A Fuzzy Selection Compressive Sampling Matching Pursuit Algorithm for its Practical Application

In compressive sampling matching pursuit algorithm, it requires that the sparsity information of original signal to control the size of the preliminary atomic set and the maximum number of the algorithm iteration. This weakens the reconstruction accuracy, increases the computation complexity and limits its practical application capacity. To overcome the problem, an improved method is proposed. The proposed method firstly sets a fixed step-size as the assumed sparsity to expand the preliminary atomic set at the initial stage when the sparsity information is unknown. Secondly, the proposed algorithm adopts the fuzzy threshold strategy to select the more relevant atoms from the preliminary atomic set to expand the candidate atomic set. Finally, the double threshold control method, multiply stages setting and variable step-size method are used to control the iteration stop condition and adjust the estimated sparsity. When the two threshold iteration stop conditions are simultaneously satisfied, the iteration stops, which shows that the reconstructed signal better approximated the original signal, and the reconstruction performance is the best. Otherwise, if only one of the conditions is satisfied, the size of the estimated sparsity is increased by the variable step size method to reduce the error between the reconstructed signal and original signal. In addition, we extended the proposed algorithm to the multiple measurement vectors scenario for joint sparse signal recovery. Simulation results indicate that the proposed algorithm is better than the other method in terms of the reconstruction performance in single measurement vector and multiple measurement vector cases.