In this work, we focus on the inverse medium scattering problem (IMSP), which aims to recover unknown scatterers based on measured scattered data. Motivated by the efficient direct sampling method (DSM) introduced in [23], we propose a novel direct sampling-based deep learning approach (DSM-DL)for reconstructing inhomogeneous scatterers. In particular, we use the U-Net neural network to learn the relation between the index functions and the true contrasts. Our proposed DSM-DL is computationally efficient, robust to noise, easy to implement, and able to naturally incorporate multiple measured data to achieve high-quality reconstructions. Some representative tests are carried out with varying numbers of incident waves and different noise levels to evaluate the performance of the proposed method. The results demonstrate the promising benefits of combining deep learning techniques with the DSM for IMSP.

翻译：本文聚焦于逆介质散射问题（IMSP），其目标是根据实测散射数据重建未知散射体。受文献[23]中高效直接采样方法（DSM）的启发，我们提出一种新型基于直接采样的深度学习方法（DSM-DL），用于重建非均匀散射体。具体而言，我们采用U-Net神经网络学习指标函数与真实对比度之间的映射关系。所提出的DSM-DL方法具有计算高效、抗噪性强、易于实现的特点，并能自然融合多组测量数据以实现高质量重建。通过改变入射波数量及不同噪声水平开展代表性测试，评估所提方法的性能。结果表明，将深度学习技术与DSM相结合，为逆介质散射问题带来了显著优势。