A Weak Selection Stochastic Gradient Matching Pursuit Algorithm

In the existing stochastic gradient matching pursuit algorithm, the preliminary atomic set includes atoms that do not fully match the original signal. This weakens the reconstruction capability and increases the computational complexity. To solve these two problems, a new method is proposed. Firstly, a weak selection threshold method is proposed to select the atoms that best match the original signal. If the absolute gradient coefficients were greater than the product of the maximum absolute gradient coefficient and the threshold that was set according to the experiments, then we selected the atoms that corresponded to the absolute gradient coefficients as the preliminary atoms. Secondly, if the scale of the current candidate atomic set was equal to the previous support atomic set, then the loop was exited; otherwise, the loop was continued. Finally, before the transition estimation of the original signal was calculated, we determined whether the number of columns of the candidate atomic set was smaller than the number of rows of the measurement matrix. If this condition was satisfied, then the current candidate atomic set could be regarded as the support atomic set and the loop was continued; otherwise, the loop was exited. The simulation results showed that the proposed method has better reconstruction performance than the stochastic gradient algorithms when the original signals were a one-dimensional sparse signal, a two-dimensional image signal, and a low-rank matrix signal.