Image compressed sensing based on dictionary learning via bilinear generalized approximate message passing

Sparse representation matrix is of great significance for compressed sensing (CS). When dictionaries learned from training data are used instead of predefined dictionaries, signal reconstruction accuracy would be improved. In this paper, we learn dictionaries for compressed image reconstruction based on bilinear generalized approximate message passing (BiGAMP). Stochastic mapping is performed on the training data which are composed of image blocks, to conform to the statistical model of BiGAMP methodology. Square dictionary and overcomplete dictionary are learned respectively for blocked image sparse representation, and are applied to image CS reconstruction. Simulation results show that our learned dictionaries lead to improved image CS reconstruction performance in comparison to predefined dictionaries and dictionaries learned with K-SVD method.