A holographic global uniqueness in passive imaging
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915254220357632 |
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| author | Novikov, Roman |
| author_facet | Novikov, Roman |
| contents | We consider a radiation solution $ψ$ for the Helmholtz equation in an exterior region in $\mathbb R^3$. We show that the restriction of $ψ$ to any ray $L$ in the exterior region is uniquely determined by its imaginary part $\Imψ$ on an interval of this ray. As a corollary, the restriction of $ψ$ to any plane $X$ in the exterior region is uniquely determined by $\Imψ$ on an open domain in this plane. These results have holographic prototypes in the recent work Novikov (2024, Proc. Steklov Inst. Math. 325, 218-223). In particular, these and known results imply a holographic type global uniqueness in passive imaging and for the Gelfand-Krein-Levitan inverse problem (from boundary values of the spectral measure in the whole space) in the monochromatic case. Some other surfaces for measurements instead of the planes $X$ are also considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10333 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A holographic global uniqueness in passive imaging Novikov, Roman Analysis of PDEs Mathematical Physics 35J05, 35J08, 35P25, 35R30 We consider a radiation solution $ψ$ for the Helmholtz equation in an exterior region in $\mathbb R^3$. We show that the restriction of $ψ$ to any ray $L$ in the exterior region is uniquely determined by its imaginary part $\Imψ$ on an interval of this ray. As a corollary, the restriction of $ψ$ to any plane $X$ in the exterior region is uniquely determined by $\Imψ$ on an open domain in this plane. These results have holographic prototypes in the recent work Novikov (2024, Proc. Steklov Inst. Math. 325, 218-223). In particular, these and known results imply a holographic type global uniqueness in passive imaging and for the Gelfand-Krein-Levitan inverse problem (from boundary values of the spectral measure in the whole space) in the monochromatic case. Some other surfaces for measurements instead of the planes $X$ are also considered. |
| title | A holographic global uniqueness in passive imaging |
| topic | Analysis of PDEs Mathematical Physics 35J05, 35J08, 35P25, 35R30 |
| url | https://arxiv.org/abs/2405.10333 |