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

Recovery of signals under the condition on RIC and ROC via prior support information