A neural network scheme for recovering scattering obstacles with limited phaseless far-field data

We consider a geometrical inverse scattering problem of recovering impenetrable obstacles by the associated far-field measurements. The case with phaseless or even limited-aperture far-field data has recently received considerable attentions in the literature due to its practical importance and theoretical challenge. We propose a two-layer sequence-to-sequence neural network that can effectively and efficiently tackle this inverse problem with limited-aperture phaseless data. Superposing the incident waves in generating the training dataset is a crucial ingredient in the architecture of the network. The network state is selectively updated to preserve the specific structure of the underlying data through a gated idea and the use of the long-term memory function from the Long Short-Term Memory (LSTM) neural network. The weights and offsets of the network are updated by optimization algorithms. Both theoretical convergence analysis and extensive numerical experiments are conducted for the proposed method. (c) 2020 Elsevier Inc. All rights reserved.