  In this paper, the sufficient condition in terms of the RIC and ROC for the
stable and robust recovery of signals in both noiseless and noisy settings was
established via weighted $l_{1}$ minimization when there is partial prior
information on support of signals. An improved performance guarantee has been
derived.
  We can obtain a less restricted sufficient condition for signal
reconstruction and a tighter recovery error bound under some conditions via
weighted $l_{1}$ minimization. When prior support estimate is at least $50\%$
accurate, the sufficient condition is weaker than the analogous condition by
standard $l_{1}$ minimization method, meanwhile the reconstruction error upper
bound is provably to be smaller under additional conditions. Furthermore, the
sufficient condition is also proved sharp.
