  This paper introduces a novel deep neural network architecture for solving
the inverse scattering problem in frequency domain with wide-band data, by
directly approximating the inverse map, thus avoiding the expensive
optimization loop of classical methods. The architecture is motivated by the
filtered back-projection formula in the full aperture regime and with
homogeneous background, and it leverages the underlying equivariance of the
problem and compressibility of the integral operator. This drastically reduces
the number of training parameters, and therefore the computational and sample
complexity of the method. In particular, we obtain an architecture whose number
of parameters scale sub-linearly with respect to the dimension of the inputs,
while its inference complexity scales super-linearly but with very small
constants. We provide several numerical tests that show that the current
approach results in better reconstruction than optimization-based techniques
such as full-waveform inversion, but at a fraction of the cost while being
competitive with state-of-the-art machine learning methods.
