Fast image reconstruction methods for fully 3D multispectral optical bioluminescence tomography

We investigate fast iterative image reconstruction methods for fully 3D multispectral optical bioluminescence tomography where inhomogeneous optical properties are modeled using the finite element method (FEM). We compare two approaches to incorporating the forward model into the solution of the inverse problem. In the direct calculation approach we compute the full forward model by repeated solution of the FEM problem, once for each potential source location. In the on-the-fly approach, we do not explicitly solve for the full forward model. Instead, the solution to the forward problem is included implicitly in the formulation of the inverse problem, and the FEM is solved once at each iteration for the current image estimate. In both approaches we use reordered Cholesky factorization and substitution (CFS) to solve the FEM problem. We compare the computation cost of these two approaches, concluding that the on-the-fly approach can lead to substantial reductions in cost when combined with a rapidly converging iterative algorithm.