Efficient modeling and compensation of ultrasound attenuation losses in photoacoustic imaging

Wave attenuation can be considered from the dual viewpoints of assuming a complex wavenumber or a complex frequency. Experimentally, the first viewpoint is preferable if the wave signal can be measured over time, and the second is preferable if the wave signal can be measured over space. These two approaches are discussed in the context of photoacoustic imaging where a short laser pulse excites a broadband ultrasound signal in a sample (e.g., some biological tissue) which can be recorded by detectors configured around the target. Reconstruction of the initial pressure distribution from the detector signals clearly poses an inverse problem. For the complex frequency viewpoint the damping rates of the spatial Fourier modes are calculated using Szabo's wave equation which describes ultrasound propagation in attenuating media obeying a frequency power law. For a symmetric sample problem, a mathematical regularization method is applied to compensate for attenuation losses. It is shown for this important special case that with the complex frequency approach regularization can be performed faster and with more accurate results.