Abstract: The compressive sensing is a new theory,which attracted wide attentions from the world once it was proposed,In this study,we evaluated the advantages and disadvantages among various reconstruction algorithm through theoretical summary and simulation experiment,aiming at providing theoretical support for the research and application in the future,First of all,this thesis systematically summarized the theoretical framework and the main components of Compressive Sensing,and then carried out one-dimensional and two-dimensional simulation experiment by using OMP reconstruction algorithm,The result shows that the Compressive Sensing algorithm can reconstruct the original signal in a high probability even under a low sampling rate,In the case of the sampling rate is 0.5,the compressing rate was achieved to 53%-60%,Finally,in order to estimate the time spent during reconstructing and reconstruction precision of various reconstruction algorithm,we carried out another simulation experiment through standard test image based on the brief summary of the characteristics of these algorithms,The study shows that IRLS algorithm can provide a higher reconstruction accuracy,while the GPSR algorithm costs the minimum time to reconstruct the image.