k-Sparse Vector Recovery via ℓ1-αℓ2 Local Minimization.

This paper studies the ℓ 1 - α ℓ 2 local minimization model for α ∈ (0 , 2 ] , which is the first time to consider the case of α > 1 . We obtain the necessary and sufficient conditions for a fixed sparse signal to be recovered from this model. Based on this condition, we also obtain the necessary and sufficient conditions for any k-sparse signal to be recovered from ℓ 1 - α ℓ 2 local minimization model with 0 < α < 1 , α = 1 and 1 < α ≤ 2 . The experimental data show that the size of α is positively correlated with the success rate of signal recovery. [ABSTRACT FROM AUTHOR]