  The inverse scattering problem is of critical importance in a number of
fields, including medical imaging, sonar, sensing, non-destructive evaluation,
and several others. The problem of interest can vary from detecting the shape
to the constitutive properties of the obstacle. The challenge in both is that
this problem is ill-posed, more so when there is limited information. That
said, significant effort has been expended over the years in developing
solutions to this problem. Here, we use a different approach, one that is
founded on data. Specifically, we develop a deep learning framework for shape
reconstruction using limited information with single incident wave, single
frequency, and phase-less far-field data. This is done by (a) using a compact
probabilistic shape latent space, learned by a 3D variational auto-encoder, and
(b) a convolutional neural network trained to map the acoustic scattering
information to this shape representation. The proposed framework is evaluated
on a synthetic 3D particle dataset, as well as ShapeNet, a popular 3D shape
recognition dataset. As demonstrated via a number of results, the proposed
method is able to produce accurate reconstructions for large batches of complex
scatterer shapes (such as airplanes and automobiles), despite the significant
variation present within the data.
