Efficient Sparse Bayesian Learning Model for Image Reconstruction Based on Laplacian Hierarchical Priors and GAMP

In this paper, we present a novel sparse Bayesian learning (SBL) method for image reconstruction. We integrate the generalized approximate message passing (GAMP) algorithm and Laplacian hierarchical priors (LHP) into a basic SBL model (called LHP-GAMP-SBL) to improve the reconstruction efficiency. In our SBL model, the GAMP structure is used to estimate the mean and variance without matrix inversion in the E-step, while LHP is used to update the hyperparameters in the M-step.The combination of these two structures further deepens the hierarchical structures of the model. The representation ability of the model is enhanced so that the reconstruction accuracy can be improved. Moreover, the introduction of LHP accelerates the convergence of GAMP, which shortens the reconstruction time of the model. Experimental results verify the effectiveness of our method.