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We propose a novel iterative numerical method to solve the three-dimensionalinverse obstacle scattering problem of recovering the shape of the obstaclefrom far-field measurements. To address the inherent ill-posed nature of theinverse problem, we advocate the use of a trained latent representation ofsurfaces as the generative prior. This prior enjoys excellent expressivitywithin the given class of shapes, and meanwhile, the latent dimensionality islow, which greatly facilitates the computation. Thus, the admissible manifoldof surfaces is realistic and the resulting optimization problem is lessill-posed. We employ the shape derivative to evolve the latent surfacerepresentation, by minimizing the loss, and we provide a local convergenceanalysis of a gradient descent type algorithm to a stationary point of theloss. We present several numerical examples, including also backscattered andphaseless data, to showcase the effectiveness of the proposed algorithm.

Solving Inverse Obstacle Scattering Problem with Latent Surface Representations