  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.
