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We consider the recovery of high-dimensional sparse signals via -minimization under mutual incoherence condition, which is shown to be sufficient for sparse signals recovery in the noiseless and noise cases. We study both -minimization under the constraint and the Dantzig selector. Using the two -minimization methods and a technical inequality, some results are obtained. They improve the results of the error bounds in the literature and are extended to the general case of reconstructing an arbitrary signal.