Quality-factor inspired deep neural network solver for solving inverse scattering problems

Deep neural networks have been applied to address electromagnetic inverse scattering problems (ISPs) and shown superior imaging performances, which can be affected by the training dataset, the network architecture and the applied loss function. Here, the quality of data samples is cared and valued by the defined quality factor. Based on the quality factor, the composition of the training dataset is optimized. The network architecture is integrated with the residual connections and channel attention mechanism to improve feature extraction. A loss function that incorporates data-fitting error, physical-information constraints and the desired feature of the solution is designed and analyzed to suppress the background artifacts and improve the reconstruction accuracy. Various numerical analysis are performed to demonstrate the superiority of the proposed quality-factor inspired deep neural network (QuaDNN) solver and the imaging performance is finally verified by experimental imaging test.

💡 Research Summary

The paper introduces a novel deep‑learning framework for solving electromagnetic inverse scattering problems (ISPs), addressing three critical aspects that have been under‑explored in prior works: (1) the quality of training samples, (2) the network architecture, and (3) the loss function.
First, the authors define a “quality factor” (Q‑BP) that quantifies how informative each training sample is. Q‑BP is computed as the product of the structural similarity index (SSIM) and the inverse of the root‑mean‑square error (RMSE) between a conventional back‑propagation (BP) reconstruction and the ground‑truth contrast distribution. A high Q‑BP indicates that the BP result is already accurate, whereas a low Q‑BP signals a difficult case that contains richer information for learning. By evaluating Q‑BP on 2 000 MNIST‑derived digit samples, the authors categorize them into four quality levels (Excellent, Good, Fair, Poor) and discover a strong correlation between quality level and the contrast range of the scatterer. They then deliberately over‑represent the “Poor” class (40 % of the training set) while keeping the remaining classes in proportion (10 % Excellent, 20 % Good, 30 % Fair). This biased composition forces the network to focus on hard‑to‑reconstruct examples, improving its ability to generalize to challenging scenarios.

Second, the network architecture, named ReSE‑U‑Net, builds upon the classic U‑Net but incorporates three enhancements: residual connections, Squeeze‑and‑Excitation (SE) channel‑attention blocks, and a feature‑transformation layer. Residual connections mitigate degradation and gradient‑vanishing problems in deep networks, allowing the model to propagate information even when some layers fail to learn useful features. SE blocks adaptively recalibrate channel‑wise responses, which is especially beneficial under low‑SNR conditions because they can suppress noisy channels and amplify informative ones without adding significant computational overhead. The feature‑transformation layer (a 3 × 3 convolution followed by batch normalization) stabilizes training when handling complex‑valued inputs (real and imaginary parts of the BP image). The input to the network consists of two channels (real and imaginary parts of the BP reconstruction), and the output is the estimated relative permittivity (contrast) map.

Third, the loss function is a weighted sum of four terms: (i) an ℓ₂ contrast loss, (ii) a structural similarity term (1 − SSIM²) to encourage visual fidelity, (iii) a physics‑based field loss that penalizes inconsistencies between the predicted contrast and the forward‑modeled scattered field, and (iv) a total‑variation (TV) regularizer that promotes smoothness of the reconstructed image. The weight α for the field loss is set automatically as the ratio of the contrast energy to the scattered‑field energy, while β (the TV weight) is tuned within