A Model-Informed Deep Learning Algorithm for Solving the Phaseless Inverse Scattering Problem
Abstract
We study in this paper an unsupervised, two-step, model-informed deep learning framework for solving the phaseless inverse scattering problem. The objective is to reconstruct a compactly supported function that characterizes a scatterer from boundary measurements of the modulus of the total wave corresponding to multiple incident waves. In the first step, the phaseless data are transformed into an imaging function that is directly related to the underlying scatterer. Motivated by the contrast source method, we derive a coupled system of model equations using the Lippmann-Schwinger integral equation and a spectral-based equation involving the imaging function. In the second step, the unknown scatterer and contrast source function are each parameterized as independent feedforward neural networks, which are trained simultaneously at each iteration using the derived system of model equations. The Lippmann-Schwinger integral equation enforces the underlying physics as a model constraint, while the spectral-based equation incorporating the imaging function supplies geometric information on the shape and location of the unknown scatterer. The resulting framework achieves accurate and efficient reconstructions while maintaining robustness to measurement noise. Furthermore, transforming some aspects of the problem to the spectral domain enables an effective reduction in the computational cost, allowing us to recover the unknown scatterer quickly. Numerical experiments in both two- and three-dimensional settings demonstrate the effectiveness, stability, and practical potential of the proposed approach.
Related
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- Solving the scattering problem for open wave-guide networks, II: Outgoing estimates
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- A Safeguarded Accelerated Proximal ADMM Algorithm for Solving Structured Cardinality Penalized Optimization Problems
BibTeX
@misc{nguyen2026modelinformed,
title = {{A Model-Informed Deep Learning Algorithm for Solving the Phaseless Inverse Scattering Problem}},
author = {Dinh-Liem Nguyen and Nhung H. Nguyen and Aravinth Ravi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33070},
eprint = {2609.33070},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33070},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Model-Informed Deep Learning Algorithm for Solving the Phaseless Inverse Scattering Problem
AU - Dinh-Liem Nguyen
AU - Nhung H. Nguyen
AU - Aravinth Ravi
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33070
UR - https://arxiv.org/abs/2609.33070
AB - We study in this paper an unsupervised, two-step, model-informed deep learning framework for solving the phaseless inverse scattering problem. The objective is to reconstruct a compactly supported function that characterizes a scatterer from boundary measurements of the modulus of the total wave corresponding to multiple incident waves. In the first step, the phaseless data are transformed into an imaging function that is directly related to the underlying scatterer. Motivated by the contrast source method, we derive a coupled system of model equations using the Lippmann-Schwinger integral equation and a spectral-based equation involving the imaging function. In the second step, the unknown scatterer and contrast source function are each parameterized as independent feedforward neural networks, which are trained simultaneously at each iteration using the derived system of model equations. The Lippmann-Schwinger integral equation enforces the underlying physics as a model constraint, while the spectral-based equation incorporating the imaging function supplies geometric information on the shape and location of the unknown scatterer. The resulting framework achieves accurate and efficient reconstructions while maintaining robustness to measurement noise. Furthermore, transforming some aspects of the problem to the spectral domain enables an effective reduction in the computational cost, allowing us to recover the unknown scatterer quickly. Numerical experiments in both two- and three-dimensional settings demonstrate the effectiveness, stability, and practical potential of the proposed approach.
ER -