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 meshfree fashion. We efficiently express the obstacle shape as the zero-level set of a signed distance function which is implicitly determined by a small number of 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 instead of a grid-size-dependent extraction method of surface points such as Marching Cubes. The 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. The proposed framework makes the inverse scattering problem more tractable with fewer parameters to optimize in comparison to the memory-inefficient grid-based approaches and outputs highquality reconstruction results.