| Compressed sensing theory is a novel sampling theory, and has been widely applied to the field of image processing, pattern recognition, automatic control and biological sensors. As one of the crucial issues, the reconstruction algorithm plays a key role in the application of compressed sensing. Mixed l1-l2norm minimization problem as a convex optimization model of compressed sensing, in recent years has attracted many scholars. In this paper, some new effective algorithms are proposed for solving mixed l1-l2norm minimization problem.(i)Combined with diagonal sparse quasi-newton method, a so-called modified GPSR algorithm is proposed based on gradient Projection for Sparse Reconstruction. The numerical results show that the algorithm is effective and feasible.(ii) A neural network was presented based on scaled gradient projection. The proposed neural network is shown to be stable in the sense of Lyapunov and converges to the optimal solution of the original problem. The numerical results show that the proposed neural network is feasible and efficient.(iii)A algorithm is given based on an adaptive line search scheme. The new algorithm can achieve convergence rate of O(1/k2), where k is the number of iterations and has a lower bound than Nemirovski line search scheme. Finally, the numerical experiments show that the new algorithm is more effective than Nemirovski line search scheme. |
PDF Full Text Request