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

Abstract

Abstract In this paper, we study the robust recovery of signals for general noise by ℓ 1 - 2 / ℓ p \ell_{1-2}/\ell_{p} ( 2 ≤ p < + ∞ 2\leq p<+\infty ) minimization with partially known support (PKS). A recovery condition for ℓ 1 - 2 / ℓ p \ell_{1-2}/\ell_{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 \ell_{1-2}/\ell_{p} minimization exhibits better recovery performance than ℓ 1 - 2 / ℓ p \ell_{1-2}/\ell_{p} minimization.