In cognitive radio (CR), the problem of limited spectral resources is solved by enabling unlicensed systems to opportunistically utilize the unused licensed bands. Compressive Sensing (CS) has been successfully applied to alleviate the sampling bottleneck in wideband spectrum sensing leveraging the sparseness of the signal spectrum in open-access networks. This has inspired the design of a number of techniques that identify spectrum holes from sub-Nyquist samples. However, the existence of interference emanating from low-regulated transmissions, which cannot be taken into account in the CS model because of their non-regulated nature, greatly degrades the identification of licensed activity. Capitalizing on the sparsity described by licensed users, this paper introduces a feature-based technique for primary user's spectrum identification with interference immunity which works with a reduced amount of data. The proposed method detects which channels are occupied by primary users' and also identify the primary users transmission powers without ever reconstructing the signals involved. Simulation results show the effectiveness of the proposed technique for interference suppression and primary user detection.