Bernoulli-Gaussian (BG) model in Expectation-Maximization Bernoulli-Gaussian Approximate Message Passing (EM-BG-AMP) algorithm is constrained by its symmetry and restricted in the approximation of the actual signal prior distribution. Gaussian-Mixture (GM) model in Expectation-Maximization Gaussian-Mixture Approximate Message Passing (EM-GM-AMP) algorithm is a high-order model of BG model and has quite high complexity. In order to solve these problems, the Bernoulli-Asymmetric-Gaussian (BAG) model was proposed. Based on the new model, by further derivation, the Expectation-Maximization Bernoulli-Asymmetric-Gaussian Approximate Message Passing (EM-BAG-AMP) algorithm was obtained. The main idea of the proposed algorithm was based on the assumption that the input signal obeyed the BAG model. Then the proposed algorithm used Generalized Approximate Message Passing (GAMP) to reconstruct signal and update the model parameters in iteration. The experimental results show that, when processing different images, compared to EM-BG-AMP,the time and the Peak Signal-to-Noise Ratio (PSNR) values of EM-BAG-AMP are increased respectively by 1.2% and 0.1-0.5 dB, especially in processing images with simple texture and obvious color difference changing, the PSNR values are increased by 0.4-0.5 dB. EM-BAG-AMP is the expansion and extension of EM-BG-AMP and can better adapt to the actual signal.

Abstract: To overcome the shortcoming that random measurement matrix is hard for hardware implementation due to its randomly generated elements, a new structural and sparse deterministic measurement matrix was proposed by studying the theory of measurement matrix in Compressed Sensing (CS). The new matrix was based on parity check matrix in Quasi-Cyclic Low Density Parity Check (QC-LDPC) code over finite field. Due to the good channel decoding performance of QC-LDPC code, the CS measurement matrix based on it was expected to have good performance. To verify the performance of the new matrix, CS reconstruction experiments aiming at one-dimensional signals and two-dimensional signals were conducted. The experimental results show that, compared with the commonly used matrices, the proposed matrix has lower reconstruction error under the same reconstruction algorithm and compression ratio. The proposed method achieves certain improvement (about 0.5-1dB) in Peak Signal-to-Noise Ratio (PSNR). Especially, if the new matrix is applied to hardware implementation, the need for physical storage space and the complexity of the hardware implementation should be greatly reduced due to the quasi-cyclic and symmetric properties in the structure.