  Implicit representation of shapes as level sets of multilayer perceptrons has
recently flourished in different shape analysis, compression, and
reconstruction tasks. In this paper, we introduce an implicit neural
representation-based framework for solving the inverse obstacle scattering
problem in a mesh-free fashion. We express the obstacle shape as the zero-level
set of a signed distance function which is implicitly determined by network
parameters. To solve the direct scattering problem, we implement the implicit
boundary integral method. It uses projections of the grid points in the tubular
neighborhood onto the boundary to compute the PDE solution directly in the
level-set framework. The proposed implicit representation conveniently handles
the shape perturbation in the optimization process. To update the shape, we use
PyTorch's automatic differentiation to backpropagate the loss function w.r.t.
the network parameters, allowing us to avoid complex and error-prone manual
derivation of the shape derivative. Additionally, we propose a deep generative
model of implicit neural shape representations that can fit into the framework.
The deep generative model effectively regularizes the inverse obstacle
scattering problem, making it more tractable and robust, while yielding
high-quality reconstruction results even in noise-corrupted setups.
