Inverse source problem for discrete Helmholtz equation

Abstract We consider multi-frequency inverse source problem for the discrete Helmholtz operator on the square lattice Z d , d ⩾ 1 . We consider this problem for the cases with and without phase information. We prove uniqueness results and present examples of non-uniqueness for this problem for the c...

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Bibliographic Details
Published inInverse problems Vol. 40; no. 10; pp. 105005 - 105021
Main Authors Novikov, Roman, Lal Sharma, Basant
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.10.2024
Subjects
discrete Helmholtz operators
monochromatic inverse scattering in the Born approximation
multi-frequency inverse source problem
phase retrieval
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Summary:Abstract We consider multi-frequency inverse source problem for the discrete Helmholtz operator on the square lattice Z d , d ⩾ 1 . We consider this problem for the cases with and without phase information. We prove uniqueness results and present examples of non-uniqueness for this problem for the case of compactly supported source function, and a Lipshitz stability estimate for the phased case is established. Relations with inverse scattering problem for the discrete Schrödinger operators in the Born approximation are also provided.
Bibliography:IP-104346.R2
ISSN:0266-5611
1361-6420
DOI:10.1088/1361-6420/ad7054