Compressive sensing reconstruction is a new theory of signal acquisition and processing, which breaks through the traditional sampling theorem’s requirements on Nyquist sampling frequency and the original signal can be reconstructed for sampling times far less than the requirements of sampling theorem. At first, three methods of constructing random matrix are introduced. And then, different kinds of compressive sensing algorithms are introduced, and two of them are simulated and compared. At last, based on this, the influence of the algorithm on image reconstruction quality under different noise levels of measurement matrix is simulated. Through simulation analysis, total variation augmented lagrangian 3 (TVAL3) algorithm is outstanding in image reconstruction time and noise reduction.