Gradient-Based Quantitative Photoacoustic Image Reconstruction for Molecular Imaging

The aim in quantitative photoacoustic imaging (QPI) is to recover the spatial distributions of the optical absorption and scattering coefficients from an absorbed energy density distribution (a conventional photoacoustic image). This paper proposes a gradient-based minimisation approach and demonstrates that functional gradients may be calculated efficiently by using a finite element model of light transport based on the diffusion approximation, in conjunction with a related adjoint model. The gradients calculated using this adjoint method are tested against finite-difference estimates, and inversions for the absorption or scattering coefficient distributions (from simulated data) are shown for the case where the other coefficient is known a priori. Simultaneous estimation for both absorption and scattering is ill-posed, and so multiwavelength inversion, in which the specific absorption spectra of the constituent chromophores and the wavelength-dependence of the scatter are known, is proposed as a means of ameliorating the ill-posedness. The unknown parameters are now the spatial variation of the chromphore concentrations and scattering coefficient. It is shown that the functional gradients for both of these can be obtained straightforwardly from the gradients for absorption and scatter and require no significant additional calculations. A simulated example is given in which the distributions of two chromophores with different spectra are recovered from absorbed energy images obtained at multiple wavelengths, when the scattering is assumed known.