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This letter considers the problem of recovering signals via dual frame based ℓ1-analysis model under the assumption that signals are compressible in a general frame. Our main result shows that Weibull random matrices (not only subgaussian matrices) with optimal number of measurements could guarantee accurate recovery of signals with high probability. We derive that result by generalizing a recent Lemma due to Foucart and with the help of the parameterized representation of any dual frame. Our result should be significant for existing and upcoming ℓ1-analysis models for signal recovery.