Fast Robust Sparse Bayesian Learning Image Reconstruction Model Based on Generalized Approximate Message Passing

Sparse Bayesian learning (SBL) is an algorithm for high-dimensional data processing based on Bayesian statistical theory. Its goal is to improve the generalization ability and efficiency of the model by introducing sparsity, that is, retaining only some important features of the image. However, the traditional Sparse Bayesian Learning algorithm involves the operation of n$\boldsymbol{\times}$n dimensional matrix inversion during iterative update, which seriously affects the efficiency and speed of image reconstruction. In order to overcome the above defects, in this paper, we propose a fast robust Sparse Bayesian Learning image reconstruction model based on generalized approximate message passing (GAMP-FRSBL). The damped Gaussian generalized approximate message passing algorithm (Damped GGAMP) is introduced on the basis of SBL to avoid the matrix inversion problem. Combined with the convex optimization strategy, the block coordinate descent (BCD) method is used to iteratively update the parameters to improve the reconstruction efficiency of the model. Finally, experiments are conducted on Indor and Mondrian images, DOTA, COCO and UCM datasets to verify the effectiveness of the GAMP-FRSBL in image reconstruction.