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This letter introduces a novel algorithm to construct sensing and measurement dictionaries in compressive sensing using alternating projection method. The cumulative and mutual cross coherence of the constructed dictionaries are lower than those of Gaussian random dictionary. The concept of General Restricted Isometry Constant (GRIC) is introduced. Low cumulative cross coherence puts bound on GRIC and small GRIC improves successful recovery rate of OMP algorithm. Experiments demonstrate that OMP algorithm performs better using dictionaries constructed by the proposed algorithm than Gaussian random dictionaries and those constructed by Schnass' algorithm.