论文标题
无网状逆向障碍物散射的隐式神经表示
Implicit Neural Representation for Mesh-Free Inverse Obstacle Scattering
论文作者
论文摘要
形状的隐式表示为多层感知的水平集，最近在不同的形状分析，压缩和重建任务中蓬勃发展。在本文中，我们介绍了一个基于隐式神经表示的框架，用于以无网格的方式解决反向障碍物散射问题。我们将障碍物形状表示为签名距离函数的零级集，该集由网络参数隐式确定。为了解决直接散射问题，我们实施了隐式边界积分方法。它使用管状邻域中的网格点的投影到边界上，直接在级别集框架中计算PDE解决方案。提出的隐式表示方便地处理优化过程中的形状扰动。为了更新形状，我们使用Pytorch的自动差异来反向损失函数W.R.T.网络参数，使我们避免了形状衍生物的复杂和容易出错的手动推导。此外，我们提出了一个可以适合框架的隐式神经形状表示的深层生成模型。深层生成模型有效地将逆障碍物散射问题正常，使其更加易加和健壮，同时即使在噪声浪费的设置中也产生了高质量的重建结果。
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.
