Image Reconstruction by Frequency Extrapolation and Deep Learning in Three-Layer Medium

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This paper proposes a novel multi-frequency extended Deep Learning (DL) model for electromagnetic image reconstruction under Transverse Magnetic (TM) wave incidence in layered media, inspired by conventional microwave imaging techniques that combine nonlinear inversion algorithms with neural networks to improve reconstruction performance. The proposed framework adopts a two-stage neural network architecture. In the first stage, a Deep Residual Convolutional Neural Network (DRCNN) is employed to extrapolate multi-frequency scattered fields from single-frequency input data, thereby enriching the frequency-dependent scattering information available for reconstruction. Subsequently, the extrapolated multi-frequency scattered fields are fed into a Deep Convolutional Encoder–Decoder (DCED) network to reconstruct an accurate dielectric constant distribution within the imaging domain. To validate the effectiveness of the proposed approach, two representative comparison methods are considered: (1) a hybrid framework combining the Back-Propagation Scheme (BPS) with a Convolutional Neural Network (CNN), and (2) a framework integrating the Dominant Current Scheme (DCS) with a CNN. In both approaches, conventional inversion algorithms are first utilized to generate coarse initial reconstructions, which are subsequently refined by the neural network. Numerical simulations and experimental results show that the proposed multi-frequency extension model achieves lower reconstruction error and higher structural similarity than the reference methods. These results confirm the effectiveness and potential of the proposed framework for advanced electromagnetic imaging applications.