Electrical and Electronics Engineering Department, Middle East Technical University, Ankara, Turkey.
ASELSAN A.Ş, Ankara, Turkey.
Int J Numer Method Biomed Eng. 2024 Jun;40(6):e3818. doi: 10.1002/cnm.3818. Epub 2024 Mar 31.
In microwave imaging, the adjoint method is widely used for the efficient calculation of the update direction, which is then used to update the unknown model parameter. However, the utilization and the formulation of the adjoint method differ significantly depending on the imaging scenario and the applied optimization algorithm. Because of the problem-specific nature of the adjoint formulations, the dissimilarities between the adjoint calculations may be overlooked. Here, we have classified the adjoint method formulations into two groups: the direct and indirect methods. The direct method involves calculating the derivative of the cost function, whereas, in the indirect method, the derivative of the predicted data is calculated. In this review, the direct and indirect adjoint methods are presented, compared, and discussed. The formulations are explicitly derived using the two-dimensional wave equation in frequency and time domains. Finite-difference time-domain simulations are conducted to show the different uses of the adjoint methods for both single source-multiple receiver, and multiple transceiver scenarios. This study demonstrated that an appropriate adjoint method selection is significant to achieve improved computational efficiency for the applied optimization algorithm.
在微波成象中，伴随方法被广泛用于有效计算更新方向，然后使用该更新方向更新未知模型参数。然而，伴随方法的使用和公式化在很大程度上取决于成象场景和应用的优化算法。由于伴随公式的特定于问题的性质，可能会忽略伴随计算之间的差异。在这里，我们将伴随方法公式分为两组：直接方法和间接方法。直接方法涉及计算成本函数的导数，而在间接方法中，计算预测数据的导数。在本综述中，介绍、比较和讨论了直接和间接伴随方法。使用频域和时域中的二维波动方程显式推导出公式。进行了有限差分时域模拟，以展示伴随方法在单源-多接收器和多收发器场景中的不同用途。这项研究表明，选择适当的伴随方法对于提高应用优化算法的计算效率非常重要。
