Abstract: Compressed sensing is an emerging compressive sampling technique for the signal sampling and reconstruction. The sampling number of original signal, based on this theory, is much less than that based on Nyquist theory. CS senses unknown signal and compresses it meanwhile, and it will have broad application prospects in many areas. The issue to tailor the reconstruction algorithms has obtained much attention and been intensively studied. The properties of the existing reconstruction algorithms are fistly analyzed, then this paper has reviewed the theory of greedy pursuit type algorithms, done a large number of experiments on them, given the advantages and disadvantages and the improvement programs for the shortcomings of each orthogonal matching pursuit type algorithms and some other classics reconstruction algorithms, finally, applied them to the image reconstruction. The reconstruction performance, robustness and complexity of various algorithms are given by experimental simulations, and the advantages and disadvantages of various algorithms are validated.disadvantages and the improvement programs for the shortcomings of each orthogonal matching pursuit type algorithms, finally, applied them to the image reconstruction. The reconstruction performance, robustness and complexity of various algorithms are given by experimental simulations, and the advantages and disadvantages of various algorithm are validated.