Stability for Quantitative Photoacoustic Tomography Revisited

Eric Bonnetier (1) , Mourad Choulli (2) , Faouzi Triki (3)

1 IF - Institut Fourier
2 IECL - Institut Élie Cartan de Lorraine
3 EDP - Equations aux Dérivées Partielles

This paper is concerned with the stability issue in determining absorption and diffusion coefficients in quantitative photoacoustic imaging. Assuming that the optical wave is generated by point sources in a region where the optical coefficients are known, we derive pointwise Hölder stability estimate of the inversion. This result shows that the reconstruction of the optical coefficients is stable in the region close to the optical illumination sources and deteriorate exponentially far away. Our stability estimate is therefore in accordance with known experimental observations.

Mots clés: Elliptic equations; diffusion coefficient; absorption coefficient; stability estimates; multiwave imaging

Domaines: Equations aux dérivées partielles [math.AP]

Eric Bonnetier, Mourad Choulli, Faouzi Triki. Stability for Quantitative Photoacoustic Tomography Revisited. Research in the Mathematical Sciences , inPress. ⟨hal-02133521v1⟩