Fluorescence diffuse optical tomography using the split Bregman method

Purpose: Standard image reconstruction methods for fluorescence Diffuse Optical Tomography (fDOT) generally make use of L2-regularization. A better choice is to replace the L2 by a total variation functional that effectively removes noise while preserving edges. Among the wide range of approaches available, the recently appeared Split Bregman method has been shown to be optimal and efficient. Furthermore, additional constraints can be easily included. We propose the use of the Split Bregman method to solve the image reconstruction problem for fDOT with a nonnegativity constraint that imposes the reconstructed concentration of fluorophore to be positive. Methods: The proposed method is tested with simulated and experimental data, and results are compared with those yielded by an equivalent unconstrained optimization approach based on Gauss–Newton (GN) method, in which the negative part of the solution is projected to zero after each iteration. In addition, the method dependence on the parameters that weigh data fidelity and nonnegativity constraints is analyzed. Results: Split Bregman yielded a reduction of the solution error norm and a better full width at tenth maximum for simulated data, and higher signal-to-noise ratio for experimental data. It is also shown that it led to an optimum solution independently of the data fidelity parameter, as long as the number of iterations is properly selected, and that there is a linear relation between the number of iterations and the inverse of the data fidelity parameter. Conclusions: Split Bregman allows the addition of a nonnegativity constraint leading to improve image quality.