Photoacoustic Tomography with Direction Dependent Data: An Exact Series Reconstruction Approach
This provides a theoretical solution for a known practical bottleneck in photoacoustic imaging with directional detectors, but is limited to spherical geometry.
The paper derives exact frequency-domain reconstruction formulas for photoacoustic tomography when measured data combine acoustic pressure and its normal derivative on a spherical surface, showing robustness and that the measurement model significantly affects the recovered initial pressure.
Photoacoustic image reconstruction often assumes that the restriction of the acoustic pressure on the detection surface is given. However, commonly used detectors often have a certain directivity and frequency dependence, in which case the measured data are more accurately described as a linear combination of the acoustic pressure and its normal derivative on the detection surface. In this paper, we consider the inverse source problem for data that are a combination of an acoustic pressure of the wave equation and its normal derivative For the special case of a spherical detection geometry we derive exact frequency domain reconstruction formulas. We present numerical results showing the robustness and validity of the derived formulas. Moreover, we compare several different combinations of the pressure and its normal derivative showing that used measurement model significantly affects the recovered initial pressure.