A Global stability estimate for the photo-acoustic inverse problem in layered media

Kui Ren (1) , Faouzi Triki (2)

1 University of Texas at Austin [Austin]
2 EDP - Equations aux Dérivées Partielles

This paper is concerned with the stability issue in determining absorption and diffusion coefficients in photoacoustic imaging. Assuming that the medium is layered and the acoustic wave speed is known we derive global Hölder stability estimates of the photo-acoustic inversion. These results show that the reconstruction is stable in the region close to the optical illumination source, and deteriorate exponentially far away. Several experimental pointed out that the resolution depth of the photo-acoustic modality is about tens of millimeters. Our stability estimates confirm these observations and give a rigorous quantification of this depth resolution.

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

Kui Ren, Faouzi Triki. A Global stability estimate for the photo-acoustic inverse problem in layered media. European Journal of Applied Mathematics, 2019, 30 (3), pp.505-528. ⟨10.1017/S0956792518000268⟩. ⟨hal-01562924⟩