# Implicit Neural Representation for Mesh-Free Inverse Obstacle Scattering

arXiv: https://arxiv.org/abs/2206.02027 · HTML: https://mlsanity.com/paper/2206.02027/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 41 references that are in the map.
- First posted on arXiv 4 Jun 2022.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [MeshSDF: Differentiable Iso-Surface Extraction](https://mlsanity.com/paper/2006.03997/) (2020)
- [Controlling Neural Level Sets](https://mlsanity.com/paper/1905.11911/) (2019)
- [DeepMesh: Differentiable Iso-Surface Extraction](https://mlsanity.com/paper/2106.11795/) (2021)
- [Solving Inverse Problems with NerfGANs](https://mlsanity.com/paper/2112.09061/) (2021)
- [Automatic shape derivatives for transient PDEs in FEniCS and Firedrake](https://mlsanity.com/paper/2001.10058/) (2020)

## Built on by (most cited first, 9 of 9)

- [Capturing dynamical correlations using implicit neural representations](https://mlsanity.com/paper/2304.03949/) (2023)
- [Glimpse: Generalized Locality for Scalable and Robust CT](https://mlsanity.com/paper/2401.00816/) (2024)
- [FunkNN: Neural Interpolation for Functional Generation](https://mlsanity.com/paper/2212.14042/) (2022)
- [Deep Injective Prior for Inverse Scattering](https://mlsanity.com/paper/2301.03092/) (2023)
- [Back-Projection Diffusion: Solving the Wideband Inverse Scattering Problem with Diffusion Models](https://mlsanity.com/paper/2408.02866/) (2024)
- [Deep Variational Inverse Scattering](https://mlsanity.com/paper/2212.04309/) (2022)
- [Estimating Uncertainty in PET Image Reconstruction via Deep Posterior Sampling](https://mlsanity.com/paper/2306.04664/) (2023)
- [ODE-DPS: ODE-based Diffusion Posterior Sampling for Inverse Problems in Partial Differential Equation](https://mlsanity.com/paper/2404.13496/) (2024)
- [LoFi: Neural Local Fields for Scalable Image Reconstruction](https://mlsanity.com/paper/2411.04995/) (2024)

## Abstract (arXiv)

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.