ON THE INJECTIVITY OF THE ATTENUATED WAVE FORWARD OPERATOR WITH DIRECTION DEPENDENT DATA

This paper investigates the inverse problems for the photoacoustic imaging in attenuating media, where the wave propagation is described by an attenuated wave equation with some attenuation coefficient. We define the attenuated wave forward operator as the transform that assigns to a given function f the solution of the attenuated wave equation on the detector surface (where the detectors are located) with the initial function f. Here we study the injectivity of the attenuated wave forward operator, its normal derivative and their combination. This means that the initial function is uniquely determined by the knowledge of the solution of the attenuated wave equation on the unit sphere.