Research on Improvement of Stagewise Weak Orthogonal Matching Pursuit Algorithm

One of the key technologies of compressed sensing is the signal reconstruction. And the two important indicators of signal reconstruction are the reconstruction probability and the time consumed. The Stagewise Weak Orthogonal Matching Pursuit (SWOMP) is widely used because the sparsity does not need to be a priori condition. The use of fixed threshold parameter in the iterative process can easily lead to overestimation and underestimation. Inspired by the idea of “the initial stage is approaching quickly and the final stage is approaching gradually,” that is, the search rule of “firstly fast and then slow,” an improved algorithm replacing the fixed threshold selection with S-shaped function value in each iteration is proposed to overcome the shortcoming that the fixed threshold parameter is selected in every iteration of SWOMP algorithm. Through compared experiment of six different S-shaped functions, the results show that the influence of different S-shaped functions on the SWOMP algorithm is different, and the improved SWOMP algorithm with the sixth S-shaped function has the best reconstruction effect.