Numerical reconstruction of polygonal obstacles by diffracted waves
Abstract
We present a numerical method for recovering rigid polygonal obstacles in two dimensions, based on the diffraction-based inverse scattering theory of Bao, Chen, Lu, and Xiong. A single pulse is emitted from a point source, and the resulting wave field is measured on a receiver curve. After isolating the diffracted signals, we recover the visible vertices from arrival times and the corner orientations and opening angles from amplitudes. The use of amplitude information permits local reconstruction in the reflection shadow, where reflected waves do not reach the receiver. The amplitudes also determine the direction of a shadowed edge adjacent to a visible vertex, enabling local non-line-of-sight imaging. Numerical experiments for a convex corner, a concave corner, a triangle, a pentagon and a star-shaped obstacle confirm that the visible portion of the boundary can be recovered stably from diffracted signals. A further convex-corner test with additive noise at level 0.2% on the single arc L1 confirms that the tip and opening remain recoverable.
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BibTeX
@misc{chen2026numerical,
title = {{Numerical reconstruction of polygonal obstacles by diffracted waves}},
author = {Xi Chen and Kuangmiao Xiong and Boxi Xu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31271},
eprint = {2610.31271},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31271},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Numerical reconstruction of polygonal obstacles by diffracted waves
AU - Xi Chen
AU - Kuangmiao Xiong
AU - Boxi Xu
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31271
UR - https://arxiv.org/abs/2610.31271
AB - We present a numerical method for recovering rigid polygonal obstacles in two dimensions, based on the diffraction-based inverse scattering theory of Bao, Chen, Lu, and Xiong. A single pulse is emitted from a point source, and the resulting wave field is measured on a receiver curve. After isolating the diffracted signals, we recover the visible vertices from arrival times and the corner orientations and opening angles from amplitudes. The use of amplitude information permits local reconstruction in the reflection shadow, where reflected waves do not reach the receiver. The amplitudes also determine the direction of a shadowed edge adjacent to a visible vertex, enabling local non-line-of-sight imaging. Numerical experiments for a convex corner, a concave corner, a triangle, a pentagon and a star-shaped obstacle confirm that the visible portion of the boundary can be recovered stably from diffracted signals. A further convex-corner test with additive noise at level 0.2% on the single arc L_1 confirms that the tip and opening remain recoverable.
ER -