KSOM: Kernel-Subspace Optimization Method for Full-Wave Inverse Scattering Imaging

In the domain of full-wave inverse scattering imaging problems, subspace-based optimization methods (SOM) often perform suboptimal performance under significant noise conditions due to the intrinsic ill-posedness and nonlinearity of the problem. This paper introduces the kernel-subspace optimization method (KSOM), an innovative approach that combines the robust framework of SOM with the adaptive learning strengths of kernel methods. KSOM transforms the subspace into the reproducing kernel Hilbert space (RKHS), and the iterative process of SOM is learned within this space using the minimum mean square error criterion. The experimental results show that, compared with the classic SOM algorithm, the KSOM algorithm has significantly improved performance: the SSIM index evaluation increased by 21.43% on average, and the PSNR index increased by 9.53% on average. This advancement opens new avenues for integrating machine learning techniques with physics-based models in computational electromagnetics.