Wideband spectrum sensing remains one of the challenging problems facing the wide deployment of cognitive radio networks. Compressive sensing (CS) was proposed as a promising approach to this problem by utilizing the sparse structure of the underutilized spectrum to capture the spectrum with fewer measurements and simpler hardware requirements. Most of the work in compressive spectrum sensing solely exploits the spatial- and frequency-domain structure of the spectrum neglecting the temporal structure arising from the regularity of primary user (PU) traffic patterns. In this paper, we explore the effectiveness of incorporating PU traffic patterns in compressive spectrum sensing. This achieves improved sensing performance by exploiting the statistics of the PU activity in the CS recovery algorithms. The experimental analysis through simulation shows that the proposed schemes can substantially improve the receiver operating characteristic performance at lower sampling rate noisy spectrum measurements.