The Dantzig Selector: Sparse Signals Recovery via l_p-q Minimization

In the paper, we proposed the Dantzig selector based on the $l_{p-q}$ ($0<p\le 1,1<q\le 2$) minimization for the signal recovery. First, we establish the convex combination representation of sparse vectors under the $l_{p-q}$ minimization problem. Next, we give the signal recovery guarantees that based on two classes of restricted isometry property frames. Last, some graphical illustrations are presented for the sufficient conditions of the signal recovery.