Multi-start iterative reconstruction of the radiative parameter distributions in participating media based on the transient radiative transfer equation

Simultaneous reconstruction of the radiative parameter distributions in participating media, based on the transient radiative transfer equation (TRTE), was investigated. The discrete ordinate method was employed to solve the direct TRTE for two-dimensional participating media. A multi-start iterative technique, based on the conjugate gradient (CG) method, was proposed to accelerate the convergence speed of the inverse procedure. The maximum a posteriori (MAP) estimation was used to overcome the retrieval difficulties resulting from the ill-posed nature of the inverse problem. The gradient of the objective function was obtained using adjoint differentiation. All the simulation results show that MAP combined with the multi-start iterative CG technique is effective in simultaneously reconstructing the distributions of absorption and scattering coefficients in two-dimensional inhomogeneous media, even with noisy data.