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The problem of inverse scattering proposed by Angles and Mallat in 2018,concerns training a deep neural network to invert the scattering transformapplied to an image. After such a network is trained, it can be used as agenerative model given that we can sample from the distribution of principalcomponents of scattering coefficients. For this purpose, Angles and Mallatsimply use samples from independent Gaussians. However, as shown in this paper,the distribution of interest can actually be very far from normal andnon-negligible dependencies might exist between different coefficients. Thismotivates using models for this distribution that allow for non-lineardependencies between variables. Within this paper, two such models areexplored, namely a Variational AutoEncoder and a Generative AdversarialNetwork. We demonstrate the results obtained can be extremely realistic on somedatasets and look better than those produced by Angles and Mallat. Theconducted meta-analysis also shows a clear practical advantage of suchconstructed generative models in terms of the efficiency of their trainingprocess compared to existing generative models for images.

Modelling nonlinear dependencies in the latent space of inverse scattering