A Projection-Based Algorithm for Constrained L1- Minimization Optimization with Application to Sparse Signal Reconstruction

In this paper, a projection-base algorithm is proposed for solving the constrained L1-minimization problem. Furthermore, the algorithm is utilized to sparse signal reconstruction. The L1 -minimization is first converted into some equations which are described by the projections onto a hyer box set and the nonnegative quadrant. Then a iterative algorithm is proposed for solving the L1 -minimization problem. Next, the algorithm is applied to sparse signal reconstruction described as an L1- minimization problem subject to L∞ -norm noise constraint, or equivalently bound constraint. Finally, several experiments are presented to show the performance of the proposed algorithm.