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This paper (1) presents a new centralized collaborative sensing technique for cognitive radio systems which combines algebraic tools and compressive sampling techniques. The proposed approach consists of the detection of spectrum holes using spectrum distribution discontinuities detector fed by compressed measurements. The compressed sensing algorithm is designed to take advantage from the primary signals sparsity and to keep the linearity and properties of the original signal in order to be able to apply algebraic detector on the compressed measurements. Collaboration among radios enables the cognitive network to detect hidden primary users and makes it more robust against fading and unknown channel conditions. Furthermore, as an important key point, collaboration makes it possible to sample more compressively at each radio, i.e., each radio performs sampling with a lower rate. The complexity of the proposed detector is also discussed and compared with the energy detector as reference algorithm. The comparison shows that the proposed technique outperforms energy detector in addition to its low complexity.