Fourier--Hankel Moment Recovery in Acoustic Scattering: Multichannel Stabilization and Radial Interface Resolution
Abstract
We study direct recovery of visible phase centers and concentric radial interfaces from full-aperture acoustic far-field data under the Born approximation. Two complementary moment structures are extracted from the two-angle Fourier matrix. At fixed positive total Fourier order, the nonnegative-order channels share the same leading phase-center moment, and a generalized least-squares combination yields an exact variance gain over a single Fourier row. The corresponding Hankel rank and shifted pencil recover distinct phase centers. Signed moments reveal off-center cavities but become degenerate when material and cavity centers coincide. Zero-total-order coefficients retain complementary radial Bessel moments. For a piecewise-constant radial average, low-frequency extrapolation produces a second finite exponential sequence whose nodes are the squared interface radii. We establish rank and perturbation results for both reductions. Numerical experiments verify multichannel stabilization, concentric-cavity resolution, and recovery of multiple radial interfaces. A final full-wave Helmholtz experiment, generated without the Born substitution, assesses the Born-derived reconstruction under model mismatch and shows how nonlinear scattering eventually appears as an additional Hankel tail.
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BibTeX
@misc{deng2026fourierhankel,
title = {{Fourier--Hankel Moment Recovery in Acoustic Scattering: Multichannel Stabilization and Radial Interface Resolution}},
author = {Zhiliang Deng and Xiaofei Guan and Xiaomei Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.29678},
eprint = {2606.29678},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.29678},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Fourier--Hankel Moment Recovery in Acoustic Scattering: Multichannel Stabilization and Radial Interface Resolution
AU - Zhiliang Deng
AU - Xiaofei Guan
AU - Xiaomei Yang
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2606.29678
UR - https://arxiv.org/abs/2606.29678
AB - We study direct recovery of visible phase centers and concentric radial interfaces from full-aperture acoustic far-field data under the Born approximation. Two complementary moment structures are extracted from the two-angle Fourier matrix. At fixed positive total Fourier order, the nonnegative-order channels share the same leading phase-center moment, and a generalized least-squares combination yields an exact variance gain over a single Fourier row. The corresponding Hankel rank and shifted pencil recover distinct phase centers. Signed moments reveal off-center cavities but become degenerate when material and cavity centers coincide. Zero-total-order coefficients retain complementary radial Bessel moments. For a piecewise-constant radial average, low-frequency extrapolation produces a second finite exponential sequence whose nodes are the squared interface radii. We establish rank and perturbation results for both reductions. Numerical experiments verify multichannel stabilization, concentric-cavity resolution, and recovery of multiple radial interfaces. A final full-wave Helmholtz experiment, generated without the Born substitution, assesses the Born-derived reconstruction under model mismatch and shows how nonlinear scattering eventually appears as an additional Hankel tail.
ER -