  In the context of compressed sensing, the nonconvex $\ell_q$ minimization
with $0<q<1$ has been studied in recent years. In this paper, by generalizing
the sharp bound for $\ell_1$ minimization of Cai and Zhang, we show that the
condition $\delta_{(s^q+1)k}<\dfrac{1}{\sqrt{s^{q-2}+1}}$ in terms of
\emph{restricted isometry constant (RIC)} can guarantee the exact recovery of
$k$-sparse signals in noiseless case and the stable recovery of approximately
$k$-sparse signals in noisy case by $\ell_q$ minimization. This result is more
general than the sharp bound for $\ell_1$ minimization when the order of RIC is
greater than $2k$ and illustrates the fact that a better approximation to
$\ell_0$ minimization is provided by $\ell_q$ minimization than that provided
by $\ell_1$ minimization.
