Iterative Reconstruction for Bioluminescence Tomography with Total Variation Regularization

Bioluminescence tomography(BLT) is an instrumental molecular imaging modality designed for the 3D location and quantification of bioluminescent sources distribution in vivo. In our context, the diffusion approximation(DA) to radiative transfer equation(RTE) is utilized to model the forward process of light propagation. Mathematically, the solution uniqueness does not hold for DA-based BLT which is an inverse source problem of partial differential equations and hence is highly ill-posed. In the current work, we concentrate on a general regularization framework for BLT with Bregman distance as data fidelity and total variation(TV) as regularization. Two specializations of the Bregman distance, the least squares(LS) distance and Kullback-Leibler(KL) divergence, which correspond to the Gaussian and Poisson environments respectively, are demonstrated and the resulting regularization problems are denoted as LS+TV and KL+TV. Based on the constrained Landweber(CL) scheme and expectation maximization(EM) algorithm for BLT, iterative algorithms for the LS+ TV and KL+TV problems in the context of BLT are developed, which are denoted as CL-TV and EM-TV respectively. They are both essentially gradient-based algorithms alternatingly performing the standard CL or EM iteration step and the TV correction step which requires the solution of a weighted ROF model. Chambolle's duality-based approach is adapted and extended to solving the weighted ROF subproblem. Numerical experiments for a 3D heterogeneous mouse phantom are carried out and preliminary results are reported to verify and evaluate the proposed algorithms. It is found that for piecewise-constant sources both CL-TV and EM-TV outperform the conventional CL and EM algorithms for BLT.