Deep Semi-Supervised Prior for Microwave Imaging

Most deep-learning models estimate the dielectric permittivity of targets from measurements of scattered fields or initial images, such as back projections. While these methods enable fast and accurate image reconstruction, they typically require a large dataset of ground-truth dielectric permittivity images, which is often expensive or impractical to obtain for real-world applications like brain stroke imaging. Limited access to such extensive training datasets can lead to overfitting and poor generalization. A general strategy to mitigate overfitting is the use of network weight regularization, such as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> or <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub>-norm. In this paper, we propose a novel data-driven weight regularization based on the physics of wave propagation and formulated using the maximum a posteriori (MAP) estimation of network weights. This prior model is integrated into a semi-supervised learning framework, requiring only a small training set of paired samples alongside unlabeled measurements. The integration of the U-Net architecture with a semi-supervised prior enables precise reconstruction of permittivity functions, even for intricate structures such as the human brain. Extensive two-dimensional (2D) and three-dimensional (3D) numerical simulations, along with experimental validations, demonstrate that the proposed Deep Semi-Supervised Prior (DSSP) significantly outperforms conventional weight regularization methods in terms of accuracy and efficiency, particularly in realistic scenarios with limited access to ground-truth images.