A Wavelet-Based Compressive Deep Learning Scheme for Inverse Scattering Problems

Recently, physics-assisted deep learning schemes (DLSs) have demonstrated state-of-the-art performance for solving inverse scattering problems (ISPs). However, most learning approaches typically require a high computational overhead and a big memory footprint, which prohibits further applications. In this work, a wavelet-based compressive scheme (WCS) is proposed in solving ISPs, where the multi-subspace information is explored by wavelet bases and branched between each encoder and decoder path. It is shown that the proposed WCS can be simply adapted to commonly used DLSs, such as the back-propagation scheme (BPS) and the dominant current scheme (DCS), to reduce the computational and storage load. Specifically, benefiting from compressive and multi-resolution properties of wavelet and with the help of the factorized convolution method, more than 99.7% trainable weights are reduced in both illustrated BP-WCS and DC-WCS, whereas the performance deterioration is limited around 1% in terms of traditional BPS and DCS. Extensive numerical and experimental tests are conducted for quantitative validations. Comparisons are also made among UNet, a well-known compressive method (Mobile-UNet), and the proposed method. It is expected that the suggested compression technique would find its applications on deep learning-based electromagnetic inverse problems under source-limited scenarios.