The balance between computational complexity and the architecture bottlenecks the development of Neural Networks (NNs), An architecture that is too large or too small will influence the performance to a large extent in terms of generalization and computational cost. In the past, saliency analysis has been employed to determine the most suitable structure, however, it is time-consuming and the performance is not robust. In this paper, a family of new algorithms for pruning elements (weighs and hidden neurons) in Neural Networks is presented based on Compressive Sampling (CS) theory. The proposed framework makes it possible to locate the significant elements, and hence find a sparse structure, without computing their saliency. Experiment results are presented which demonstrate the effectiveness of the proposed approach.