Sparse Blind Compressed Sensing Based on Bilinear Generalized Approximate Message Passing

By combining the bilinear nature of both the bilinear generalized approximate message passing (BiGAMP) methodology and the sparse blind compressed sensing (BCS) problem, a novel sparse BCS scheme is proposed. Based on BiGAMP, this scheme learns the sparse dictionary and sparse coefficients directly from the undersampled measurements, and then recovers the unknown signals by taking the standard compressed sensing as post-processing. Numerical investigation shows that this BiGAMP-based sparse BCS scheme performs better than the direct sparse BCS method, and is more adaptive to the signal under consideration than the standard CS with dictionary learning.