Adaptive Bayesian augmented Lagrangian algorithm for fluorescence molecular tomography

Fluorescence molecular tomography (FMT) is a noninvasive imaging technique that enables the quantitative three-dimensional reconstruction of fluorescent probe distributions <i>in vivo</i>. However, FMT reconstruction is limited in accuracy and reliability due to light scattering and the ill-posed inverse problem. In this paper, the adaptive Bayesian augmented Lagrangian (ABAL) algorithm is proposed, which adaptively adjusts the regularization parameter to promote sparsity and enhance robustness to noise, while significantly improving computational efficiency. By integrating sparse Bayesian learning (SBL) with the augmented Lagrangian (AL) framework, the approach addresses the computational challenges and non-convexity introduced by the iterative adjustment of regularization parameters in SBL. The inverse problem is reformulated as a weighted <i>L</i>₁ minimization with adaptive regularization and solved via the AL method, enhancing computational efficiency and mitigating the risk of local minima. Moreover, the adaptive regularization mechanism enables the method to dynamically adjust to data-specific characteristics, avoiding over-regularization or under-regularization and improving both stability and reconstruction accuracy. To evaluate the effectiveness of our method, a series of numerical simulations and implantation experiments were conducted. Results confirm that the ABAL method can achieve relatively accurate reconstruction performance compared to other approaches, with an average minimum localization error (LE) of 0.358 mm and an average Dice coefficient of 0.775. These results show relatively high localization accuracy, shape recovery, and robustness of the ABAL method in FMT reconstruction, indicating its potential for practical FMT application.