Implicit Neural Representation for Mesh-Free Inverse Obstacle Scattering

Abstract: 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.