Compressed sensing (CS) sampling is a sampling method which is based on the signal sparse. Much information can be extracted from as little as possible of the data by applying CS, and this method is the idea of great theoretical and applied prospects. In the framework of compressed sensing theory, the sampling rate is no longer decided in the bandwidth of the signal, but it depends on the structure and content of the information in the signal. In this paper, the signal is the sparse in the Fourier transform and random sparse sampling is advanced by programing random observation matrix for peak random base. The signal is successfully restored by Bregman algorithm. The signal is described in the transform space, and a theoretical framework is established with new signal descriptions and processing. The case is maked to ensure that the information loss, signal is sampled at much lower than the Nyquist sampling theorem requiring rate, but also the signal is completely restored in high probability. The random sampling has following advantages alias-free, sampling frequency need not obey the Nyquist limit, and there is higher frequency resolution The random sampling can measure the signals which their frequencies component are close and it can implement the higher frequencies measurement with lower sampling frequency. © 2016 Institute of Advanced Engineering and Science. All rights reserved.