A Primal-Dual Reconstruction Algorithm for Fluorescence and Bioluminescence Tomography

We introduce a new primal-dual reconstruction algorithm for fluorescence and bioluminescence tomography. As often in optical tomography, image reconstruction is performed by optimizing a multi-term convex cost function. Current reconstruction methods employed in the field are usually limited to cost functions with a smooth data fidelity term; quadratic in general. In addition, the use of a composite regularization term (a sum of multiple terms) requires a substantial adaptation of these methods. Typically one would have to solve a subproblem via a primal-dual method at each iteration. The primal-dual scheme presented here is designed to handle directly cost functions composed of multiple, possibly non-smooth, terms. This allows more freedom for the design of tailored cost functions leading to enhanced reconstructions. We illustrate the method on two cases. First, we use a cost function composed of $ℓ _{ 1 }$ fidelity and regularization terms. We compare to the reconstructions obtained with the quadratic fidelity counterpart. Second, we employ a cost function composed of three terms : $ℓ _{ 1 }$ for data fidelity, total-variation plus (2,1)-mixed norms for regularization.