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Wideband spectrum sensing in cognitive radio networks remains an open challenge due to wideband spectrum acquisition implementation. Compressed spectrum sensing provides a powerful approach to acquire wideband signals. We purpose a probabilistic Space-time Bayesian Compressed Spectrum Sensing (ST-BCSS) to combat the noise in wideband compressed spectrum sensing. We present an informative hierarchical prior probabilistic model to recover the compressed spectrum by exploiting the temporal and spatial prior information. These priori information endows the robustness of spectrum sensing subject to noise and low sampling rate. We present a probabilistic framework to address how to represent, convey and fuse multi-prior information to improve the local compressed spectrum reconstruction. Numerical simulation results demonstrate that the ST-BCSS algorithm improves the performance of compressed spectrum sensing under low sampling rate and low Signal Noise Ratio (SNR), compared with the traditional Basis Pursuit and Orthogonal Matching Pursuit algorithms. A correlation based algorithm for the detection of reconstruction failure due to non-sparse spectrum is also proposed and demonstrated using numerical simulations.