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Inverse random potential scattering for the polyharmonic wave equation using far-field patterns

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Jianliang Li, Peijun Li, Xu Wang, Guanlin Yang

Analysis of PDEs · Submitted 22 Jul 2024

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Furthermore, in the context of the inverse scattering problem, the uniqueness is attained in recovering the microlocal strengths of both the covariance and relation operators of the random potential.

how it is stated · asserted 1.00 read the record →

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arXiv ID2407.15681 (version 2)
Pith ID26JRMCWD, Pith's permanent record of this paper and its review
CitationGuanlin Yang, Jianliang Li, Peijun Li, Xu Wang. "Inverse random potential scattering for the polyharmonic wave equation using far-field patterns." arXiv:2407.15681 (2024). https://pith.science/paper/26JRMCWD
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,302 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.31 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

This paper addresses the inverse scattering problem of a random potential associated with the polyharmonic wave equation in two and three dimensions. The random potential is represented as a centered complex-valued generalized microlocally isotropic Gaussian random field, where its covariance and relation operators are characterized as conventional pseudo-differential operators. Regarding the direct scattering problem, the well-posedness is established in the distribution sense for sufficiently large wavenumbers through analysis of the corresponding Lippmann--Schwinger integral equation. Furthermore, in the context of the inverse scattering problem, the uniqueness is attained in recovering the microlocal strengths of both the covariance and relation operators of the random potential. Notably, this is accomplished with only a single realization of the backscattering far-field patterns averaged over the high-frequency band.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 This paper addresses the inverse scattering problem of a random potential associated with the polyharmonic wave equation in two and three dimensions. background 0.54 0.64 0.04 asserted 0.88
s1 The random potential is represented as a centered complex-valued generalized microlocally isotropic Gaussian random field, where its covariance and relation operators are characterized as conventional pseudo-differential operators. method 0.69 0.52 0.04 asserted 1.00
s2 Regarding the direct scattering problem, the well-posedness is established in the distribution sense for sufficiently large wavenumbers through analysis of the corresponding Lippmann--Schwinger integral equation. method 0.35 0.82 0.03 asserted 1.00
s3 Furthermore, in the context of the inverse scattering problem, the uniqueness is attained in recovering the microlocal strengths of both the covariance and relation operators of the random potential. result 0.99 0.89 0.66 asserted 1.00
s4 Notably, this is accomplished with only a single realization of the backscattering far-field patterns averaged over the high-frequency band. result 0.55 0.89 0.30 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

This paper addresses the inverse scattering problem of a random potential associated with the polyharmonic wave equation in two and three dimensions. The random potential is represented as a centered complex-valued generalized microlocally isotropic Gaussian random field, where its covariance and relation operators are characterized as conventional pseudo-differential operators. Regarding the direct scattering problem, the well-posedness is established in the distribution sense for sufficiently large wavenumbers through analysis of the corresponding Lippmann--Schwinger integral equation. Furthermore, in the context of the inverse scattering problem, the uniqueness is attained in recovering the microlocal strengths of both the covariance and relation operators of the random potential. Notably, this is accomplished with only a single realization of the backscattering far-field patterns averaged over the high-frequency band.

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3 arXiv papers cite this in 3 sentences

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