Electrical Engineering Department, Chalmers University of Technology, 41296 Gothenburg, Sweden.
Thayer School of Engineering, Dartmouth College, Hanover, NH 03755, USA.
Sensors (Basel). 2021 Jan 22;21(3):729. doi: 10.3390/s21030729.
This paper focuses on the construction of the Jacobian matrix required in tomographic reconstruction algorithms. In microwave tomography, computing the forward solutions during the iterative reconstruction process impacts the accuracy and computational efficiency. Towards this end, we have applied the discrete dipole approximation for the forward solutions with significant time savings. However, while we have discovered that the imaging problem configuration can dramatically impact the computation time required for the forward solver, it can be equally beneficial in constructing the Jacobian matrix calculated in iterative image reconstruction algorithms. Key to this implementation, we propose to use the same simulation grid for both the forward and imaging domain discretizations for the discrete dipole approximation solutions and report in detail the theoretical aspects for this localization. In this way, the computational cost of the nodal adjoint method decreases by several orders of magnitude. Our investigations show that this expansion is a significant enhancement compared to previous implementations and results in a rapid calculation of the Jacobian matrix with a high level of accuracy. The discrete dipole approximation and the newly efficient Jacobian matrices are effectively implemented to produce quantitative images of the simplified breast phantom from the microwave imaging system.
本文专注于层析重建算法中所需的雅可比矩阵的构建。在微波层析成像中，在迭代重建过程中计算正向解会影响准确性和计算效率。为此，我们应用离散偶极子近似法进行正向求解，显著节省了时间。然而，虽然我们发现成像问题的配置会极大地影响正向求解器所需的计算时间，但它在构建迭代图像重建算法中计算的雅可比矩阵方面同样有益。实现这一目标的关键是，我们建议在离散偶极子近似解的正向和成像域离散化中使用相同的模拟网格，并详细报告这种定位的理论方面。通过这种方式，节点伴随方法的计算成本降低了几个数量级。我们的研究表明，与以前的实现相比，这种扩展是一个显著的改进，导致雅可比矩阵的快速计算和高精度。离散偶极子近似法和新的高效雅可比矩阵有效地实现了从微波成像系统产生简化乳房模型的定量图像。
