Abstract：
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.
摘要：
在微波成像中,伴随方法被广泛用于更新方向的有效计算，，然后用于更新未知模型参数。然而,根据成像场景和应用的优化算法，伴随方法的利用率和公式显着不同。由于伴随公式的特定问题性质，伴随计算之间的差异可能会被忽视。这里,我们将伴随方法公式分为两组:直接法和间接法。直接法涉及计算成本函数的导数，然而,在间接方法中，计算预测数据的导数。在这次审查中,提出了直接伴随方法和间接伴随方法，比较,并讨论。公式是使用频域和时域中的二维波动方程明确得出的。进行了有限差分时域仿真，以显示单源多接收机的伴随方法的不同用途，和多个收发器场景。这项研究表明，适当的伴随方法选择对于提高应用优化算法的计算效率具有重要意义。
