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This paper introduces a novel deep neural network architecture for solvingthe inverse scattering problem in frequency domain with wide-band data, bydirectly approximating the inverse map, thus avoiding the expensiveoptimization loop of classical methods. The architecture is motivated by thefiltered back-projection formula in the full aperture regime and withhomogeneous background, and it leverages the underlying equivariance of theproblem and compressibility of the integral operator. This drastically reducesthe number of training parameters, and therefore the computational and samplecomplexity of the method. In particular, we obtain an architecture whose numberof parameters scale sub-linearly with respect to the dimension of the inputs,while its inference complexity scales super-linearly but with very smallconstants. We provide several numerical tests that show that the currentapproach results in better reconstruction than optimization-based techniquessuch as full-waveform inversion, but at a fraction of the cost while beingcompetitive with state-of-the-art machine learning methods.

Solving the Wide-band Inverse Scattering Problem via Equivariant Neural Networks