Subspace-Based Conjugate-Gradient Method for Solving Inverse Scattering Problems

The conjugate-gradient method (CGM) is a traditional approach to solve the inverse scattering problem (ISP). This method requires the solution of both the forward problem and the calculation of the gradient direction of the cost functional during the optimization procedure. The most popular approach is the linearized CGM, in which the total electric field is assumed to be independent of the variable of interest, and the solution of the forward scattering problem is determined from the best available contrast. In this article, a subspace-based CGM (S-CGM) is proposed to improve the performance of the linearized CGM. This approach retrieves the deterministic part of the variational-induced current. Therefore, the total electric field is estimated by adding the variational-induced current. This new total electric field approximation is more accurate than that of the linearized CGM, and thus, it achieves a faster convergence speed and higher accuracy. The proposed method is tested against both synthetic and experimental data. The reconstruction results show that the S-CGM has good accuracy, short computation time, and robustness to noise.