Fourier method for inverse source problem using correlation of passive measurements

Kristoffer Linder-Steinlein; Mirza Karamehmedovic; Faouzi Triki

Fourier method for inverse source problem using correlation of passive measurements

Kristoffer Linder-Steinlein, Mirza Karamehmedovic, Faouzi Triki

Research output: Contribution to conference › Conference abstract for conference › Research › peer-review

51 Downloads (Pure)

Abstract

We consider the inverse source problem for a Cauchy wave equation with passive crosscorrelation data. We propose to consider the cross-correlation as a wave equation itself and reconstruct the cross-correlation in the support of the source for the original Cauchy wave equation. Having access to the cross-correlation in the support of the source, we use a Fourier method to reconstruct the source of the original Cauchy wave equation. We show the inverse source problem is ill-posed and suffer from non-uniqueness when the mean of the source is zero, and provide a uniqueness result and stability estimate in case of non-zero mean.

Original language	English
Publication date	2023
Publication status	Published - 2023
Event	11^th Applied Inverse Problems Conference - Georg-August-Universität, Göttingen, Germany Duration: 4 Sept 2023 → 8 Sept 2023

Conference

Conference	11^th Applied Inverse Problems Conference
Location	Georg-August-Universität
Country/Territory	Germany
City	Göttingen
Period	04/09/2023 → 08/09/2023

Access to Document

FulltextFinal published version, 288 KB

OpenUrl availability

Full text

Cite this

@conference{b3475635efac4569b4120bae40f48862,

title = "Fourier method for inverse source problem using correlation of passive measurements",

abstract = "We consider the inverse source problem for a Cauchy wave equation with passive crosscorrelation data. We propose to consider the cross-correlation as a wave equation itself and reconstruct the cross-correlation in the support of the source for the original Cauchy wave equation. Having access to the cross-correlation in the support of the source, we use a Fourier method to reconstruct the source of the original Cauchy wave equation. We show the inverse source problem is ill-posed and suffer from non-uniqueness when the mean of the source is zero, and provide a uniqueness result and stability estimate in case of non-zero mean.",

author = "Kristoffer Linder-Steinlein and Mirza Karamehmedovic and Faouzi Triki",

year = "2023",

language = "English",

pages = "151--151",

note = "11<sup>th</sup> Applied Inverse Problems Conference, AIP 2023 ; Conference date: 04-09-2023 Through 08-09-2023",

}

Fourier method for inverse source problem using correlation of passive measurements. / Linder-Steinlein, Kristoffer ; Karamehmedovic, Mirza; Triki, Faouzi.
2023. 151-151 Abstract from 11^th Applied Inverse Problems Conference, Göttingen, Lower Saxony, Germany.

Research output: Contribution to conference › Conference abstract for conference › Research › peer-review

TY - ABST

T1 - Fourier method for inverse source problem using correlation of passive measurements

AU - Linder-Steinlein, Kristoffer

AU - Karamehmedovic, Mirza

AU - Triki, Faouzi

PY - 2023

Y1 - 2023

N2 - We consider the inverse source problem for a Cauchy wave equation with passive crosscorrelation data. We propose to consider the cross-correlation as a wave equation itself and reconstruct the cross-correlation in the support of the source for the original Cauchy wave equation. Having access to the cross-correlation in the support of the source, we use a Fourier method to reconstruct the source of the original Cauchy wave equation. We show the inverse source problem is ill-posed and suffer from non-uniqueness when the mean of the source is zero, and provide a uniqueness result and stability estimate in case of non-zero mean.

AB - We consider the inverse source problem for a Cauchy wave equation with passive crosscorrelation data. We propose to consider the cross-correlation as a wave equation itself and reconstruct the cross-correlation in the support of the source for the original Cauchy wave equation. Having access to the cross-correlation in the support of the source, we use a Fourier method to reconstruct the source of the original Cauchy wave equation. We show the inverse source problem is ill-posed and suffer from non-uniqueness when the mean of the source is zero, and provide a uniqueness result and stability estimate in case of non-zero mean.

M3 - Conference abstract for conference

SP - 151

EP - 151

T2 - 11<sup>th</sup> Applied Inverse Problems Conference

Y2 - 4 September 2023 through 8 September 2023

ER -

Fourier method for inverse source problem using correlation of passive measurements

Abstract

Conference

Access to Document

OpenUrl availability

Fingerprint

Cite this