We derive a sharp nonasymptotic bound of parameter estimation of the L1/2 regularization.The bound shows that the solutions of the L1/2 regularization can achieve a loss within logarithmic factor of an ideal mean squared error and therefore underlies the feasibility and effectiveness of the L1/2regularization.Interestingly,when applied to compressive sensing,the L1/2 regularization scheme has exhibited a very promising capability of completed recovery from a much less sampling information.As compared with the Lp(0 < p < 1) penalty,it is appeared that the L1/2 penalty can always yield the most sparse solution among all the Lp penalty when 1/2 ≤ p < 1,and when 0 < p < 1/2,the Lp penalty exhibits the similar properties as the L1/2 penalty.This suggests that the L1/2 regularization scheme can be accepted as the best and therefore the representative of all the Lp(0 < p < 1) regularization schemes.
Hai ZHANGZong Ben XUYao WANGXiang Yu CHANGYong LIANG
