A quantitative direct sampling method for inhomogeneities from multi-frequency backscattering measurements

Yukun Guo; Xiaodong Liu

doi:10.1088/1361-6420/ae963b

A quantitative direct sampling method for inhomogeneities from multi-frequency backscattering measurements

Yukun Guo
, Xiaodong Liu^*

^*Corresponding author for this work

School of Mathematics, Harbin Institute of Technology
CAS - Academy of Mathematics and System Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

The inverse scattering problem from the multi-frequency backscattering data is a long-standing open problem. We advance the theory by proving a uniqueness result. Moreover, we introduce a direct sampling method for quantitatively reconstructing unknown inhomogeneities. Comprehensive numerical experiments validate the robustness, accuracy, and computational effectiveness of the proposed quantitative direct sampling method.

Original language	English
Article number	085008
Journal	Inverse Problems
Volume	42
Issue number	8
DOIs	https://doi.org/10.1088/1361-6420/ae963b
State	Published - Aug 2026
Externally published	Yes

Keywords

Born approximation
Helmholtz equation
inverse medium scattering
multi-frequency backscattering data
quantitative direct sampling method

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10.1088/1361-6420/ae963b

Cite this

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title = "A quantitative direct sampling method for inhomogeneities from multi-frequency backscattering measurements",

abstract = "The inverse scattering problem from the multi-frequency backscattering data is a long-standing open problem. We advance the theory by proving a uniqueness result. Moreover, we introduce a direct sampling method for quantitatively reconstructing unknown inhomogeneities. Comprehensive numerical experiments validate the robustness, accuracy, and computational effectiveness of the proposed quantitative direct sampling method.",

keywords = "Born approximation, Helmholtz equation, inverse medium scattering, multi-frequency backscattering data, quantitative direct sampling method",

author = "Yukun Guo and Xiaodong Liu",

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AU - Guo, Yukun

AU - Liu, Xiaodong

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PY - 2026/8

Y1 - 2026/8

N2 - The inverse scattering problem from the multi-frequency backscattering data is a long-standing open problem. We advance the theory by proving a uniqueness result. Moreover, we introduce a direct sampling method for quantitatively reconstructing unknown inhomogeneities. Comprehensive numerical experiments validate the robustness, accuracy, and computational effectiveness of the proposed quantitative direct sampling method.

AB - The inverse scattering problem from the multi-frequency backscattering data is a long-standing open problem. We advance the theory by proving a uniqueness result. Moreover, we introduce a direct sampling method for quantitatively reconstructing unknown inhomogeneities. Comprehensive numerical experiments validate the robustness, accuracy, and computational effectiveness of the proposed quantitative direct sampling method.

KW - Born approximation

KW - Helmholtz equation

KW - inverse medium scattering

KW - multi-frequency backscattering data

KW - quantitative direct sampling method

UR - https://www.scopus.com/pages/publications/105047651518

U2 - 10.1088/1361-6420/ae963b

DO - 10.1088/1361-6420/ae963b

M3 - 文章

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VL - 42

JO - Inverse Problems

JF - Inverse Problems

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ER -

A quantitative direct sampling method for inhomogeneities from multi-frequency backscattering measurements

Abstract

Keywords

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