A group matching pursuit for image reconstruction

Matching Pursuit (MP) is a fast and effective sparse representation algorithm, so it and its improved algorithms are used to solve the problem of Compressive Sensing (CS) reconstruction. MP finds the support of the unknown signal sequentially based on the correlation values between the basis vectors and the measurement vector. As the sampling rate decreases, the signal could not be reconstructed successfully. The nature image wavelet coefficients always remain a residual dependency structure which we can use to improve the CS reconstruction, such as an aggregation of neighborhood and the significant coefficients appear at the locations of the image edges. Make full use of the priors are mentioned above, we propose a Group Matching Pursuit (GMP) algorithm base on the edge. In GMP, with the neighborhood structure employed as a spatial constraint, the coefficients are organized as groups to restrain each other. Then the extracted image edge is used as the prior information to improve the reconstruction quality. Finally, we propose a Bayesian Group Matching Pursuit (BGMP) algorithm. In BGMP the group coefficients are modeled by a multivariate Gaussian distribution, and solved by a maximum a posteriori probability (MAP) estimate. Experiments have shown that, the methods based on GMP have a better reconstruction in solving the reconstruction problem of CS.