Inverse source problem for discrete Helmholtz equation

Roman Novikov (1) , Basant Lal Sharma (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 IIT Kanpur - Indian Institute of Technology Kanpur

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.

Mots clés: discrete Helmholtz operators; multi-frequency inverse source problem; phase retrieval; monochromatic inverse scattering in the Born approximation

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Roman Novikov, Basant Lal Sharma. Inverse source problem for discrete Helmholtz equation. 2024. ⟨hal-04473450v2⟩