  Quantitative photoacoustic tomography is an emerging imaging technique aimed
at estimating the distribution of optical parameters inside tissues from
photoacoustic images, which are formed by combining optical information and
ultrasonic propagation. This optical parameter estimation problem is ill-posed
and needs to be approached within the framework of inverse problems.
Photoacoustic images are three-dimensional and high-resolution. Furthermore,
high-resolution reconstructions of the optical parameters are targeted.
Therefore, in order to provide a practical method for quantitative
photoacoustic tomography, the inversion algorithm needs to be able to perform
successfully with problems of prominent size. In this work, an efficient
approach for the inverse problem of quantitative photoacoustic tomography is
proposed, assuming an edge-preferring prior for the optical parameters. The
method is based on iteratively combining priorconditioned LSQR with a lagged
diffusivity step and a linearisation of the measurement model, with the needed
multiplications by Jacobians performed in a matrix-free manner. The algorithm
is tested with three-dimensional numerical simulations. The results show that
the approach can be used to produce accurate and high quality estimates of
absorption and diffusion in complex three-dimensional geometries with moderate
computation time and cost.
