Robust signal recovery for ℓ 1–2 minimization via prior support information

In this paper, a theoretical analysis on the signal recovery is provided by weighted l1-2 minimization when partial support information is available. We establish a sufficient condition for the weighted l1-2 minimization, which in absence of prior support information is proved to be much better than the state-of-the-art one. In particular, if at least 50% of the estimated support information is accurate, the sufficient condition is weaker than the analogous one of the standard l1-2 minimization. In addition, a series of numerical experiments are conducted by the modified DCA-l1-2 method to support the performance of weighted l1-2 minimization. The excellent recovery performance of weighted l1-2 minimization is showed compared with the state-of-the-art weighted l1 minimization and weighted lq(0 < q < 1) minimization when the measurement matrix is highly coherent.