Robust signal recovery via l1-2/lp minimization with partially known support

In this paper, we study the robust recovery of signals for general noise by l(1-2)/l(p) (2 <= p < + infinity) minimization with partially known support (PKS). A recovery condition for l(1-2)/l(p) minimization by incorporating prior support information is established, and an error estimate is obtained. In particular, the obtained results not only provide a new theoretical guarantee to robustly recover signals for general noise, but also improve and generalize the state- of-the-art ones. In addition, a series of numerical experiments are carried out to confirm the validity of the proposed method, which show that incorporating prior support information for l(1-2)/l(p) minimization exhibits better recovery performance than l(1-2)/l(p) minimization.