In compressed sensing (CS for short) theory

the projection matrix optimization is a kind of approach of improving performance by increasing the amount of information of observational data.This paper presents a CS projection matrix optimization algorithm based on quasi-Newton method.The algorithm is divided into two steps.First

use threshold function to restrain the non-diagonal elements in order to make the Mutual Coherence between the projection matrix and sparse dictionary approximate Welch bound.Second

use Rank two to check and get Hessian matrix inverse to amend the direction of the gradient search.Two steps are alternately performed until the projection matrix which meets the requirement of the optimal solution is worked out.This algorithm always maintains descent and has a super-linear convergence rate

which requires less computation.Experimental results show that when signal sparse degree or observation data is identical

this proposed algorithm outperforms other algorithms.