We propose the Forward-Backward Synergistic Acceleration Pursuit (FBSAP) algorithm in this paper. The FBSAP algorithm inherits the advantages of the Forward-Backward Pursuit (FBP) algorithm, which has high success rate of reconstruction and does not necessitate the sparsity level as a priori condition. Moreover, it solves the problem of FBP that the atom can be selected only by the fixed step size. By mining the correlation between candidate atoms and residuals, we innovatively propose the forward acceleration strategy to adjust the forward step size adaptively and reduce the computation. Meanwhile, we accelerate the algorithm further in backward step by fusing the strategy proposed in Acceleration Forward-Backward Pursuit (AFBP) algorithm. The experimental simulation results demonstrate that FBSAP can greatly reduce the running time of the algorithm while guaranteeing the success rate in contrast to FBP and AFBP.
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