 2 ml 0.207 0.171 0.199 0.189 0.213 0.202 0.286 位置C：24 ml 0.481 0.364 0.476 0.446 0.491 0.474 0.619 位置C：14 ml 0.407 0.308 0.404 0.375 0.417 0.397 0.528 位置C： 2 ml 0.244 0.180 0.243 0.227 0.250 0.240 0.333
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表 3 图像误差/归一化均方距离
脑出血分布 Tikhonov Landweber CGLS NR NR (优化迭代策略) 改进NR (无投影算子) 改进NR 位置A：24 ml 0.962/1.182 0.993/1.005 0.956/0.968 0.957/0.969 0.961/0.975 0.959/0.970 0.910/0.949 位置A：14 ml 1.022/1.030 1.510/1.527 1.163/1.174 1.184/0.987 0.991/0.977 0.975/0.983 0.947/0.876 位置A： 2 ml 1.867/1.872 2.709/2.610 2.505/2.514 2.517/2.525 1.662/1.666 1.860/1.865 1.544/1.550 位置B：24 ml 0.970/0.983 0.994/1.007 0.967/0.980 0.969/0.983 0.970/0.984 0.971/0.984 0.938/0.967 位置B：14 ml 1.013/1.022 1.525/1.540 1.043/1.052 1.135/1.145 0.997/0.993 1.144/1.153 0.968/0.920 位置B： 2 ml 1.825/1.779 2.226/2.247 2.098/2.111 2.256/2.262 1.716/1.675 1.887/1.891 1.501/1.505 位置C：24 ml 0.965/0.978 0.993/1.006 0.961/0.974 0.964/0.977 0.966/0.980 0.965/0.978 0.933/0.961 位置C：14 ml 0.990/0.989 1.540/1.567 1.038/1.046 1.101/1.111 0.981/0.967 1.107/1.117 0.962/0.910 位置C： 2 ml 1.663/1.622 1.877/1.765 1.855/1.860 2.026/2.038 1.575/1.510 1.705/1.710 1.354/1.358
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表 4 图像重建时间(s)/迭代次数
脑出血分布 Tikhonov Landweber CGLS NR NR (优化迭代策略) 改进NR (无投影算子) 改进NR 位置A：24 ml 0.064/1 0.027/300 0.002/40 0.750/12 1.949/33 0.411/8 0.223/5 位置A：14 ml 0.078/1 0.029/303 0.002/45 0.801/13 1.841/30 0.406/8 0.217/5 位置A： 2 ml 0.071/1 0.041/460 0.002/52 1.134/17 2.133/35 0.410/8 0.287/6 位置B：24 ml 0.061/1 0.026/300 0.001/38 0.706/11 1.534/25 0.405/8 0.285/6 位置B：14 ml 0.068/1 0.032/332 0.002/40 0775/12 1.797/30 0.391/8 0.235/5 位置B： 2 ml 0.063/1 0.042/510 0.002/46 0.983/15 1.910/32 0.393/8 0.293/6 位置C：24 ml 0.061/1 0.026/302 0.002/39 0.765/12 1.527/26 0.414/8 0.253/5 位置C：14 ml 0.070/1 0.030/303 0.002/40 0.770/12 1.678/28 0.413/8 0.297/6 位置C： 2 ml 0.064/1 0.030/310 0.002/44 1.053/15 1.873/31 0.396/8 0.295/6
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