Trust-Region Methods for Sparse Relaxation
  In this paper, we solve the l2-l1 sparse recovery problem by transforming the objective function of this problem into an unconstrained differentiable function and apply a limited-memory trust-region method. Unlike gradient projection-type methods, which uses only the current gradient, our approach uses gradients from previous iterations to obtain a more accurate Hessian approximation. Numerical experiments show that our proposed approach eliminates spurious solutions more effectively while improving the computational time to converge. 
Lasith Adhikari, Jennifer B. Erway, Shelby Lockhart, and Roummel F.   Marcia
math.NA