Microphone arrays are today employed to specify the sound source locations in numerous real time applications such as speech processing in large rooms or acoustic echo cancellation. Signal sources may exist in the near field or far field with respect to the microphones. Current Neural Networks (NNs) based source localization approaches assume far field narrowband sources. One of the important limitations of these NN-based approaches is making balance between computational complexity and the development of NNs; an architecture that is too large or too small will affect the performance in terms of generalization and computational cost. In the previous analysis, saliency subject 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 compression of NNs is presented based on Compressive Sampling (CS) theory. The proposed framework makes it possible to find a sparse structure for NNs, and then the designed neural network is compressed by using CS. The key difference between our algorithm and the state-of-the-art techniques is that the mapping is continuously done using the most effective features; therefore, the proposed method has a fast convergence. The empirical work demonstrates that the proposed algorithm is an effective alternative to traditional methods in terms of accuracy and computational complexity.