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Joint Bayesian and Greedy Recovery for Compressive Sensing

Greedy algorithms are widely used for sparse recovery in compressive sensing. Conventional greedy algorithms employ the inner product vector of signal residual and sensing matrix to determine the support, which is based on the assumption that the indexes of the larger-magnitude entries of the inner product vector are more likely to be contained in the correct supports. However, this assumption may be not valid when the number of measurements is not sufficient, leading to the selection of an incorrect support. To improve the accuracy of greedy recovery, we propose a novel greedy algorithm to recover sparse signals from incomplete measurements. The entries of a sparse signal are modelled by the type-II Laplacian prior, such that the k indexes of the correct support are indicated by the largest k variance hyperparameters of the entries. Based on the proposed model, the supports can be recovered by approximately estimating the hyperparameters via the maximum a posteriori process. Simulation results demonstrate that the proposed algorithm outperforms the conventional greedy algorithms in terms of recovery accuracy, and it exhibits satisfactory recovery speed.