Limited-memory-BFGS-based iterative algorithm for multispectral bioluminescence tomography with Huber regularization

Multispectral bioluminescence tomography is becoming a promising tool because it can resolve the biodistibution of bioluminescent reporters associated with cellular and subcellular function through several millimeters with to centimeters of tissues in vivo. Generally, to recover the bioluminescent sources, the source reconstruction problem is formulated as a nonlinear least-squares-type bounds constrained optimization problem. However, bioluminescence tomography (BLT) is an ill-posed problem. For the sake of stability and uniqueness of BLT, many algorithms have been proposed to regularize the problem, such as L₂ norm and L₁ norm. Here, we proposed a new regularization method with Huber function to regularize BLT problem to obtain robustness like L₁ and rapid convergence of L ₂. Furthermore, the computational burden is largely increased with the use of spectral data. Therefore, there is a critical need to develop a fast reconstruction algorithm for solving multispectral bioluminescence tomography. In the paper, a limited memory quasi-Newton algorithm for solving the large-scale optimization problem is proposed to fast localize the bioluminescent source. In the numerical simulation, a heterogeneous phantom was used to evaluate the performance of the proposed algorithm with the Monte Carlo based synthetic data. Additionally, the real mouse experiments were conducted to further evaluate the proposed algorithm. The results demonstrate the potential and merits of the proposed algorithm.