Cone-beam X-ray luminescence computed tomography via Laplacian scale mixture prior-driven variational Bayesian method

Cone-beam X-ray luminescence computed tomography (CB-XLCT), as an emerging optical molecular imaging modality, has garnered extensive attention due to its capability to monitor the dynamic changes in early-stage tumors. However, the reconstruction of CB-XLCT has been impeded by the low absorption and pronounced scattering properties inherent in biological tissues. Here, a variational Bayesian method based on the Laplacian scale mixture prior has been proposed for the modeling and recovery of sparse signals for CB-XLCT. Within this framework, the scale variable is governed by an inverse gamma distribution, which is employed as the conjugate prior to the Laplacian, thereby enabling an adaptive representation of sparsity levels and enhancing model flexibility. The Laplace approximation has been utilized to derive an analytical form of the posterior distribution, converting the intractable posterior into a Gaussian distribution. Under this approximation, the maximum a posteriori (MAP) estimate has been shown to correspond to the expected value. Additionally, signal recovery has been conducted within the variational Bayesian structure using the expectation-maximization (EM) algorithm, resulting in substantial improvements in reconstruction accuracy. The performance of our method has been assessed through numerical simulations and implantation experiments. Results have demonstrated superior performance in both source localization and morphological restoration, thereby highlighting its potential for advancing CB-XLCT toward preclinical and clinical applications.