The phase retrieval problem for solutions of the Helmholtz equation
Language
en
Article de revue
This item was published in
Inverse Problems. 2017p. Article 105007
IOP Publishing
English Abstract
In this paper we consider the phase retrieval problem for Herglotz functions, that is, solutions of the Helmholtz equation ∆u + λ 2 u = 0 on domains Ω ⊂ R d , d ≥ 2. In dimension d = 2, if u, v are two such solutions then ...Read more >
In this paper we consider the phase retrieval problem for Herglotz functions, that is, solutions of the Helmholtz equation ∆u + λ 2 u = 0 on domains Ω ⊂ R d , d ≥ 2. In dimension d = 2, if u, v are two such solutions then |u| = |v| implies that either u = cv or u = c¯ v for some c ∈ C with |c| = 1. In dimension d ≥ 3, the same conclusion holds under some restriction on u and v: either they are real valued or zonal functions or have non vanishing mean.Read less <
English Keywords
phase retrieval
Helmholtz equation
ANR Project
Analyse Variationnelle en Tomographies photoacoustique, thermoacoustique et ultrasonore - ANR-12-BS01-0001
Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003
Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003
Origin
Hal imported