In this study, we present a new fixed point method for l_1-norm regularization problems arising from sparse solution recovery in compressive sensing. The problem is reformulate as an equivalent non-smooth equation, then the combination of both an effective trust-region and a fixed point strategy are used to solve it. Modify the shrinkage parameter based on dogleg technique show that the new algorithm is more efficient and robustness. The proposed approach is global convergence and the rate of convergence is q-linear
