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On the computational complexity of the conjugate-gradient method for solving inverse scattering problems
Journal of Electromagnetic Waves and Applications ( IF 1.3 ) Pub Date : 2021-06-29 , DOI: 10.1080/09205071.2021.1946862
Jose O. Vargas 1 , André Costa Batista 1 , Lucas S. Batista 2 , Ricardo Adriano 2
Affiliation  

This paper presents an efficient implementation of the inversion algorithm based on the conjugate-gradient method (CGM) for solving inverse scattering problems. The original CGM provides good image reconstruction and robustness to noise-corrupted data. This method requires the solution of the forward scattering problem and the Fréchet derivative operator of the cost function at each iteration step. However, these procedures can make the computational cost prohibitive, even for moderately sized problems. To avoid the computational burden, a two-step conjugate gradient fast Fourier transform (CG-FFT) procedure is proposed. Such an approach reduces the computational cost and storage requirements of the CGM implementation. The efficient CGM is found to share a computational complexity similar to the distorted-Born iterative method (DBIM). Thus the convergence speed and accuracy of the CGM is compared with the DBIM. Numerical tests using both synthetic and experimental data show effectiveness for solving 2D inverse scattering problems.



中文翻译:

关于求解逆散射问题的共轭梯度法的计算复杂度

本文提出了一种基于共轭梯度法 (CGM) 的反演算法的有效实现,用于解决逆散射问题。原始 CGM 提供了良好的图像重建和对噪声破坏数据的鲁棒性。该方法需要在每个迭代步骤中求解前向散射问题和成本函数的 Fréchet 导数算子。然而,即使对于中等规模的问题,这些过程也会使计算成本过高。为了避免计算负担,提出了两步共轭梯度快速傅立叶变换(CG-FFT)程序。这种方法降低了 CGM 实现的计算成本和存储要求。发现有效的 CGM 共享类似于失真出生迭代方法 (DBIM) 的计算复杂性。因此将 CGM 的收敛速度和精度与 DBIM 进行比较。使用合成数据和实验数据的数值测试显示了解决二维逆散射问题的有效性。

更新日期:2021-06-29
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