Image reconstruction with the Heaviside equation in photoacoustic tomography accounting for dispersive acoustic media

A challenging issue in photoacoustic biomedical imaging is to take into account the presence of dispersive acoustic media, since these are prone to induce amplitude attenuation and scattering of the photoacoustic frequency components. These perturbations are largely the cause for which the photoacoustic tomographic image reconstruction from projections lacks a plane-wave transport formalism. Attending this problem, we further develop an analytic formalism of the transport and its numerical implementation accounting for dispersive acoustic media. We differentiate three variations of an acoustically perturbing media. Our object of interest is a numerical description of the light absorption map of a coronal human breast image. Then, we analyze conditions for which the propagation of photoacoustic perturbations can obey the generalized Heaviside telegraph equation. In addition, we provide a study of the causality consistency of the wave propagation models. We observe transport implications due to the presence of dispersive acoustic media and derive model adjustments that include attenuation and diffusion approximations within the two-dimensional forward problem. Next, we restore the inverse problem description with the deduced perturbation components. Finally, we solve the nonlinear inverse problem with a numerical strategy for a filtered backprojection reconstruction. At a stage prior to the image reconstruction, we compensate for the effect of acoustic attenuation and diffusion to calculate the inversions of the wave perturbations located within the projections. In this way, we manage to significantly reduce reconstruction artifacts. In consequence, we prevent the use of some additional image processing of noise reduction. We demonstrate a feasible strategy on how to solve the stated nonlinear inverse problem of photoacoustic tomography accounting for dispersive acoustic media. In particular, we emphasize efforts to achieve an analytical description, and thus an algorithm is placed, for imaged sound perturbations to be cleaned from acoustic scattering in a simplified manner.