A Compressed Sensing reconstruct algorithm based on trust region method of nonsmooth optimization

The signal reconstruction problems of Compressed Sensing is equal to a nonsmooth optimization problem. Since the original signal is sparse, a new l 1 -Minimization reconstruction algorithm is proposed based on modified trust region method of nonsmooth optimization. The algorithm can also reconstruct signal in super-linear convergence rate. Simulation results show that the algorithm is robust in reconstructing the original signal.