Oracle Inequalities for Corrupted Compressed Sensing

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In this paper, we establish the oracle inequalities of highly corrupted linear observations b = Ax0 + f0 + e ∈ R m .Here the vector x0 ∈ R n with n ≫ m is a (approximately) sparse signal and f0 ∈ R m is a sparse error vector with nonzero entries that can be possible infinitely large, e ∼ N (0, σ 2 Im) represents the Gaussian random noise vector.We extend the oracle inequality x -x0 2 2 i min{|x0(i)| 2 , σ 2 } for Dantzig selector and Lasso models in [E.