Adjoint based Hessian evaluation for SPN modeled optical tomography

Hessian matrices are important in inversion algorithms due to their potential of use in full Newton schemes, analysis of reconstruction results, and in experimental design. We present for the first time an adjoint based evaluation of the Hessian matrix for the SPN-approximation modeled forward operator in optical tomography. The Hessians so calculated are numerically validated with respect to finite difference calculations. We present comparisons between computational requirements of the present scheme with a mixed scheme which evaluates the Hessian as the first difference of the adjoint based Jacobians.