This work presents a new centralized cooperative compressive spectrum sensing scheme for wideband cognitive radios (CRs), which combines intelligent graphical Boxplot rule detector and compressive sampling technique. The received signal at each CR sensing receiver in the presence of jamming attack signal and adding white Gaussian noise is transformed into a digital signal using an analog-to-information converter via random-demodulator. The proposed approach consists of the anomaly detection using Boxplot rule technique applied to the compressed measurements obtained from each CR user collected in matrix form called sampling matrix. Cooperation among CR users allows the CR users to detect anomalies or attacks in the presence of noise and jamming attack signal. Furthermore, as an important solution, cooperation makes it possible between all CRs to sample more compressively at every CR, that is, every CR user gives minimum number of samples denoted by Ns. Two hypotheses are proposed in this paper H0 and H1 to know if there is anomalies problem using one of the robust graphical techniques. The results show that the proposed technique performs well in addition to its low complexity. Copyright © 2014 John Wiley & Sons, Ltd.