In this paper, we propose a novel Compressive Sensing (CS)-enhanced spectrum sensing approach for Cognitive Radio (CR) systems. The new framework enables cyclic feature detection with a significantly reduced sampling rate. We associate the new framework with a novel model-based greedy reconstruction algorithm: interdependent matching pursuit (IMP). For IMP, the hidden block sparsity owing to the symmetry present in the cyclic spectrum is exploited which effectively reduces the degree of freedom of problem. Compared with conventional CS with independent support selection, a remarkable spectrum reconstruction improvement is achieved by IMP.