The Dantzig selector: recovery of signal via l1 - αl2 minimization

In the paper, we proposed the Dantzig selector based on the l(1) - alpha l(2) (0 < alpha <= 1) minimization for the signal recovery. In the Dantzig selector, the constraint parallel to A(inverted perpendicular)(b - Ax )parallel to(infinity) <= eta for some small constant eta > 0 means the columns of A has very weakly correlated with the error vector e = Ax - b. First, recovery guarantees based on the restricted isometry property are established for signals. Next, we propose the effective algorithm to solve the proposed Dantzig selector. Last, we illustrate the proposed model and algorithm by extensive numerical experiments for the recovery of signals in the cases of Gaussian, impulsive and uniform noises. And the performance of the proposed Dantzig selector is better than that of the existing methods.