  In this paper, we apply the scattering transform (ST), a nonlinear map based
off of a convolutional neural network (CNN), to classification of underwater
objects using sonar signals. The ST formalizes the observation that the filters
learned by a CNN have wavelet like structure. We achieve effective binary
classification both on a real dataset of Unexploded Ordinance (UXOs), as well
as synthetically generated examples. We also explore the effects on the
waveforms with respect to changes in the object domain (e.g., translation,
rotation, and acoustic impedance, etc.), and examine the consequences coming
from theoretical results for the scattering transform. We show that the
scattering transform is capable of excellent classification on both the
synthetic and real problems, thanks to having more quasi-invariance properties
that are well-suited to translation and rotation of the object.
