Robust recovery of a kind of weighted l1-minimization without noise level.

This paper studies a kind of weighted l 1 -minimization that is motivated by function interpolation. Combining with the weighted robust null space property, we first propose a new sufficient condition for robust recovery via the weighted l 1 -minimization when the measurements are corrupted by arbitrary noise without requiring the proper estimation of noise level. Second, we investigate the instance optimality of the weighted l 1 -minimization decoder according to the weighted quotient property and the weighted restricted isometry property (RIP). In addition, to give a better error estimation in a general problem to recover noisy compressible signals, we improve the ω -RIP constant δ ω , 3 s from 1 / 3 to (1 7 − 1) / 8 by using the weighted sparsity and Stechkin-type estimate. Our results show that the weighted l 1 -minimization remains not only stable but also robust to reconstruct signals with noisy observations. [ABSTRACT FROM AUTHOR]