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Spectrum sensing is the fundamental task in Cognitive Radio (CR). Due to the fact that signal sparsity level is usually unavailable at CR receiver, this paper presents a blind compressive spectrum sensing approach when the sparsity level is unknown. For the sake of energy saving, each CR receiver applies Compressed Sensing (CS) to achieve less sub-Nyquist rate sample rates in order to reduce measurement number in the proposed algorithm. Then, it finds reconstruction information for detection without degrading the whole performance, for sparisty level information is not required in the detection process. Finally, simulation results are presented to testify the proposed algorithm's effectiveness in the reduction of the processed data, hence energy saving could be achieved.