  In this letter, we present a unified result for the stable recovery bound of
Lq(0 < q < 1) optimization model in compressed sensing, which is a constrained
Lq minimization problem aware of the noise in a linear system. Specifically,
without using the restricted isometry constant (RIC), we show that the error
between any global solution of the noise-aware Lq optimization model and the
ideal sparse solution of the noiseless model is upper bounded by a constant
times the noise level,given that the sparsity of the ideal solution is smaller
than a certain number. An interesting parameter {gamma} is introduced, which
indicates the sparsity level of the error vector and plays an important role in
our analysis. In addition, we show that when {\gamma} > 2, the recovery bound
of the Lq (0 < q < 1) model is smaller than that of the L1 model, and the
sparsity requirement of the ideal solution in the Lq(0 < q < 1) model is weaker
than that of the L1 model.
