Uniqueness of two phaseless non-overdetermined inverse acoustics problems in 3-d

Abstract

Uniqueness is proven for two non-overdetermined 3-d inverse problems of the determination of the spatially distributed sound speed in the frequency dependent acoustic PDE. The main new point is the assumption that only the modulus of the scattered complex valued wave field is measured on a certain set. The phase is unknown.

Keywords:

• phaseless inverse problem for the acoustic equation uniqueness

AMS Subject Classifications:

• 35R30
• 35L05

Acknowledgments

This research was supported by US Army Research Laboratory and US Army Research Office grant W911NF-11-1-0399. The author is grateful to Professors Paul E. Sacks and Boris R. Vainberg for valuable discussions. The author is also grateful to anonymous referees for their valuable comments, which have helped to improve the quality of the presentation.