ℓ1–2 minimisation for compressed sensing with partially known signal support

In this study, the authors mainly discuss the robust signal recovery by $\ell _{1-2}$ℓ1−2 minimisation with incorporating prior support information, which is not considered in previous works. A robust recovery condition is established and an recovery error estimation is obtained, in particular, the obtained results generalise the state-of-the-art ones. In addition, by proposing a modified algorithm, the numerical experiments show that incorporating prior support information for $\ell _{1-2}$ℓ1−2 minimisation exhibits better recovery performance than standard $\ell _{1-2}$ℓ1−2 minimisation.