科研之友
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摘要
We derive a sharp nonasymptotic bound of parameter estimation of the L-1/2 regularization. The bound shows that the solutions of the L-1/2 regularization can achieve a loss within logarithmic factor of an ideal mean squared error and therefore underlies the feasibility and effectiveness of the L-1/2 regularization. Interestingly, when applied to compressive sensing, the L-1/2 regularization scheme has exhibited a very promising capability of completed recovery from a much less sampling information. As compared with the L-p (0 <p < 1) penalty, it is appeared that the L-1/2 penalty can always yield the most sparse solution among all the L-p, penalty when 1/2 <= p < 1, and when 0 <p < 1/2, the 4, penalty exhibits the similar properties as the L-1/2 penalty. This suggests that the L-1/2 regularization scheme can be accepted as the best and therefore the representative of all the Lp (0 < p < 1) regularization schemes.
