  Quantitative Photoacoustic tomography (QPAT) is an emerging medical imaging
modality which offers the possibility of combining the high resolution of the
acoustic waves and large contrast of optical waves by quantifying the molecular
concentration in biological tissue.
  In this paper, we prove properties of the forward operator that associate
optical parameters from measurements of a reconstructed Photoacoustic image.
This is often referred to as the optical inverse problem, that is nonlinear and
ill-posed. The proved properties of the forward operator provide sufficient
conditions to show regularized properties of approximated solutions obtained by
Tikhonov-type approaches. The proposed Tikhonov- type approaches analyzed in
this contribution are concerned with physical and numerical issues as well as
with \textit{a priori} information on the smoothness of the optical
coefficients for with (PAT) is particularly a well-suited imaging modality.
