We propose a novel iterative numerical method to solve the three-dimensional inverse obstacle scattering problem of recovering the shape of the obstacle from far-field measurements. To address the inherent ill-posed nature of the inverse problem, we advocate the use of a trained latent representation of surfaces as the generative prior. This prior enjoys excellent expressivity within the given class of shapes, and meanwhile, the latent dimensionality is low, which greatly facilitates the computation. Thus, the admissible manifold of surfaces is realistic and the resulting optimization problem is less ill-posed. We employ the shape derivative to evolve the latent surface representation, by minimizing the loss, and we provide a local convergence analysis of a gradient descent type algorithm to a stationary point of the loss. We present several numerical examples, including also backscattered and phaseless data, to showcase the effectiveness of the proposed algorithm.

翻译：我们提出了一种新的迭代数值方法，用于解决三维逆向障碍散射问题，即从远场测量数据中恢复障碍物的形状。针对逆向问题固有的不适定性，我们倡导使用经过训练的隐式表面表示作为生成先验。该先验在给定形状类别内具有出色的表达能力，同时其隐式维度较低，这极大便利了计算过程。因此，可允许的表面流形更加真实，由此产生的优化问题不适定性也得到缓解。通过最小化损失函数，我们采用形状导数来演化隐式表面表示，并提供了梯度下降类算法收敛至损失函数稳定点的局部收敛性分析。最后，我们通过包括背散射数据和无相位数据在内的多个数值算例，展示了所提算法的有效性。