Photoacoustic image reconstruction in an attenuating medium using singular-value decomposition

Photoacoustic tomography (PAT) or optoacoustic tomography reconstructs an image of the optical absorption function of a medium using the ultrasound signals induced when it is exposed to pulsed electromagnetic radiation. These signals are generated due to the thermal expansion caused by localized heating from the absorption of pulsed electromagnetic radiation [1]. The majority of the image reconstruction algorithms in PAT so far have assumed a non-dispersive acoustic medium. The effect of frequency-dependent attenuation on acoustic waves can be significant since PAT uses broadband detection. Reconstructed images may exhibit distortion and artifacts if these effects are not taken into account. Previous work on dispersive acoustic media done by our group [2] focused on incorporating the frequency-dependent attenuation effects into the PAT model. In this paper, we will use an approach similar to that by Schotland et al. [3] [4], in optical diffusion tomography, to derive an inversion formula for the optical absorption function using singular-value decomposition (SVD). This formula is applicable in a planar geometry where the array of transducers lies in a plane. It provides an insight into the conditioning of the inverse problem and offers a promising method for image reconstruction in an attenuating medium.