Reconstruction algorithms are critical for the successful use of the compressive sensing theory. To reduce the signal reconstruction time and ensure the relatively high reconstruction accuracy of the directional pursuit algorithm

an algorithm for compressive sensing signal reconstruction is studied. In this paper

a nonmonotone memory gradient pursuit algorithm(MGP)for reconstructed signals is proposed. Under the framework of direction pursuit based on optimization theory

the algorithm first adopts a regularization orthogonal matching strategy to select atom sets fast and efficiently. However

both the least square method part for residual minimization and the direction update part of regularization orthogonal matching are abandoned. Instead

the search step size is determined by a non-monotonic linear search strategy

Furthermore the update direction is fixed with the memory gradient algorithm which increases the degree of freedom of parameter selection. After that

estimated values of sparse coefficients are established. The proposed algorithm takes full advantage of globally fast and stable convergence of the memory gradient algorithm with Armijo line search to avoid local optimal solution under some mild condition. By choosing a larger accepted step size at each iteration

Therefore the evaluation of optimization function can be effectively reduced. Besides that

by formula derivation and clever manipulation

the parameter of the direction search can be calculated more rapidly. In this way

the efficiency of convergence is improved. Derivation of direction parameter formula in the original memory gradient method is achieved

and it is more efficiently. The computational cost for memory gradient algorithm is 30% less than that of approximate conjugate gradient pursuit algorithm. Moreover

the MGP algorithm is less insensitive to Gaussian noise than other greedy iteration algorithms. Finally

the one dimension signal and image signal is reconstructed accurately.The reconstruction quality is better when sample rate exceeds 0.2. The experiment results of one-dimensional signal and two-dimensional image signal demonstrate that the algorithm is striking a balance between efficiency and reconstruction accuracy and that it has an improved signal reconstruction performance. Additionally

under the same test conditions the proposed algorithm outperforms other similar reconstruction algorithm in time and quality.