Iterative projection based sparse reconstruction for face recognition

This paper presents a projection based iterative method (PIM) for solving the L1-minimization problem with its application to sparse representation and reconstruction. First, the unconstrained basis pursuit denoising (BPDN) problem is transformed into the cross-and-bouquet (CAB) form with a variable λ, and an iterative algorithm is proposed based on the projection method with the gradient of ‖x‖1 being transformed into a piecewise-linear function, which enhances the convergence of the algorithm. The global convergence of the algorithm is proved by Lyapunov method. Then, experiments conducted on random Gaussian sparse signals reconstruction and five well-known face data sets present the effectiveness and robustness of the proposed algorithm. It is also shown that the algorithm is robust to different sparsity levels and amplitude of signals, and has higher convergence rate and recognition accuracy compared with other L1-minimization algorithms especially in the case of noise interference.