Adaptive Online Variational Bayesian Method based on Normal-Generalized Inverse Gaussian Prior for Bioluminescence...

Bioluminescence tomography (BLT), a non- invasive optical imaging technique, enables the quantitative analysis of the spatial distribution of targeted regions in vivo. Despite its high sensitivity, BLT is constrained by the ill-posed property of the inverse problem. To address this, an adaptive online variational Bayesian (AOVB-NGIG) method with a normal-generalized inverse Gaussian (N-GIG) prior is introduced for BLT reconstruction. This prior effectively captures the sparsity and complexity of the signal, making the approximation of the posterior distribution more controllable and achieving an optimal balance between sparsity and morphological preservation. Variational inference is employed to preserve the conjugacy of the prior information, transforming the optimization problem into a convex task by minimizing the variational lower bound. This approach reduces temporal and spatial complexities while maintaining consistency within the same distribution family. To avoid local optima, an adaptive learning rate adjustment method (AdaDelta) is applied, dynamically updating parameters by computing the exponential weighted averages of the squared gradients and parameter update magnitudes. The performance of the AOVB-NGIG method was evaluated through numerical simulation experiments, demonstrating superior accuracy in tumor spatial localization and morphological reconstruction compared to the L₁ -norm total variation (L₁ -TV), fast iterative shrinkage-thresholding algorithm (FISTA), and k-singular value decomposition (K-SVD) methods.Clinical Relevance- The performance of BLT reconstruction is significantly enhanced by the proposed AOVB-NGIG method. This improvement establishes a robust foundation for advancing preclinical and clinical pharmaceutical research.