Stable Recovery of Signals From Highly Corrupted Measurements

In this paper, we consider the stable recovery of sparse or proximately sparse signals x ∈ ℝ
ⁿ
from highly corrupted linear measurements b = Ax + f + e, where f ∈ ℝ
^m
is a sparse error vector whose nonzero entries may be arbitrarily large and e ∈ ℝ
^m
is a stochastic noise. We propose an extended Dantzig selector model that considers sparsity of both x and f. We establish sufficient conditions under the restricted isometry property, which guarantee the signal stable recovery from an extended Dantzig selector model and extended Lasso model.