Uniform RIP Bounds for Recovery of Signals with Partial Support Information by Weighted $ℓ_p$-Minimization (CSIAM Transactions on Applied Mathematics, 2024)
In this paper, we consider signal recovery in both noiseless and noisy casesvia weighted $ℓ_p \ (0 < p ≤ 1)$ minimization when some partial support information onthe signals is available. The uniform sufficient condition based on restricted isometryproperty (RIP) of order $tk$ for any given constant $t>d$ ($d≥1$ is determined by the priorsupport information) guarantees the recovery of all $k$-sparse signals with partial support information. The new uniform RIP conditions extend the state-of-the-art resultsfor weighted $ℓ_p$-minimization in the literature to a complete regime, which fill the gapfor any given constant $t > 2d$ on the RIP parameter, and include the existing optimalconditions for the $ℓ_p$-minimization and the weighted $ℓ_1$-minimization as special cases.