基于随机平均梯度下降和对比源反演的非线性逆散射算法研究

采用非线性对比源反演(CSI)算法求解电磁逆散射问题时，在每次迭代过程中都涉及到求解散射场数据关于对比源和总场的微分，即Jacobi矩阵，该矩阵求解导致算法存在计算代价大和收敛速度慢等问题。该文在CSI框架下，采用一种基于随机平均梯度下降的对比源反演算法(SAG-CSI)代替原来的全梯度交替共轭梯度算法来重构介质目标介电常数的空间分布信息。该方法在每次迭代中只需计算随机抽取的部分测量数据在目标函数中的梯度信息，同时目标函数对未抽中的测量数据的梯度信息保持不变，用以上两部分梯度信息共同求解出目标函数的最优值。由模拟数据结果表明，该方法与传统CSI方法在成像精度相比拟的情况下，降低了计算代价并提高算法收敛速度。

Stochastic Average Gradient Descent Contrast Source Inversion Based Nonlinear Inverse Scattering Method for Complex Objects Reconstruction

When using the nonlinear Contrast Source Inversion (CSI) algorithm to solve the electromagnetic inverse scattering problem, each iteration involves finding the differential of the dissolution radiation field data about the contrast source and the total field, i.e., the Jacobi matrix. the solution of the matrix leads to the problem of large computational cost and slow convergence speed of the algorithm. in this paper, a Contrast Source Inversion algorithm based on Stochastic Average Gradient descent (SAG-CSI) is used instead of the original full gradient alternating Conjugate Gradient algorithm to reconstruct the spatial distribution information of the dielectric constant of the dielectric target under the CSI framework. the method only needs to calculate the gradient information of the randomly selected part of the measurement data in the objective function in each iteration, while the objective function keeps the gradient information of the unscented measurement data, and the optimal value of the objective function is solved together with the above two parts of the gradient information. The simulation results show that the proposed method reduces the computational cost and improves the convergence speed of the algorithm when compared with the traditional CSI method.