An inertial projection neural network for sparse signal reconstruction via l1−2 minimization

In this paper, an inertial projection neural network (IPNN) is proposed for the reconstruction of sparse signals. Firstly, a nonconvex l1−2 minimization problem is presented for sparse signal reconstruction from highly coherent measurement matrices, instead of our familiar l1 minimization which used standard convex relaxation. For solving this nonconvex l1−2 minimization problem, the IPNN is introduced. Under certain condition, the convergence of IPNN is proved. Finally, a series of experiments on various applications are conducted and experimental results show the effectiveness and performance of IPNN for the introduced l1−2 minimization method.