Numerical Analysis Series: Subspace-based Optimization Methods for Solving Electromagnetic Inverse Scattering Problem
Friday, May 13, 3PM – 4PM
Xudong Chen, National University of Singapore
This talk presents a numerical method to solve inverse scattering problems (ISP). The recently proposed subspace-based optimization method (SOM) is found to be effective in solving ISP. The essence of the SOM is that a part of the secondary source is determined from the spectrum analysis without using any optimization, whereas the rest is determined by an optimization method. Since the optimization is carried out in a smaller dimensional space, the algorithm significantly speeds up the convergence. There is a great flexibility in partitioning the space of secondary source into two orthogonally complementary subspaces: the signal subspace and the noise subspace. This flexibility enables the algorithm to perform robustly against noise. On the basis of the SOM, a twofold SOM (TSOM) and its variation, the FFT-TSOM, are proposed to solve in a more stable and more efficient manner the two-dimensional (2D) and three-dimensional (3D) electromagnetic ISP. Numerical simulations validate the efficacy of the proposed method: robustness against noise, fast convergence, high resolution, and the ability to deal with scatterers of special shapes. The SOM can be also applied to solve electric impedance tomography (EIT) problem and transport-based imaging problems.
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