Gaussian weighted block sparse Bayesian learning strategy based on K-means clustering algorithm for accurate bioluminescence tomography in glioma

As a preclinical imaging modality, bioluminescence tomography (BLT) is designed to locate and quantify threedimensional (3D) information of viable tumor cells in a living organism non-invasively. However, because of the ill-posedness of the inverse problem of reconstruction, BLT is hard to achieve the accurate recovery of the distribution of light sources. In this study, we proposed a Gaussian weighted block sparse Bayesian learning strategy based on K-means clustering algorithm (GBSBLK) for accurate BLT reconstruction. GBSBLK integrated the structured sparsity assumption, the K-means clustering strategy, and the block sparse Bayesian learning (BSBL) framework to overcome the over-smoothness and over-sparsity in BLT reconstructions, and without using the tumor segmentation from anatomical images as a priori. To better define the structured sparsity, we used the K-means clustering algorithm to directly cluster all the mesh points to get the K blocks. Furthermore, to prevent from over-smoothness of the light source, we applied Gaussian weighted distance prior to build the intra-block correlation matrix. At last, we used the BSBL framework to ensure the accuracy and robustness of the backward iterative computation. Results of both numerical simulations and in vivo experiments demonstrated that GBSBLK achieved the accurate quantitative analysis not only in tumor spatial positioning but also morphology recovery. We believe that GBSBLK can achieve great benefit in the application of BLT for quantitative analysis.