A distributed wideband spectrum compressive sensing approach based on consensus optimization was developed.The cognitive radio users firstly collected the time-domain sampling by compressive sampling and recover the local spectrum.Then the spectrum of primary users is recovered jointly by cooperative cognitive radio users

which utilizes iterative consensus optimization to reach globally sensing outcomes via one-hop local communication only.In particular

a weighted consensus-averaging constraint is introduced to reduce the number of the consensus constraints

which lowers the computation loads and expedites the convergence.The convergence of the proposed distributed cooperative spectrum sensing scheme is proved analytically.Simulations demonstrate that the proposed scheme can effectively sense the spectrum from compressive sample.