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Wideband Spectrum Sensing (WSS) is considered as one of the challenging issues in Cognitive Radio (CR) dealing with the opportunistic utilization of a wide frequency band. Compressive sampling (CS, also known as compressive sensing) has been introduced recently with a revolutionary idea to detect the sparse wideband spectrum by using a much lower sampling rate. However, in traditional compressive sensing approach, the sparsity of a received signal is always utilized as prior knowledge, which can't be obtained in practical Cognitive Radio Networks (CRN) in advance. In this paper, an Optimized Adaptive Compressive Sampling (OACS) algorithm is proposed to recover original signals via proper sampling rate, which doesn't need any information of sparsity. Furthermore, a Cross Validation (CV) method is introduced that enables cognitive radios (CRs) to automatically terminate the signal acquisition once the stopping criterion is satisfied, avoiding wasting hardware resources. Both theoretical analysis and experimental simulations show that the proposed algorithm can achieve satisfactory signal recovery using lower sampling rate than traditional CS recovery approaches.