Meaney Paul M, Yagnamurthy Navin K, Paulsen Keith D
Thayer School of Engineering. Dartmouth College, Hanover, NH, USA.
Phys Med Biol. 2002 Apr 7;47(7):1101-19. doi: 10.1088/0031-9155/47/7/308.
Gauss-Newton image reconstruction in microwave imaging can be formulated in terms of a single complex quantity, the wave number squared (k2), with the understanding that the relative permittivity and conductivity images can be extracted afterwards through a simple constitutive relationship. However, this approach ignores the fact that the magnitude of the average real and imaginary components can be considerably out of balance depending on the operating frequency and tissue characteristics which can inadvertently imbalance the process in favour of one parameter over the other. In an effort to achieve property recovery which is balanced, we introduce a pre-scaling procedure at the property update stage of the reconstruction. Utilization of this concept in conjunction with our two-step regularization process for both simulation and phantom experiments demonstrates that the penalty term weighting parameters for the optimal mean-squared property errors for the two recovered distributions (relative permittivity and conductivity) together with that yielding the lowest least-squared electric field error coincide only when the scaling is applied. The scheme provides a means for simultaneous optimization of the two permittivity and conductivity images.
微波成像中的高斯 - 牛顿图像重建可以用一个单一的复数量——波数平方（k²）来表述，前提是可以通过简单的本构关系随后提取相对介电常数和电导率图像。然而，这种方法忽略了这样一个事实，即平均实部和虚部的大小可能会因工作频率和组织特性而严重失衡，这可能会无意中使过程偏向一个参数而不利于另一个参数。为了实现平衡的特性恢复，我们在重建的特性更新阶段引入了一种预缩放程序。在模拟和体模实验中，将这一概念与我们的两步正则化过程结合使用表明，只有在应用缩放时，两个恢复分布（相对介电常数和电导率）的最优均方特性误差的惩罚项加权参数以及产生最低最小二乘电场误差的参数才会重合。该方案提供了一种同时优化两个介电常数和电导率图像的方法。
